Santa Fe Institute Events Wiki - User contributions [en]

File:Foraging.pdf

2009-09-01T16:26:49Z

Kbehrman:

File:August12 V8 1 Behrman.zip.doc

2009-08-25T20:41:10Z

Kbehrman:

Foraging on the move

2009-08-25T20:40:35Z

Kbehrman: /* Simulations */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

[[Image:Flocking.jpg]]

Figure 1: Shows an illustration of the flocking rules for one focal individual. Panel A demonstrates separate and B demonstrates align and cohere. The solid circle around the focal individual is the minimum separation distance, the larger dashed circle is the vision, and the arrow represents the heading.

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

'''PLOTS:'''
Here are the results from our early July simulations (10 replicates for each combination of energy and population size) ... not particularly interesting, but good for reference
[[Image:3Jul09_sims_flockT.jpg|400px|thumb|right]]
[[Image:3Jul09_sims_forageT.jpg|400px|thumb|left]]

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
* Next simulation: fixing the energy-threshold to 2.5 to check if the mean and variance values change.
** population: 300
** energy-forage: 2.5
** repetitions: 1-10
** max_gen: 1000

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

The simulations with the parameters above are still running... probably will take more 3 days to finish. I learned from Allison that if we want to do repetitions, we have to write them explicitly, example for 5 repetitions: 'repetitions [1 2 3 4 5]'.

''meeting:''

* Analysis of the plots from the previous simulations:
** It doesn't look like increasing the number of generations changes convergence
** (still haven't checked if changing ticks/gen changes convergence)
** The foraging and flocking thresholds are both converging after 100/200 hundred generations, however, the variance doesn't seem to decrease with time. Maybe the individuals are not being selected well...
* Discussion of a new fitness measure for reproduction -- at the end of each generation, all individuals reproduce in proportion to their fitness value (ghosts are automatically), instead of the current method where all survivors (non-ghosts) have equal chance of reproducing. We thought of 2 possible fitness measures:
# An individual's fitness is just their total energy at the end of a generation. This is semi biologically realistic since individuals would be reproducing after migration and reproduction success is probably related to energy levels.
# An individual's fitness is some combination of how well they foraged and flocked throughout the simulation. This is maybe less biologically realistic, but it does reward individuals that do both activities well, which is what we're interested in.
** One possible measure for this second value could be: (Nbar/max(Nbar) + Ebar/max(Ebar)), where
*** Nbar: average of the number of neighbors at each time step for an individual
*** max(Nbar): maximum value of Nbar across all individuals
*** Ebar: average of the the energy values at each time step for an individual
*** max(Ebar): maximum value of Ebar across all individuals
** Note that we would presumably not want to average across all ticks for a generation, but have some sort of burn-in period (e.g. take the last 100 ticks of a 200 tick generation?)

* Implement the new fitness measure. From a first impression it seems it will be quite computational expensive to compute the averages above at each time step...
* Set up more computers with netlogo to run more simulations at the same time (Allison will check with Iain about using lab computers).
* Run new simulations with the current parameter values (check the values in the previous meeting post) but with the new fitness measure.
* Run new simulations with new group size values.
* Upload the output files (excel) from the simulations on the wiki -- Liliana
* Upload the matlab code to process NetLogo output -- Andrew
* Write a draft of the report for next meeting (only two more meetings before the deadline!)

* currently running the following on Couzin lab computer (to start checking ticks/gen effect):
** N = 300
** energy-forage = 2.5
** gen-end-time = 300
** 1000 generations
** 5 reps

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve implemented new fitness measures
* Andrew added code section to wiki
* Liliana uploaded data files
* Allison started running one simulation on lab computers (can you run NetLogo on Linux?)

''meeting:''
* discussed parameter setting to use in simulations
* discussed how to edit final report

''for next time:''
* Kate will start google-doc account
* Liliana/Allison will work on writing introduction
* Steve will write up description of flocking death method
* Kate will work on diagrams
* Andrew will work on results/discussion
* Steve will make changes to netlogo model (add header to output file, make max-gen variable)
* everyone will run simulations reps with these parameters:
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 150

==== ''' 18 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve added to the wiki the new version of the model with instructions to run new simulations
* Allison and Liliana have been working on abstract/introduction
* Kate added diagrams to the report
* Andrew is working on the analysis

''meeting:''

* brief discussion of some preliminary results of the simulations with the new selection model
* discussion of the number of simulations that we have with the new selection model (steve did five, kate did one, liliana did one, allison did two, andrew did one)
* we will put results online (from simulations that are still running)
* we will work on the discussion and results after all simulations finish

==== ''' 25 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Simulations ===

Here is a list of the different simulations that have being done. Please post the date of simulation, parameters, output files and data analysis plots.

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
** output file: [[Media:file22july.xls|here]]
[[Image:july_22.jpg|700px]]

* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

** output file: [[Media:file27july.xls|here]]
[[Image:july_27.jpg|700px]]

* 12 August
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve in gzipped tarball (results and screenshots): [[Media:August12_v8_1_Lade.tar.gz.doc]]

* 17 August (started on the 10th):
** population: 300
** energy_forage: 2.5
** repetitions: 10
** max_gen: 1000
** results and screenshots: [[Media:Aug10_v7_10runs_salvador.zip.doc]]

* 24 Aug: (test to see if ticks/gen makes a difference)
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 300
** results from one set of runs [[Media:August24_v8_1_Shaw.zip.doc]]

* '''V8 - output results:'''
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve: [[Media:August12_v8_1_Lade.tar.gz.doc]]
** 1 run from Liliana: [[Media:August19_V8_1_Salvador.tar.gz.doc]]
** 1 run from andrew: [[Media:August12_V8_1_Berdahl.tar.gz.doc]]
** 1 run from Kate: [[Media:August12_V8_1_Behrman.zip.doc]]
** 2 runs from Allison: [[Media:August12_v8_1_Shaw.zip.doc]] -- sorry for the delay

=== Code ===

==== Net Logo ====
For detailed descriptions of each version, see the header of the code.
* [[Media:FlockingForaging_evolve_v2.nlogo|v2]]
* [[Media:FlockingForaging_evolve_v3.nlogo|v3]]: Added new plots, change initial positions
* [[Media:FlockingForaging_evolve_v4.nlogo|v4]]: New plots
* [[Media:FlockingForaging_evolve_v5.nlogo|v5]]: More plots; make flocking rule override foraging ('''note header in code claims the opposite!'''); create for continuous generations (as opposed to discrete)
* [[Media:FlockingForaging_evolve_v6.nlogo|v6]]: Put in 'ghosts' for discrete generations; two thresholds for ending discrete generation; some changes to threshold ranges. This is the version that was used for simulations at the CSSS.
* [[Media:FlockingForaging_evolve_v7.nlogo|v7]]: Export data at of each generation only
* [[Media:FlockingForaging_evolve_v8.nlogo|v8]]: Added alternative fitness models
* [[Media:FlockingForaging_evolve_v8_1.nlogo|v8.1]] with [[Media:ExpAugust12_v8_1.csv.doc|prepared output file]]. With modifications discussed at the meeting 11 August. Instructions for use:
# Download the code and prepared output file to the same directory.
# Remove ".doc" extension off output file (had to put it there to be able to upload it!). Open netlogo file.
# Open Behavior Space, click 'Edit' for the only experiment listed. To avoid the screenshots being overwritten, I suggest setting the "repnum" parameter different for each run. We may as well have different ones for each of us, so initially please set (inside the vary variables box) repnum to 100 (Allison), 200 (Liliana), 300 (Kate), 400 (Andrew), 500 (Steve), e.g. ["repnum" 100]. If you do new runs, change this number to avoid overwriting and to keep track of them.
# Click 'OK' and 'Run'. Select 'Neither' for output format. If you do choose something, nothing will be stored there.
# As usual, unticking 'update view' and 'update plots and monitors' (and setting the slider to 'faster'?) will make it run faster.
# If the simulation finishes quickly, run it again with a new repnum (e.g. ["repnum" 101]). If it finished VERY quickly, consider running more than one repetition: for two repetitions, Allison might set ["repnum" 102 103]. Don't change the "repetitions" box. Note all new data will be appended to the end of the previous output file, but new screenshot files will appear.

==== Matlab ====

*[[Media:visualize_V_8_1_data.tar.gz.doc]]: Matlab code to visualize the data generated by the version 8.1 netlogo code

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Final Report (Under construction!) ===

Please download file, update, and upload the new version.

File: [[Media: foraging_on_the_move_report.doc]]

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

File:August12 V8 1 Behrman.tar.gz.doc

2009-08-21T00:15:37Z

Kbehrman:

Foraging on the move

2009-08-21T00:15:01Z

Kbehrman: /* Simulations */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

[[Image:Flocking.jpg]]

Figure 1: Shows an illustration of the flocking rules for one focal individual. Panel A demonstrates separate and B demonstrates align and cohere. The solid circle around the focal individual is the minimum separation distance, the larger dashed circle is the vision, and the arrow represents the heading.

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

'''PLOTS:'''
Here are the results from our early July simulations (10 replicates for each combination of energy and population size) ... not particularly interesting, but good for reference
[[Image:3Jul09_sims_flockT.jpg|400px|thumb|right]]
[[Image:3Jul09_sims_forageT.jpg|400px|thumb|left]]

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
* Next simulation: fixing the energy-threshold to 2.5 to check if the mean and variance values change.
** population: 300
** energy-forage: 2.5
** repetitions: 1-10
** max_gen: 1000

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

The simulations with the parameters above are still running... probably will take more 3 days to finish. I learned from Allison that if we want to do repetitions, we have to write them explicitly, example for 5 repetitions: 'repetitions [1 2 3 4 5]'.

''meeting:''

* Analysis of the plots from the previous simulations:
** It doesn't look like increasing the number of generations changes convergence
** (still haven't checked if changing ticks/gen changes convergence)
** The foraging and flocking thresholds are both converging after 100/200 hundred generations, however, the variance doesn't seem to decrease with time. Maybe the individuals are not being selected well...
* Discussion of a new fitness measure for reproduction -- at the end of each generation, all individuals reproduce in proportion to their fitness value (ghosts are automatically), instead of the current method where all survivors (non-ghosts) have equal chance of reproducing. We thought of 2 possible fitness measures:
# An individual's fitness is just their total energy at the end of a generation. This is semi biologically realistic since individuals would be reproducing after migration and reproduction success is probably related to energy levels.
# An individual's fitness is some combination of how well they foraged and flocked throughout the simulation. This is maybe less biologically realistic, but it does reward individuals that do both activities well, which is what we're interested in.
** One possible measure for this second value could be: (Nbar/max(Nbar) + Ebar/max(Ebar)), where
*** Nbar: average of the number of neighbors at each time step for an individual
*** max(Nbar): maximum value of Nbar across all individuals
*** Ebar: average of the the energy values at each time step for an individual
*** max(Ebar): maximum value of Ebar across all individuals
** Note that we would presumably not want to average across all ticks for a generation, but have some sort of burn-in period (e.g. take the last 100 ticks of a 200 tick generation?)

* Implement the new fitness measure. From a first impression it seems it will be quite computational expensive to compute the averages above at each time step...
* Set up more computers with netlogo to run more simulations at the same time (Allison will check with Iain about using lab computers).
* Run new simulations with the current parameter values (check the values in the previous meeting post) but with the new fitness measure.
* Run new simulations with new group size values.
* Upload the output files (excel) from the simulations on the wiki -- Liliana
* Upload the matlab code to process NetLogo output -- Andrew
* Write a draft of the report for next meeting (only two more meetings before the deadline!)

* currently running the following on Couzin lab computer (to start checking ticks/gen effect):
** N = 300
** energy-forage = 2.5
** gen-end-time = 300
** 1000 generations
** 5 reps

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve implemented new fitness measures
* Andrew added code section to wiki
* Liliana uploaded data files
* Allison started running one simulation on lab computers (can you run NetLogo on Linux?)

''meeting:''
* discussed parameter setting to use in simulations
* discussed how to edit final report

''for next time:''
* Kate will start google-doc account
* Liliana/Allison will work on writing introduction
* Steve will write up description of flocking death method
* Kate will work on diagrams
* Andrew will work on results/discussion
* Steve will make changes to netlogo model (add header to output file, make max-gen variable)
* everyone will run simulations reps with these parameters:
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 150

==== ''' 18 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve added to the wiki the new version of the model with instructions to run new simulations
* Allison and Liliana have been working on abstract/introduction
* Kate added diagrams to the report
* Andrew is working on the analysis

''meeting:''

* brief discussion of some preliminary results of the simulations with the new selection model
* discussion of the number of simulations that we have with the new selection model (steve did five, kate did one, liliana did one, allison did two, andrew did one)
* we will put results online (from simulations that are still running)
* we will work on the discussion and results after all simulations finish

==== ''' 25 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Simulations ===

Here is a list of the different simulations that have being done. Please post the date of simulation, parameters, output files and data analysis plots.

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
** output file: [[Media:file22july.xls|here]]
[[Image:july_22.jpg|700px]]

* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

** output file: [[Media:file27july.xls|here]]
[[Image:july_27.jpg|700px]]

* 12 August
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve in gzipped tarball (results and screenshots): [[Media:August12_v8_1_Lade.tar.gz.doc]]

* 17 August (started on the 10th):
** population: 300
** energy_forage: 2.5
** repetitions: 10
** max_gen: 1000
** results and screenshots: [[Media:Aug10_v7_10runs_salvador.zip.doc]]

* '''V8 - output results:'''
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve: [[Media:August12_v8_1_Lade.tar.gz.doc]]
** 1 run from Liliana: [[Media:August19_V8_1_Salvador.tar.gz.doc]]
** 1 run from andrew: [[Media:August12_V8_1_Berdahl.tar.gz.doc]]
** 1 run from Kate: [[Media:August12_V8_1_Behrman.tar.gz.doc]]

=== Code ===

==== Net Logo ====
For detailed descriptions of each version, see the header of the code.
* [[Media:FlockingForaging_evolve_v2.nlogo|v2]]
* [[Media:FlockingForaging_evolve_v3.nlogo|v3]]: Added new plots, change initial positions
* [[Media:FlockingForaging_evolve_v4.nlogo|v4]]: New plots
* [[Media:FlockingForaging_evolve_v5.nlogo|v5]]: More plots; make flocking rule override foraging ('''note header in code claims the opposite!'''); create for continuous generations (as opposed to discrete)
* [[Media:FlockingForaging_evolve_v6.nlogo|v6]]: Put in 'ghosts' for discrete generations; two thresholds for ending discrete generation; some changes to threshold ranges. This is the version that was used for simulations at the CSSS.
* [[Media:FlockingForaging_evolve_v7.nlogo|v7]]: Export data at of each generation only
* [[Media:FlockingForaging_evolve_v8.nlogo|v8]]: Added alternative fitness models
* [[Media:FlockingForaging_evolve_v8_1.nlogo|v8.1]] with [[Media:ExpAugust12_v8_1.csv.doc|prepared output file]]. With modifications discussed at the meeting 11 August. Instructions for use:
# Download the code and prepared output file to the same directory.
# Remove ".doc" extension off output file (had to put it there to be able to upload it!). Open netlogo file.
# Open Behavior Space, click 'Edit' for the only experiment listed. To avoid the screenshots being overwritten, I suggest setting the "repnum" parameter different for each run. We may as well have different ones for each of us, so initially please set (inside the vary variables box) repnum to 100 (Allison), 200 (Liliana), 300 (Kate), 400 (Andrew), 500 (Steve), e.g. ["repnum" 100]. If you do new runs, change this number to avoid overwriting and to keep track of them.
# Click 'OK' and 'Run'. Select 'Neither' for output format. If you do choose something, nothing will be stored there.
# As usual, unticking 'update view' and 'update plots and monitors' (and setting the slider to 'faster'?) will make it run faster.
# If the simulation finishes quickly, run it again with a new repnum (e.g. ["repnum" 101]). If it finished VERY quickly, consider running more than one repetition: for two repetitions, Allison might set ["repnum" 102 103]. Don't change the "repetitions" box. Note all new data will be appended to the end of the previous output file, but new screenshot files will appear.

==== Matlab ====

*[[Media:visualize_V_8_1_data.tar.gz.doc]]: Matlab code to visualize the data generated by the version 8.1 netlogo code

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Final Report (Under construction!) ===

Please download file, update, and upload the new version.

File: [[Media: foraging_on_the_move_report.doc]]

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-08-18T19:41:25Z

Kbehrman: /* Methods */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

[[Image:Flocking.jpg]]

Figure 1: Shows an illustration of the flocking rules for one focal individual. Panel A demonstrates separate and B demonstrates align and cohere. The solid circle around the focal individual is the minimum separation distance, the larger dashed circle is the vision, and the arrow represents the heading.

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

'''PLOTS:'''
Here are the results from our early July simulations (10 replicates for each combination of energy and population size) ... not particularly interesting, but good for reference
[[Image:3Jul09_sims_flockT.jpg|400px|thumb|right]]
[[Image:3Jul09_sims_forageT.jpg|400px|thumb|left]]

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
* Next simulation: fixing the energy-threshold to 2.5 to check if the mean and variance values change.
** population: 300
** energy-forage: 2.5
** repetitions: 1-10
** max_gen: 1000

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

The simulations with the parameters above are still running... probably will take more 3 days to finish. I learned from Allison that if we want to do repetitions, we have to write them explicitly, example for 5 repetitions: 'repetitions [1 2 3 4 5]'.

''meeting:''

* Analysis of the plots from the previous simulations:
** It doesn't look like increasing the number of generations changes convergence
** (still haven't checked if changing ticks/gen changes convergence)
** The foraging and flocking thresholds are both converging after 100/200 hundred generations, however, the variance doesn't seem to decrease with time. Maybe the individuals are not being selected well...
* Discussion of a new fitness measure for reproduction -- at the end of each generation, all individuals reproduce in proportion to their fitness value (ghosts are automatically), instead of the current method where all survivors (non-ghosts) have equal chance of reproducing. We thought of 2 possible fitness measures:
# An individual's fitness is just their total energy at the end of a generation. This is semi biologically realistic since individuals would be reproducing after migration and reproduction success is probably related to energy levels.
# An individual's fitness is some combination of how well they foraged and flocked throughout the simulation. This is maybe less biologically realistic, but it does reward individuals that do both activities well, which is what we're interested in.
** One possible measure for this second value could be: (Nbar/max(Nbar) + Ebar/max(Ebar)), where
*** Nbar: average of the number of neighbors at each time step for an individual
*** max(Nbar): maximum value of Nbar across all individuals
*** Ebar: average of the the energy values at each time step for an individual
*** max(Ebar): maximum value of Ebar across all individuals
** Note that we would presumably not want to average across all ticks for a generation, but have some sort of burn-in period (e.g. take the last 100 ticks of a 200 tick generation?)

* Implement the new fitness measure. From a first impression it seems it will be quite computational expensive to compute the averages above at each time step...
* Set up more computers with netlogo to run more simulations at the same time (Allison will check with Iain about using lab computers).
* Run new simulations with the current parameter values (check the values in the previous meeting post) but with the new fitness measure.
* Run new simulations with new group size values.
* Upload the output files (excel) from the simulations on the wiki -- Liliana
* Upload the matlab code to process NetLogo output -- Andrew
* Write a draft of the report for next meeting (only two more meetings before the deadline!)

* currently running the following on Couzin lab computer (to start checking ticks/gen effect):
** N = 300
** energy-forage = 2.5
** gen-end-time = 300
** 1000 generations
** 5 reps

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve implemented new fitness measures
* Andrew added code section to wiki
* Liliana uploaded data files
* Allison started running one simulation on lab computers (can you run NetLogo on Linux?)

''meeting:''
* discussed parameter setting to use in simulations
* discussed how to edit final report

''for next time:''
* Kate will start google-doc account
* Liliana/Allison will work on writing introduction
* Steve will write up description of flocking death method
* Kate will work on diagrams
* Andrew will work on results/discussion
* Steve will make changes to netlogo model (add header to output file, make max-gen variable)
* everyone will run simulations reps with these parameters:
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 150

==== ''' 18 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Simulations ===

Here is a list of the different simulations that have being done. Please post the date of simulation, parameters, output files and data analysis plots.

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
** output file: [[Media:file22july.xls|here]]
[[Image:july_22.jpg|700px]]

* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

** output file: [[Media:file27july.xls|here]]
[[Image:july_27.jpg|700px]]

* 12 August
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve in gzipped tarball (results and screenshots): [[Media:August12_v8_1_Lade.tar.gz.doc]]

* 17 August (started on the 10th):
** population: 300
** energy_forage: 2.5
** repetitions: 10
** max_gen: 1000
** results and screenshots: [[Media:Aug10_v7_10runs_salvador.zip.doc]]

=== Code ===

==== Net Logo ====
For detailed descriptions of each version, see the header of the code.
* [[Media:FlockingForaging_evolve_v2.nlogo|v2]]
* [[Media:FlockingForaging_evolve_v3.nlogo|v3]]: Added new plots, change initial positions
* [[Media:FlockingForaging_evolve_v4.nlogo|v4]]: New plots
* [[Media:FlockingForaging_evolve_v5.nlogo|v5]]: More plots; make flocking rule override foraging ('''note header in code claims the opposite!'''); create for continuous generations (as opposed to discrete)
* [[Media:FlockingForaging_evolve_v6.nlogo|v6]]: Put in 'ghosts' for discrete generations; two thresholds for ending discrete generation; some changes to threshold ranges. This is the version that was used for simulations at the CSSS.
* [[Media:FlockingForaging_evolve_v7.nlogo|v7]]: Export data at of each generation only
* [[Media:FlockingForaging_evolve_v8.nlogo|v8]]: Added alternative fitness models
* [[Media:FlockingForaging_evolve_v8_1.nlogo|v8.1]] with [[Media:ExpAugust12_v8_1.csv.doc|prepared output file]]. With modifications discussed at the meeting 11 August. Instructions for use:
# Download the code and prepared output file to the same directory.
# Remove ".doc" extension off output file (had to put it there to be able to upload it!). Open netlogo file.
# Open Behavior Space, click 'Edit' for the only experiment listed. To avoid the screenshots being overwritten, I suggest setting the "repnum" parameter different for each run. We may as well have different ones for each of us, so initially please set (inside the vary variables box) repnum to 100 (Allison), 200 (Liliana), 300 (Kate), 400 (Andrew), 500 (Steve), e.g. ["repnum" 100]. If you do new runs, change this number to avoid overwriting and to keep track of them.
# Click 'OK' and 'Run'. Select 'Neither' for output format. If you do choose something, nothing will be stored there.
# As usual, unticking 'update view' and 'update plots and monitors' (and setting the slider to 'faster'?) will make it run faster.
# If the simulation finishes quickly, run it again with a new repnum (e.g. ["repnum" 101]). If it finished VERY quickly, consider running more than one repetition: for two repetitions, Allison might set ["repnum" 102 103]. Don't change the "repetitions" box. Note all new data will be appended to the end of the previous output file, but new screenshot files will appear.

==== Matlab ====

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Final Report (Under construction!) ===

Please download file, update, and upload the new version.

File: [[Media: foraging_on_the_move_report.doc]]

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-08-18T19:37:35Z

Kbehrman: /* Methods */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

[[Image:flocking]]

Figure 1: Shows an illustration of the flocking rules for one focal individual. Panel A demonstrates separate and B demonstrates align and cohere. The solid circle around the focal individual is the minimum separation distance, the larger dashed circle is the vision, and the arrow represents the heading.

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

'''PLOTS:'''
Here are the results from our early July simulations (10 replicates for each combination of energy and population size) ... not particularly interesting, but good for reference
[[Image:3Jul09_sims_flockT.jpg|400px|thumb|right]]
[[Image:3Jul09_sims_forageT.jpg|400px|thumb|left]]

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
* Next simulation: fixing the energy-threshold to 2.5 to check if the mean and variance values change.
** population: 300
** energy-forage: 2.5
** repetitions: 1-10
** max_gen: 1000

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

The simulations with the parameters above are still running... probably will take more 3 days to finish. I learned from Allison that if we want to do repetitions, we have to write them explicitly, example for 5 repetitions: 'repetitions [1 2 3 4 5]'.

''meeting:''

* Analysis of the plots from the previous simulations:
** It doesn't look like increasing the number of generations changes convergence
** (still haven't checked if changing ticks/gen changes convergence)
** The foraging and flocking thresholds are both converging after 100/200 hundred generations, however, the variance doesn't seem to decrease with time. Maybe the individuals are not being selected well...
* Discussion of a new fitness measure for reproduction -- at the end of each generation, all individuals reproduce in proportion to their fitness value (ghosts are automatically), instead of the current method where all survivors (non-ghosts) have equal chance of reproducing. We thought of 2 possible fitness measures:
# An individual's fitness is just their total energy at the end of a generation. This is semi biologically realistic since individuals would be reproducing after migration and reproduction success is probably related to energy levels.
# An individual's fitness is some combination of how well they foraged and flocked throughout the simulation. This is maybe less biologically realistic, but it does reward individuals that do both activities well, which is what we're interested in.
** One possible measure for this second value could be: (Nbar/max(Nbar) + Ebar/max(Ebar)), where
*** Nbar: average of the number of neighbors at each time step for an individual
*** max(Nbar): maximum value of Nbar across all individuals
*** Ebar: average of the the energy values at each time step for an individual
*** max(Ebar): maximum value of Ebar across all individuals
** Note that we would presumably not want to average across all ticks for a generation, but have some sort of burn-in period (e.g. take the last 100 ticks of a 200 tick generation?)

* Implement the new fitness measure. From a first impression it seems it will be quite computational expensive to compute the averages above at each time step...
* Set up more computers with netlogo to run more simulations at the same time (Allison will check with Iain about using lab computers).
* Run new simulations with the current parameter values (check the values in the previous meeting post) but with the new fitness measure.
* Run new simulations with new group size values.
* Upload the output files (excel) from the simulations on the wiki -- Liliana
* Upload the matlab code to process NetLogo output -- Andrew
* Write a draft of the report for next meeting (only two more meetings before the deadline!)

* currently running the following on Couzin lab computer (to start checking ticks/gen effect):
** N = 300
** energy-forage = 2.5
** gen-end-time = 300
** 1000 generations
** 5 reps

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve implemented new fitness measures
* Andrew added code section to wiki
* Liliana uploaded data files
* Allison started running one simulation on lab computers (can you run NetLogo on Linux?)

''meeting:''
* discussed parameter setting to use in simulations
* discussed how to edit final report

''for next time:''
* Kate will start google-doc account
* Liliana/Allison will work on writing introduction
* Steve will write up description of flocking death method
* Kate will work on diagrams
* Andrew will work on results/discussion
* Steve will make changes to netlogo model (add header to output file, make max-gen variable)
* everyone will run simulations reps with these parameters:
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 150

==== ''' 18 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Simulations ===

Here is a list of the different simulations that have being done. Please post the date of simulation, parameters, output files and data analysis plots.

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
** output file: [[Media:file22july.xls|here]]
[[Image:july_22.jpg|700px]]

* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

** output file: [[Media:file27july.xls|here]]
[[Image:july_27.jpg|700px]]

* 12 August
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve in gzipped tarball (results and screenshots): [[Media:August12_v8_1_Lade.tar.gz.doc]]

* 17 August (started on the 10th):
** population: 300
** energy_forage: 2.5
** repetitions: 10
** max_gen: 1000
** results and screenshots: [[Media:Aug10_v7_10runs_salvador.zip.doc]]

=== Code ===

==== Net Logo ====
For detailed descriptions of each version, see the header of the code.
* [[Media:FlockingForaging_evolve_v2.nlogo|v2]]
* [[Media:FlockingForaging_evolve_v3.nlogo|v3]]: Added new plots, change initial positions
* [[Media:FlockingForaging_evolve_v4.nlogo|v4]]: New plots
* [[Media:FlockingForaging_evolve_v5.nlogo|v5]]: More plots; make flocking rule override foraging ('''note header in code claims the opposite!'''); create for continuous generations (as opposed to discrete)
* [[Media:FlockingForaging_evolve_v6.nlogo|v6]]: Put in 'ghosts' for discrete generations; two thresholds for ending discrete generation; some changes to threshold ranges. This is the version that was used for simulations at the CSSS.
* [[Media:FlockingForaging_evolve_v7.nlogo|v7]]: Export data at of each generation only
* [[Media:FlockingForaging_evolve_v8.nlogo|v8]]: Added alternative fitness models
* [[Media:FlockingForaging_evolve_v8_1.nlogo|v8.1]] with [[Media:ExpAugust12_v8_1.csv.doc|prepared output file]]. With modifications discussed at the meeting 11 August. Instructions for use:
# Download the code and prepared output file to the same directory.
# Remove ".doc" extension off output file (had to put it there to be able to upload it!). Open netlogo file.
# Open Behavior Space, click 'Edit' for the only experiment listed. To avoid the screenshots being overwritten, I suggest setting the "repnum" parameter different for each run. We may as well have different ones for each of us, so initially please set (inside the vary variables box) repnum to 100 (Allison), 200 (Liliana), 300 (Kate), 400 (Andrew), 500 (Steve), e.g. ["repnum" 100]. If you do new runs, change this number to avoid overwriting and to keep track of them.
# Click 'OK' and 'Run'. Select 'Neither' for output format. If you do choose something, nothing will be stored there.
# As usual, unticking 'update view' and 'update plots and monitors' (and setting the slider to 'faster'?) will make it run faster.
# If the simulation finishes quickly, run it again with a new repnum (e.g. ["repnum" 101]). If it finished VERY quickly, consider running more than one repetition: for two repetitions, Allison might set ["repnum" 102 103]. Don't change the "repetitions" box. Note all new data will be appended to the end of the previous output file, but new screenshot files will appear.

==== Matlab ====

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Final Report (Under construction!) ===

Please download file, update, and upload the new version.

File: [[Media: foraging_on_the_move_report.doc]]

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-08-18T19:36:05Z

Kbehrman: /* Methods */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

Figure 1: Shows an illustration of the flocking rules for one focal individual. Panel A demonstrates separate and B demonstrates align and cohere. The solid circle around the focal individual is the minimum separation distance, the larger dashed circle is the vision, and the arrow represents the heading.

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

'''PLOTS:'''
Here are the results from our early July simulations (10 replicates for each combination of energy and population size) ... not particularly interesting, but good for reference
[[Image:3Jul09_sims_flockT.jpg|400px|thumb|right]]
[[Image:3Jul09_sims_forageT.jpg|400px|thumb|left]]

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
* Next simulation: fixing the energy-threshold to 2.5 to check if the mean and variance values change.
** population: 300
** energy-forage: 2.5
** repetitions: 1-10
** max_gen: 1000

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

The simulations with the parameters above are still running... probably will take more 3 days to finish. I learned from Allison that if we want to do repetitions, we have to write them explicitly, example for 5 repetitions: 'repetitions [1 2 3 4 5]'.

''meeting:''

* Analysis of the plots from the previous simulations:
** It doesn't look like increasing the number of generations changes convergence
** (still haven't checked if changing ticks/gen changes convergence)
** The foraging and flocking thresholds are both converging after 100/200 hundred generations, however, the variance doesn't seem to decrease with time. Maybe the individuals are not being selected well...
* Discussion of a new fitness measure for reproduction -- at the end of each generation, all individuals reproduce in proportion to their fitness value (ghosts are automatically), instead of the current method where all survivors (non-ghosts) have equal chance of reproducing. We thought of 2 possible fitness measures:
# An individual's fitness is just their total energy at the end of a generation. This is semi biologically realistic since individuals would be reproducing after migration and reproduction success is probably related to energy levels.
# An individual's fitness is some combination of how well they foraged and flocked throughout the simulation. This is maybe less biologically realistic, but it does reward individuals that do both activities well, which is what we're interested in.
** One possible measure for this second value could be: (Nbar/max(Nbar) + Ebar/max(Ebar)), where
*** Nbar: average of the number of neighbors at each time step for an individual
*** max(Nbar): maximum value of Nbar across all individuals
*** Ebar: average of the the energy values at each time step for an individual
*** max(Ebar): maximum value of Ebar across all individuals
** Note that we would presumably not want to average across all ticks for a generation, but have some sort of burn-in period (e.g. take the last 100 ticks of a 200 tick generation?)

* Implement the new fitness measure. From a first impression it seems it will be quite computational expensive to compute the averages above at each time step...
* Set up more computers with netlogo to run more simulations at the same time (Allison will check with Iain about using lab computers).
* Run new simulations with the current parameter values (check the values in the previous meeting post) but with the new fitness measure.
* Run new simulations with new group size values.
* Upload the output files (excel) from the simulations on the wiki -- Liliana
* Upload the matlab code to process NetLogo output -- Andrew
* Write a draft of the report for next meeting (only two more meetings before the deadline!)

* currently running the following on Couzin lab computer (to start checking ticks/gen effect):
** N = 300
** energy-forage = 2.5
** gen-end-time = 300
** 1000 generations
** 5 reps

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''
* Steve implemented new fitness measures
* Andrew added code section to wiki
* Liliana uploaded data files
* Allison started running one simulation on lab computers (can you run NetLogo on Linux?)

''meeting:''
* discussed parameter setting to use in simulations
* discussed how to edit final report

''for next time:''
* Kate will start google-doc account
* Liliana/Allison will work on writing introduction
* Steve will write up description of flocking death method
* Kate will work on diagrams
* Andrew will work on results/discussion
* Steve will make changes to netlogo model (add header to output file, make max-gen variable)
* everyone will run simulations reps with these parameters:
** fitness-choice = "time average of properties"
** ["population" 100 300 500]
** ["energy-forage" 0.5 1 2.5 5]
** max gen 500
** ticks per gen 150

==== ''' 18 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Simulations ===

Here is a list of the different simulations that have being done. Please post the date of simulation, parameters, output files and data analysis plots.

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
** output file: [[Media:file22july.xls|here]]
[[Image:july_22.jpg|700px]]

* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

** output file: [[Media:file27july.xls|here]]
[[Image:july_27.jpg|700px]]

* 12 August
** Simulation parameters [[Foraging_on_the_move#11_August_2009_7pm_(GMT-4)|here]]
** 5 runs from Steve in gzipped tarball (results and screenshots): [[Media:August12_v8_1_Lade.tar.gz.doc]]

* 17 August (started on the 10th):
** population: 300
** energy_forage: 2.5
** repetitions: 10
** max_gen: 1000
** results and screenshots: [[Media:Aug10_v7_10runs_salvador.zip.doc]]

=== Code ===

==== Net Logo ====
For detailed descriptions of each version, see the header of the code.
* [[Media:FlockingForaging_evolve_v2.nlogo|v2]]
* [[Media:FlockingForaging_evolve_v3.nlogo|v3]]: Added new plots, change initial positions
* [[Media:FlockingForaging_evolve_v4.nlogo|v4]]: New plots
* [[Media:FlockingForaging_evolve_v5.nlogo|v5]]: More plots; make flocking rule override foraging ('''note header in code claims the opposite!'''); create for continuous generations (as opposed to discrete)
* [[Media:FlockingForaging_evolve_v6.nlogo|v6]]: Put in 'ghosts' for discrete generations; two thresholds for ending discrete generation; some changes to threshold ranges. This is the version that was used for simulations at the CSSS.
* [[Media:FlockingForaging_evolve_v7.nlogo|v7]]: Export data at of each generation only
* [[Media:FlockingForaging_evolve_v8.nlogo|v8]]: Added alternative fitness models
* [[Media:FlockingForaging_evolve_v8_1.nlogo|v8.1]] with [[Media:ExpAugust12_v8_1.csv.doc|prepared output file]]. With modifications discussed at the meeting 11 August. Instructions for use:
# Download the code and prepared output file to the same directory.
# Remove ".doc" extension off output file (had to put it there to be able to upload it!). Open netlogo file.
# Open Behavior Space, click 'Edit' for the only experiment listed. To avoid the screenshots being overwritten, I suggest setting the "repnum" parameter different for each run. We may as well have different ones for each of us, so initially please set (inside the vary variables box) repnum to 100 (Allison), 200 (Liliana), 300 (Kate), 400 (Andrew), 500 (Steve), e.g. ["repnum" 100]. If you do new runs, change this number to avoid overwriting and to keep track of them.
# Click 'OK' and 'Run'. Select 'Neither' for output format. If you do choose something, nothing will be stored there.
# As usual, unticking 'update view' and 'update plots and monitors' (and setting the slider to 'faster'?) will make it run faster.
# If the simulation finishes quickly, run it again with a new repnum (e.g. ["repnum" 101]). If it finished VERY quickly, consider running more than one repetition: for two repetitions, Allison might set ["repnum" 102 103]. Don't change the "repetitions" box. Note all new data will be appended to the end of the previous output file, but new screenshot files will appear.

==== Matlab ====

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Final Report (Under construction!) ===

Please download file, update, and upload the new version.

File: [[Media: foraging_on_the_move_report.doc]]

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

File:July 27.jpg

2009-07-29T12:50:45Z

Kbehrman:

File:July 22.jpg

2009-07-29T12:50:18Z

Kbehrman:

Foraging on the move

2009-07-29T12:49:17Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:july_22.jpg]]
** 27 July simulation plots (1000 generations):[[Image:july_27.jpg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T12:48:55Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:july22.jpg]]
** 27 July simulation plots (1000 generations):[[Image:July27.jpg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T12:48:24Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):
** 27 July simulation plots (1000 generations):
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T12:47:30Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:july22.jpg]]
** 27 July simulation plots (1000 generations):[[Image:July27.jpg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

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Kbehrman:

Foraging on the move

2009-07-29T03:32:19Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:July22.jpg]]
** 27 July simulation plots (1000 generations):[[Image:july27.jpg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T03:32:09Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:July22.jpg]]
** 27 July simulation plots (1000 generations):[[Inage:july27.jpg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T03:28:03Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:July22.jpeg]]
** 27 July simulation plots (1000 generations):[[Inage:july27.jpeg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-29T03:27:03Z

Kbehrman: /* 28 July 2009 7pm (GMT-4) */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

* Allison and I started to run a simulation with the following parameters: (Allison do you remember these? For some reason my netlogo file does not open anymore and I don't remember exactly which were the parameter values). I had to download the v6 version.

''meeting:''
* Main topic: discussion about parameter values.

* The previous simulation was taking too long (at least 21 days to run completely), so we aborted it and started a new one, where we changed the following parameters:
**population size: 300 (Kate found out from literature that population size varies a lot from herd to herd -- see parameters)
**max_gen: 500
**number of repetitions: 2

==== '''28 July 2009 7pm (GMT-4)''' ====

''since last time:''

Two simulations:

* 22 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 500
* 27 July:
** population: 300
** energy-forage: [0.5 1 2.5 5]
** repetitions: 2
** max_gen: 1000

''meeting:''
* Discussion and analysis of the data generated by the previous simulations. From a first impression it seems that with a longer run there is a higher convergence (check this out!). In the first simulation, the variance was MUCH higher than the mean (weird!)
** 22 July simulation plots (500 generations):[[Image:July22.jpeg]]
** 27 July simulation plots (1000 generations):[[Inage:July27.jpeg]]
* Next simulation:
** fix the energy-threshold to 2.5 to check if the mean and variance values change.
** ...

==== '''4 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

==== ''' 11 August 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-21T16:26:11Z

Kbehrman: /* Parameter Settings from Literature */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''HERD SIZE and DENSITY'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''MORTALITY'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-21T16:25:06Z

Kbehrman: /* Parameter Settings from Literature */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesn't include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''Herd Size and Density'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Arctic Caribou Herd: 417,000 (Gunn et al 1991)

'''Mortality'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-21T16:23:31Z

Kbehrman: /* Parameter Settings from Literature */

== Abstract ==
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

== Project Description ==

=== Background ===
'''GROUP LIVING:''' Animal groups are ubiquitous in nature and their formation comes with both costs and benefits. Groups provide individuals with a lower per-capita predation rate (dilution effect), shared information, and allow individuals to find both mates and resources more easily. However, groups tend to attract predators more easily than solitary individuals, can increase the transmission rate of diseases, and lead to competition for resources. In theory the size of an animal group should be determined by the payoff to an individual; at equilibrium group size, the benefit to an individual of joining a group should be equal to that of being a loner. An individual's specific position within a group can have significant fitness consequences (see Krause 1994); individuals in the center of the group are often the safest from predation (Hamilton 1971), but those on the edge are in the best position to discover and exploit new food resources '''[ref]'''.

'''FLOCKING & FORAGING:''' There is a vast literature on flocking/swarming models (e.g. '''[refs]'''), and on optimal foraging behavior (e.g. Fretwell & Lucas 1969, Schoener 1971, Charnov 1976). Some theoretical work has been done on combining foraging and flocking, but this mostly relates to what has been termed "social foraging" (see Giraldeau & Caraco 2000) and examines how how individuals can gain information about foraging locations by flocking (e.g. Clark & Mangel 1984) or on how foraging strategy should vary with respect to location within the flock (Barta et al 1997). However there is no theoretical work on how foraging individuals should behave when they are in a group that is collectively moving, a behavior seen in wildebeest, caribou and many other species of migratory ungulates. Individuals in this situation face a trade-off between foraging and keeping up with the group. Individuals that fail to forage will starve, and those that fail to keep up with the group will likely be picked off by predators '''[ref]'''. This leads to a a mixed behavior at any moment, where some individuals are concentrating on foraging and others on flocking and moving towards their destination (e.g. Planet Earth video).

'''MAMMALIAN MIGRATION:''' A recent literature review found that the majority of papers that model migration focus on birds and fish, with almost no work done on modeling mammal migration (Bauer et al 2009). The only two papers from this review that modeled terrestrial mammal migration are:
* Bergman et al (1999) found that correlated random walk model overpredicted long-range displacement of migrating caribou.
* Boone et al (2006) found that migratory pathways of wildebeest derived using an evolutionary algorithm closely matched actual migration paths chosen, suggesting that rainfall and vegetation are key determinants in wildebeest migratory behavior.

'''WILDEBEEST:''' Wildebeest in Tanzania and Kenya move in a roughly circular clockwise direction, likely following the vegetation and rainfall across the seasons. During the dry season (May-Oct), they are found mostly in the north, and move southward as the rains start, and give birth synchronously in Feb/Mar. There is a rainfall gradient (and corresponding vegetation gradient) across the region with high rainfall in the northwest and low in the southeast. (Boone et al 2006)

'''CARIBOU:''' The search for food is one of the primary drivers of caribou migration. Caribou winter in areas with a large amount of vegatation biomass (mostly lichens). In the spring they move north towards areas with seasonal vegetation that is rich in nitrogen and minerals (necessarily for rapid growth and milk production), where they give birth. In Aug/Sept as the vegetation gradient becomes less pronounced, the herds disperse in small groups, coming back together only at the end of the growing season, to migrate back south, as lichens in the wintering area become the best source of energy again. (Fancy et al 1989)

Fancy and White (1987) found that caribou were the most efficient walkers (lowest net cost of locomotion) of all ungulates tested. Wildebeest were second most efficient, suggesting that migration is an important selective pressure on locomotion efficiency.

=== Parameter Settings from Literature ===
'''MIGRATION RATES/DISTANCES:'''
* caribou migrate up to 40km/day (Fancy et al 1989)
* caribou have longest terrestrial animal migration: 1200km (Akesson 2007)
* mean migratory movement for caribou 14-26 km/day (Murray 1991)
* wildebeest migration is ~200km (Akesson 2007)
* The speed at which animal migrations can travel is dependent on three factors: speed of locomotion, rate of energy acquisition, rate of energy consumption (Akesson 2007)
* migration range shows diminishing return function with more fuel runners pay cost of extra weight (Akesson 2007)
* caribou migration rate 10-20km/day (Gunn et al 1991)
* caribou migration distance 300 to 500 km (Gunn et al. 1991)

'''ENERGY EXPENDITURE:'''
* energy cost for uphill locomotion in caribou (note: doesnt include cost of walking in snow): 22.6 (1.3 SE) kJ/(kg*m) (Fancy & White 1987)
* energy cost for horizontal caribou locomotion in snow: 1.696 KJ/(Kg*km) (Johnson et al. 2002)
* energy cost for wildebest: 4.23 kg/(individual *day) (Sinclair 1975)
* caribou are ~272kg (http://www.amnh.org/nationalcenter/Endangered/caribou/caribou.html)
* caribou are ~2m long (Kuzyk et al 1999)
* CALCULATION: (1.696kJ/kg/km)*(1km/1000m)*(272kg/ind)*(2m/body)= '''0.922kJ/ind/body'''

'''ENERGY INTAKE:'''
* maximum consumption rate for wildebeest: 4 kg/day (Note: simulation parameter not measured) (Fryxell et al. 1988)
* energy from foraging: 169.1 KJ/(kg*day) (Murray 1991)
* 0.3 g per bite for wildebeest (Murray 1991; Figure 3/4)
* ~7.96 MJ/kg dried matter for plants (Murray 1991; Table 1)
* CALCULATION: (0.3g/bite)*(1kg/1000g)*(7.96MJ/kg)*(1000kJ/MJ) = '''2.388 kJ/bite'''

'''Herd Size and Density'''
* Elk winter herd size (max,min): (14,253) (Creel and Winnie 2005)
* Elk density: 13.7 individuals/ km^2 (Creel and Winnie 2005)
* Elk distance apart with in herd: <5 body lengths (Creel and Winnie 2005)
* Wildebeest main herd size in Serengeti: 467 individuals (Fryxell et al. 1988)
* Herd size in 1960 of Caribou in Newfoundland: 450 individuals (Mahoney and Schafer 2002)
* Herd size in 2000 of Caribou in Newfoundland: 6,102 individuals (Mahoney and Schafer 2002)
* Herd size in 1992 of West Artic Caribou Herd: 417,000 (Gunn et al 1991)

'''Mortalitiy'''

=== Methods ===
''''NETLOGO MODEL'''

We created a NetLogo model to understand the balance of flocking and foraging behaviors in animal groups as they migrate. The base of our model was the NetLogo demo model (Wilensky 1998) which is based on Craig Reynolds Boids simulation (Reynolds 1987). The boids model assumes that an agent within a group moves based on two main rules. If there are other agents within a minimum separation distance radius, then the agent will turn to move away from these agents ('separate'). If there are no agents within the first radius, then the agent will align with ('align') and move towards ('cohere') any individuals within a second, larger radius ('vision'). To simulate migration, where animals are moving together in a specific direction, we add another movement rule: after agents separate, align and cohere, they also all turn towards 'north' (positive y-direction).

'''[create diagram of flocking rules?]''''

We modified this basic flocking model by also including a foraging aspect. All agents in our model have an energy level that decreases as they spend energy moving, and increases as they acquire energy from foraging while stopped. At each time-step, every agent has to make a decision whether to forage or to flock. (Since animals such as caribou forage with their heads down, making it hard to see fellow herd-mates, we assume that it is impossible to forage and flock simultaneously.) We assume that agents make the decision of whether to flock or forage based on a simple threshold: if an agent's energy level is below a certain threshold (ForageT) it will start to forage, and if the number of agents within an agent's vision radius falls below a certain threshold (FlockT), it will start to flock. In the case where an agent is below both thresholds, we assume that flocking overrides foraging. If an agent decides to forage, it stops and increases its energy level by E_forage. If an agent decides to flock it follows the movement rules described above (separate, align, cohere, and move north), takes a step forward, and decreases its energy level by E_move. Agents can die in two ways, essentially from doing a poor job foraging or flocking. If an agent's energy level falls below a certain threshold, it 'starves' and dies. Agents have some probability of dying from 'predation', which is a function of the number of other agents it can see.

'''[create diagram of death by flocking and foraging: explain flocking-die-lambda, full-energy parameters]'''

'''SELECTION'''

We implemented a genetic algorithm type method to determine the optimal threshold values for agents. For a single run, N agents are created, each with a set of ForageT and FlockT threshold values drawn from a random distribution. The simulation is run for a single generation (which ends whenever either '''20%''' of individuals die or '''150''' time-steps pass, whichever comes first). At the end of a generation, N new agents are created and the simulation is restarted. Each of these N agents gets its ForageT and FlockT threshold values from a single 'parent' -- one of the surviving agents (those that have not died from either starvation or predation) from the previous generation. These threshold values are inherited with a slight mutation rate ('''3%''' each). This process is repeated for '''100''' generations.

'''MORE:'''
* look at effects of population size and ratio of energy from foraging to energy spent moving* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== Results/Observations/Predictions ===

''' OBSERVATIONS: '''
* FlockingForaging_evolve_v2: continuous replacement means that population that isn't stable can be maintained by new individuals coming in
* FlockingForaging_evolve_v3: agents stay mostly sedentary
** ''this is fixed by changing the starting density of the simulation''
* FlockingForaging_evolve_v4.nlogo: agents evolve bimodal distribution in flocking parameter
** ''this seems to go away when flocking takes priority over foraging (instead of the reverse)''
* FlockingForaging_evolve_v4.nlogo: with mutation agents are evolving threshold for flocking larger than flock size (!) -- not sure why these are staying around since they should be unfit...

'''CHECK FOR (PREDICTIONS):'''
* Past theoretical work suggests that fragmentation of a herd results more easily for a individuals are heterogeneous in their walking speeds (Gueron et al 1993)
* Individual position within the group should change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999)
* Gueron et al (1996) found that the geometry of the group was dependent on the average speed of individuals, showing bands at slow speeds and columns at fast speeds
* if cost of moving is too high, migration should 'fail'

=== References ===
# Åkesson, S. & Hedenström, A. 2007. How migrants get there: migratory performance and orientation. BioScience, 57, 123-133.
# Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
# Bauer, S., Barta, Z., Ens, B., Hays, G., Mcnamara, J. & Klaassen, M. 2009. Animal migration: linking models and data beyond taxonomic limits. Biology Letters, 1-4.
# Bergman, C., Schaefer, J. & Luttich, S. 2000. Caribou movement as a correlated random walk. Oecologia, 123, 364-374.
# Boone, R., Thirgood, S. & Hopcraft, J. 2006. Serengeti wildebeest migratory patterns modeled from rainfall and new vegetation growth. Ecology, 87, 1987-1994.
# Charnov, E. 1976. Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9, 129-136.
# Clark, C. & Mangel, M. 1984. Foraging and flocking strategies: information in an uncertain environment. American Naturalist, 626-641.
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Fancy, S. & White, R. 1987. Energy expenditures for locomotion by barren-ground caribou. Revue canadienne de zoologie, 65, 122-128.
# Fancy, S., Pank, L., Whitten, K. & Regelin, W. 1989. Seasonal movements of caribou in arctic Alaska as determined by satellite. Canadian Journal of Zoology, 67, 644-650.
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Fryxell, J.M. et al. Why are migratory ungulates so abundant?. American Naturalist 131, 781-798(1988).
# Giraldeau, Luc-Alain and Thomas Caraco. Social foraging theory. Princeton: Princeton University Press, 2000.
# Gueron, S., Levin, S. A. & Rubenstein, D. I. 1996. The Dynamics of Herds: From Individuals to Aggregations. Journal of Theoretical Biology, 182, 85-98.
# Hamilton, W. 1971. Geometry for the selfish herd. Journal of Theoretical Biology, 31, 295-311.
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Krause, J. 1994. Differential Fitness Returns in Relation to Spatial Position on Groups. Biological Reviews, 69, 187-206.
# Parrish, J. 1999. Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation. Science, 284, 99-101.
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).
# Murray, M.G. Maximizing Energy Retention in Grazing Ruminants. Journal of Animal Ecology 60, 1029-1045(1991).
# Reynolds, Craig W. 1987. [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
# Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.
# Sinclair, A.R.E. The Resource Limitation of Trophic Levels in Tropical Grassland Ecosystems. Journal of Animal Ecology 44, 497-520(1975).
# Wilensky, U. 1998. NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Meetings ===

==== '''14 July 2009 7pm (GMT-4)''' ====

''since last time:''
* Liliana has a computer scoped out and NetLogo downloaded
* Kate added some parameters from the literature

''meeting:''
* got everyone connected and set up with Skype!
* divvyed tasks: Liliana and Kate will do B&F, Allison will do A, everyone will try D (we'll see who can get it to work)
* Kate suggested we reconsider how we initially setup our threshold distributions. Since we're using relatively few (N~300) agents to sample such a large distribution (0,100) by (0,100), chances are we aren't covering it uniformly. Also the different initial conditions between runs could account for different outcomes. Potential fixes: 1) increase number of individuals (thousands), 2) discretize the threshold distribution to 0-10-20-30-40 instead of continuous on (0,100).

==== '''21 July 2009 7pm (GMT-4)''' ====

''since last time:''

''meeting:''

=== Tasks (Current) ===
'''BIG PICTURE:'''
# setup a base ABM of flocking and foraging (done, yay!)
# see which foraging and flocking thresholds evolve
# make sure these thresholds are 'stable' under realistic conditions for caribou/wildebeest
# see how these thresholds vary with key model parameters (population size, energy from forage, predation)
# incorporate landscape

* TASK A: Since #1 is basically done above, we should write up a clear description of the model, explaining all the parameters and logic behind them, before we forget it all!!
** I posted a first draft of the model description -- please edit if you can make it more clear or have anything to add! Might also be good to add some figures. [[User:Akshaw|Akshaw]] 14:28, 17 July 2009 (UTC)

* TASK B: try varying ticks per generation and number of generations per run (ideally on a computer cluster to avoid killing someones laptop), to see if we get tighter convergence if we run long enough

* TASK C: If B doesn't produce good results, then come up with a better metric AND figure out how to export this from NetLogo (It may just make sense to export the threshold parameter values for all individuals and not just the average/stdev)

* TASK D: Related to this, it would be good to come up with an efficient way of analyzing the NetLogo data in another program. I'm partial to MATLAB but would be absolutely ok using another program if we think that would be easier. Kate and I figured out that if you delete the header lines and replace all the quotes with commas, then the csv files are easily imported into MATLAB. However some of the data imports in as text instead of numbers. The other annoying thing is that all the stats are calculated at every tick instead of every generation. It would be great if there were someway to get just stats at every generation...
** NetLogo code modified to output data from end of generations. Also to output data in CSV format for easy import into MATLAB. Still need to modify MATLAB scripts to actually analyse the data. [[User:SteveLade|SteveLade]] 03:50, 15 July 2009 (UTC)

* TASK E: We should play around with comparing the continuous vs discrete methods. This would probably just involve running a few simulations with each to make sure we're getting similar results. It may be that things evolve faster in continuous time, so that may be the way to go for our mass simulations. There's an output graph that shows the age distribution of turtles in the population, so that you can check to make sure individuals aren't dying each tick.

* TASK F: For #3 I think we basically need to know 1) average herd size, 2) average distance/speed and 3) average mortality for caribou/wildebeest migrations. Then we can setup a population of this size and our evolved parameters and see if it can make it that distance with that mortality.

* TASK G: Related to #3 -- we should think about the form of our predation mortality term and determine the best value for sigma in the function (or perhaps use a different function). It seems that there were lots of individuals dying from flocking in the simulations.

* TASK H: Once we do at least B/C/D above, we should run simulations again varying they key model parameters that we're interested in (for #4). In the meantime though, someone could run simulations with different values to get a feel for how these change the model -- perhaps they don't change the mean population value of the thresholds but do affect the distribution, or maybe they just affect migration speed, etc.

* TASK I: Figure out exactly what we want to know by incorporating landscape/resources into the model. Do we want to add resource factors as more key parameters in the model to vary -- then see how thresholds vary under different resource distributions? If so, what would key resource parameters be? Or do we just want to see how a group would move differently across different landscape types? This would be simpler but gets away from our central question.

=== Tasks (Old) ===

'''LITERATURE'''
* <s> migration models lit review (Allison) </s>
* <s> basic description of wildebeest & caribou migration cycles (Allison) </s>
* <s> appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana) </s>
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review (Allison)
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* <s> how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC) </s>
* <s> problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC) </s>
*<s> how to prevent flock from wrapping around across the boundary?
** Currently not a problem -- flock not long enough </s>
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* <s>''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
** yeah, this was a due to a bug in how I sent initial conditions -Allison</s>

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** <s> average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)) </s>
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* <s> adaptive dynamics framework to evolve parameters (Andrew & Steve) </s>
* <s> design behavior rules to determine when to forage and when to flock (Steve & Andrew) </s>
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-07-14T22:12:58Z

Kbehrman: /* Parameter Settings from Literature */

Foraging on the move

2009-07-01T05:38:44Z

Kbehrman: /* Parameter Settings from Literature */

Foraging on the move

2009-07-01T05:38:17Z

Kbehrman: /* Parameter Settings from Literature */

Foraging on the move

2009-07-01T05:35:48Z

Kbehrman: /* Parameter Settings from Literature */

Foraging on the move

2009-07-01T05:35:13Z

Kbehrman: /* Parameter Settings from Literature */

CSSS 2009 Santa Fe-Projects & Working Groups

2009-06-29T23:01:49Z

Kbehrman: /* Final Projects */

{{CSSS 2009 Santa Fe}}
==Project Groups==
===Foraging on the move===
[[Allison Shaw]]: I've moved the discussion of this idea to a separate project page -- see ([[Foraging on the move]]) for more detail and feel free to join in!

===Problem solving and mating - are they similar?===

The discussions on this project have been moved to a separate page: [[Problem solving]]

=== Interacting distribution networks ===
Moved to its own page: [[Interacting distribution networks]]

===The Effect of Gossip on Social Networks===
Moved to a separate page: [[Modeling gossip networks]]

===Radicalization of Islamic Diasporas and Reactive Control Theoretical Approach===
See [[Radicalization]]

===From Topology to Response===
[[From_Topology_to_Response]]

===[[Spiking Networks on the Cusp of Chaos]]===

Please click the title to be transported to the project page.
===Modeling behaviors between students and teachers===
Update and Details about this project, please click here !
[http://www.santafe.edu/events/workshops/index.php/Modeling_behaviors_student&teacher Modeling behaviors between students and teachers]

===Determining spatial contact networks for pathogen transmission===
Project Page: [[Spatial contact networks]]

=== Human searching strategies in an heterogeneous environment ===
Project page: [[Human searching strategies in an heterogeneous environment]]

==Brainstorming==
===Disease ecology of media hype===
How much and event gets covered in the news often appears to depends on how much it is already covered in the news. Often this distorts reality. For example, the number of searches for "swine flu" (a proxy for media hype), do not reflect the patterns of disease spread over the same period.
[[Image:Flu_trends.png|thumb|Google searches for "swine flu"|left]]
[[Image:Flu_cases.png |thumb|Actual number of swine flu cases over the same period|left]]
While the number of flu cases increased, the searches died off, as interest in the topic waned. It would be interesting to follow the origin, spread and extinction of media hype, maybe applying models commonly used to study the spread of disease. [[Alexander Mikheyev]] 

You could look at the dynamics from agent-based (ABM) perspective. There is a recent paper by Epstein and colleague that focuses on the impact of fear on disease from agent-based perspective, but does not capture this dynamics. However, my collaborator and I are currently writing a paper on the same problem you just outline from mathematical epidemiological perspective. Our results show some interesting dynamics. I think its extension in ABM might provide richer dynamics.
Another relevant paper: S. Funk, E. Gilad, C. Watkins and V.A.A Jansen (2009) the spread of awareness and its impact on epidemic outbreaks. PNAS early edition
[[Alhaji Cherif]]

===Complex networks of acupuncture points around the body===

what this project supposed to do is to set up the correlations of 720 acupuncture points complex network to do some interesting research on it. And what is important is such kind of work hasn't been done as i know. Feel free to have some discusstions on it to excite some good ideas. You could search "acupuncture" on wiki to get some general knowledge, Part of them are as belows.

Acupuncture is a technique of inserting and manipulating fine filiform needles into specific points on the body to relieve pain or for therapeutic purposes. The word acupuncture comes from the Latin acus, "needle", and pungere, "to prick". In Standard Mandarin, 針砭 (zhēn biān) (a related word, 針灸 (zhēn jiǔ), refers to acupuncture together with moxibustion).

According to traditional Chinese medical theory, acupuncture points are situated on meridians along which qi, the vital energy, flows. There is no known anatomical or histological basis for the existence of acupuncture points or meridians. Modern acupuncture texts present them as ideas that are useful in clinical practice. According to the NIH consensus statement on acupuncture, these traditional Chinese medical concepts "are difficult to reconcile with contemporary biomedical information but continue to play an important role in the evaluation of patients and the formulation of treatment in acupuncture."

The earliest written record that is available about acupuncture is Huangdi Neijing (黄帝内经 or Yellow Emperor's Inner Canon), which suggests acupuncture originated in China and would explain why it is most commonly associated with traditional Chinese medicine (TCM). Different types of acupuncture (Classical Chinese, Japanese, Tibetan, Vietnamese and Korean acupuncture) are practiced and taught throughout the world. [[Guimei Zhu]]

====Acupuncture/Chinese Alternative Medicine====

Here are some more papers regarding research that has been done on acupuncture. Some network analysis has been done. Very interesting stuff!

[[Media: AcupunctureOverview.pdf|Acupuncture Overview]]: Here is an overview of acupuncture from a journal entitled "Alternative Therapies" in 1998.

[[Media: AcupunctureGraphTheory.pdf| Acupuncture and Graph Theory]]: This paper was written in "Progress in Natural Science" in 2009 which implements the use of graph theory to make a model to understand the effects of acupunture on brain function.

[[Media: AcupunctureFibroblasts.pdf|Body-Wide Cellular Network of Fibroblast Cells]]: A paper relating the study of a body-wide network of fibroblasts to acupuncture. Written in "Histochemistry and Cell Biology" in 2004.

[[Media: AcupunctureNeedleAdmin.pdf|Acupuncture-Psychosocial Context]] And another which studies the effects of the procedure. Written in "Advanced Access Publication" in 2008.

Enjoy! [[Karen Simpson]]

===Housing prices.===
[[Image:Phoenix.jpg|thumb|Change in Phoenix home prices. Source: NYT|left]]
The New York Times has a set of [http://www.nytimes.com/interactive/2007/08/25/business/20070826_HOUSING_GRAPHIC.html?scp=3&sq=home%20prices%20graphic&st=cse dramatic graphs] showing the rise and fall of home prices in select cities. Again these graphs reminded me a bit of those produced by [http://www.math.duke.edu/education/ccp/materials/postcalc/sir/sir2.html susceptible-infected-recovered] models of disease spread. Maybe there is something to it? Or maybe this phenomenon is already well understood by economists? [[Alexander Mikheyev]] 

===Movie Turnouts===
Which would be the more popular movie -- a combination of Steven Spielberg, Eddie Murphy and Gwyneth Paltrow, or Woody Allen, Dwayne 'the rock' Johnson, and Tom Cruise? Using the adaptation and turnout models presented by Nathan Collins, could we construct a prediction for gross movie receipts or even movie ratings? [[Nathan Hodas]]

===Climate network model.===
''Requires someone with climatology knowledge.'' Lenton et al. recently published a [http://www.pnas.org/content/105/6/1786 paper] listing 'policy-relevant' 'tipping elements' in the Earth's climate system and the temperature tipping points required to initiate them. (Basically, the tipping elements are components of the climate system where a bifurcation leading to a different stable state can be induced. The tipping point is the temperature at the bifurcation.) Surely, many of these tipping elements would have feedback effects on other tipping elements or the climate system as a whole. I would like to make a network model of these tipping elements and look at the tipping (or other) dynamics of the whole system. But Lenton et al. don't discuss these feedbacks much in their model, so we need some expert knowledge. [[Steven Lade]]

[[Almut Brunner]] Sounds like a very challenging project. As climate modelling is a very broad issue in itself, I would suggest to look at a specific example of threshold values in climate models, e.g. changes in rainfall patterns in Saharan environment and its impact on vegetation cover and finally desertification. It is known, for example, that if the rainfall amount in the Sahara drops below a critical value of 100mm/yr, the vegetation cover will change extremely due to reduced water availability and hence cause irreversible environmental changes. But I am not sure, if we could model that due to complicated/complex feedback mechanism and limited access to data. Another idea could be to simulate the other extreme - increased rainfalls. Is there a critical threshold value/tipping point causing extreme floods and environmental hazards in exposed, vulnerable landscapes (e.g. lowlands, coastal regions or even around here in the Grand Canyon region for which we can certainly get some nice data?).
Looking forward to discuss these issues a bit more with you.
What kind of model did you have in mind for simulating tipping point and feedback mechanism?

[[Steven Lade]] I wasn't thinking of modelling any of the physics or ecology directly, but at a coarse level with something like
<pre>node_i (time) = f_i[global temperature(time - delay_i), outputs of other nodes(time - delay_i)]
global temperature(time) = IPCC[time] + g[outputs of nodes(time)]</pre>
Each of the nodes would be a local tipping element. Lenton et al. already provide the global average temperature thresholds for the tipping elements and the time delay for the element to actually tip. We can then specify the part of the function <code> f_i[global temperature] </code> with something like a sigmoidal function. For the base time course of global temperature we could use IPCC projections or hold it fixed and just see what the feedbacks do to it. What Lenton et al. doesn't specify in detail is these feedbacks -- i.e. the dependence of nodes and the global temperature on the other nodes. Someone suggested to me that for a more abstract study we could look at the behaviour of the system over a range of possible feedbacks.

===Synchronised magma oscillations===
''Requires someone with geological knowledge'' In a recent [http://www.springerlink.com/content/n76781712g2q3578/?p=ec0c1ffe588f473a8dbe9637a3822ebf&pi=2 paper], which was also [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WY-4WBRC9H-G&_user=554534&_coverDate=05%2F20%2F2009&_alid=931681330&_rdoc=1&_fmt=high&_orig=search&_cdi=33799&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000028338&_version=1&_urlVersion=0&_userid=554534&md5=5dc46c822607723e06f9b72fb16d1463 reported] by New Scientist, Mjelde and Faleide report on seismological measurements that allowed them to infer past rates of magma flow in the plume generally though to rise beneath Iceland. When the plume is strong it thickens the Earth's crust at this point. They found the crust thickened approximately every 15 million years, and inferred that the magma plume must also have pulsed with this period. These pulsations have also been observed in the crust under Hawaii, with almost exactly the same period! Mjelde and Faleide hypothesise that there must be some giant heating oscillation in the Earth's core which drives these two oscillations at very different parts of the Earth. But other geologists are skeptical because of the huge energy required and lack of other evidence of such oscillations. But all this reminds me of the synchronisation phenomenon, where coupled oscillators, even if only weakly coupled, tend to synchronise. So the oscillations under Hawaii and Iceland may be generated independently, but have some weak coupling that has led them to synchronise. We can make coupled oscillator models, that's easy, but someone to provide more context on possible forms of coupling and their parameterisation is more what we need. They only observe about three periods of this oscillation and the data is quite imprecise so we can't do much direct data analysis, unfortunately. [[Steven Lade]]

===Implementing Synchronization using NetLogo===
Since I just learned about NetLogo, I look forward to the tutorial sessions and would like to implement a synchronization scheme of a group of entities. If I find out how the fireflies synchronize themselves, then that would be an option. Of course, I'll be surprised if this has not been done before in NetLogo. I'll welcome any help and suggestions.[[Mahyar Malekpour]]

[[Mahyar Malekpour]]: Update June 16, 2009 - Someone asked if there is an application for this. The answer is yes, categorically, any self-organizing system needs synchronization. However, my interest here are visualization and exploration using agent-based tools. I don not intend to develop a solution to this problem, rather build on an existing agent-based model (if there is any) and enhance its capabilities.

[[Massimo Mastrangeli]]: as someone said, there is vast literature on synchronization available; you can for example get a taste in [http://www.amazon.com/SYNC-Emerging-Science-Spontaneous-Order/dp/0786868449 Sync] by Steven Strogatz (also, check out his talk [http://www.ted.com/talks/steven_strogatz_on_sync.html at TED]). I am quite interested in the idea.

===Contagion in Networks===
[[Peter Dodds]] discussed contagion in a simplified network in which all the nodes have certain amount of threshold for changing. I thought that if the thresholds are various, that can lead to new behaviors in group level. For instance, people in different cities might have different resistances against inputs. Hence, we might see that an epidemic issue spreads in one city but not in the other. Consider the cities as nodes in a higher level network. This means that we might see the same patterns in this higher level. Different nodes (cities) react differently to external inputs. This also seems to be a more realistic model of the real world. Any comments, suggestions or discussions, even in the order of minutes are appreciated!
[[Roozbeh Daneshvar]]

* Perhaps this concept could be related to ecological food webs and the success of invasive species. The "epidemic" would be an introduced species, and the "spreading of the disease" would be how successful the alien species is within that food web. There are plenty of journal articles attempting to study the success of biological invasion, and I think in addition to looking at the food web networks, generating an agent based model would be ideal! It could be related to your idea, Roozbeh, in that the cities represent "habitats", and the "epidemics" represent the introduction of an alien species.

* [[Karen Simpson]]: Introducing Agent-Based Modeling: Several concepts (external and internal inputs) have been discussed that are said to contribute to whether or not a species succeeds in it's novel environment. These include: how many individuals are in the founding population, the "strength" of any competing organisms (this would be 0 is there are no competitors), the amount resources available, the ability of organism to adapt to the new environment, physiological advantages of new species over native species (i.e. defense mechanisms), and many more. I think we could find properties of ecological foodwebs, and then introduce a species (or epidemic) into the network and see what happens based on these inputs. Let me know your thoughts.

* [[Roozbeh Daneshvar]]: Karen, this sounds interesting to me and I'd like to know more. Shall we have more discussion over it on Tuesday?

===Linking topology to dynamic response in small networks===
Imagine a small (3-7 nodes) network where every node represents a protein species, and every (directed) edge the activation relation between the proteins (i.e. A ---> B means that the protein A can react with B and activate it). Furthermore,
assume that there are two numbers associated with every node: the total number of protein molecules of the given type and the fraction of the active forms. Finally, let two nodes, R and E, be special and call them the Receptor and the Effector. What you have is a crude model of intracellular signalling.

This [http://www.cosbi.eu/templates/cosbi/php/get_paper.php?id=147 paper] considers such models and exhaustively classifies all the possible topologies (i.e. wirings) with respect to the activation pattern of the Effector in response to a standardized signal sent by the Receptor. The goal of our project would be to do the same experiment using different tools, and potentially obtain different results. The main difference would be to use stochastic (rather than deterministic) dynamics to determine the response. As the signalling systems operate with relatively low numbers of molecules, stochastic effects may be important. If we do this and have time left, we can try pushing it further and consider the issues of robustness and evolvability of these networks.

To put a nasty spin on the project, I propose that we use an obscure computational technique called [http://en.wikipedia.org/wiki/Model_checking model checking] to get the response profile of a network; partly just because we can, but partly also because it nicely deals away with the need of explicitely simulating and averaging of stochastic models.

Now, a couple of final remarks:
* Don't think of it as a network project. All networks involved will be rather trivial.
* The project group should include a biologist (to do sanity checks) and somebody familiar with parallel computing.
* Model checking is (very) expensive computationally, we will probably need a cluster.
* I have all the original results from the paper mentioned.
* The tool to use would probably be [http://www.prismmodelchecker.org/ PRISM].
[[Marek Kwiatkowski | Marek]]

: Marek, this dovetails nicely with my interests & I'd like to talk more about it with you. I have experience with -- and access to! -- a parallel cluster. No experience with prism, however. [[Rosemary Braun]]
: OK then, I am going to start a [[From Topology to Response | project page]] [[Marek Kwiatkowski | Marek]]
If you did not do this yet, I suggest you to have a look at "Small Worlds" by Duncan Watts. It containts useful information, models and mathematics on the topic. -[[Massimo Mastrangeli]]

===Pattern Generation in Dynamic Networks: Elucidating Structure-to-Behavior Relationships===
Many sorts of networks produce patterns when dynamics are active on them. The brain is a great example. In fact, the patterns generated in your head are not only interesting and perhaps beautiful, but crucial to your success in surviving and thriving in the world. Gene or protein networks are another example. Change a few genes around and suddenly your stuck with a nasty disease.

One question we can ask is: how do the patterns of behavior (or "function" if you want to presume as much) change when we change the structural connections in the dynamic network from which they emerge? Alternatively, for a given type of behavior (set of similar patterns), is there a class of networks which all exhibit this behavior? What is common between all of those networks? What is the underlying mechanistic explanation for how they all behave this way?

Some potential topics:
* Genetics - what patterns of proteins emerge depending on what genes are where on a genome? (maybe other questions ... I'm not a geneticist!)
* Spiking neural networks - I have a lot of experience with this.
* Kauffman-like Boolean networks
* Population biology / food webs?
* Economics?

We might even think of embedding this in some physical space. Perhaps neural nets drive the 'muscle' movements of creatures (a la the [http://www.karlsims.com/evolved-virtual-creatures.html Karl Sims 'Creatures'] video we saw in Olaf Sporn's lecture) or the motors of [http://people.cs.uchicago.edu/~wiseman/vehicles/test-run.html vehicles].

I have experience in Python, Java, Matlab and a few other languages and am open to working with whatever (NetLogo?). I also have experience with Information Theory, which could come in handy in digesting and analyzing the patterns.

Clearly this project could go multiple directions. Feel free to add ideas/comments here...

[[watson]]

* [[Jacopo Tagliabue]]: Premise: I don't know if it makes sense at all, and even if it fits the project. I was thinking that just not the fact that some areas are connected makes a difference, but also the way they are connected. For example, the synchronization of neurons plays a pivotal role in the proper behaviour of the brain: when some disease (such as [http://en.wikipedia.org/wiki/Multiple_sclerosis multiple sclerosis]) leads to [http://en.wikipedia.org/wiki/Demyelinating_disease demyelination], the signals in the axioms can no more be processed at the right speed. The upshot is progressive cognitive and physical disability. Can we use agend-base models and/or network analysis to better understand what happens (and why, for example, multiple sclerosis may evolve in four different ways)? If someone with some neuroscience background would like to talk about this (or just explain why this doesn't make sense at all),I'd be glad to learn!

[[Karen Simpson]]: This is interesting to me, especially in the case of food webs merely because that is what I am most familiar with. Within an ecological community, there are certain links that depict the dynamics within that community. If we remove a link (or change it somehow, maybe by redirecting it through another organism), the community is stressed. The community may be resilient and the underlying dynamics may shift back to equilibrium. On the other hand, it may lead to the extinction of certain organisms.
One way that these links are changed is by introducing another node into the system, this node representing an introduced species. The success of this species depends largely on its position in the food web and its connecting links. My question (from an ecological perspective) is: Does introducing a non-native species result in different underlying dynamics and patterns? My intuition says yes, but it largely depends on the ability of the non-native organism to succeed in it's new environment. (See my thoughts under "Contagion in Networks" for more on this topic)

* [[Massimo Mastrangeli]]: The topic looks very interesting. I read a lot on Kauffmans' approach and I would probably like to get dirty hands on it. The idea in my opinion is to create a network with a plausibly vast and interesting state space, and explore it using some tools. Analysis of the dynamics of the transitions from one steady state to another might be interesting.

=== All sorts of (mostly US-centric) data===
For fun, brainstorming, and sanity-checking:
[http://www.data.gov/ data.gov] has tons of data collected by the US Gov't.

===Modularity in complex systems - why is it there and what does it do?===
Evolving systems often switch from being highly modular to highly integrated, and vice versa. Why is this so and how does it happen? [[Wendy Ham]] and [[Roozbeh Daneshvar]].

* [[Roozbeh Daneshvar]]: Today in a slide of [[Olaf Sporns]] presentation, I noticed a graph showing the relation between order/disorder and complexity. When the system becomes too much ordered or too much disordered, in both cases complexity reduces. There is somewhere in between that we have the most amount of complexity. I was thinking that the emergence of modules are also a movement towards orderliness. But, complex systems do not go beyond a limit and still keep some non-modularity. So, Wendy, we have contrasting views on modularity. But maybe we will meet somewhere in between, where we have the most amount of complexity!
** '''Question''': Why modularity changed in human societies? Did the behavior of complexity change?
* [[Steven Lade]] Wendy, can you give some examples for evolving systems moving from "highly modular to highly integrated"? Also Roozbeh I don't understand what you mean by "behavior of complexity". Maybe we should talk.

* I like this idea. Clearly it needs some more fleshing out, but its a good direction. One thing to think about when you see modularity biologically is whether certain 'modules' can be reused multiple places. Komolgorov complexity is something that you might look at... [[watson]]

* [[Wendy Ham]] Thanks Watson, I will check out the Komolgorov reference. To Steve: Roozbeh and I started thinking about this when we discussed how some societies have evolved from having a clear demarcation between the gender roles (e.g., men work and make money, women stay home and take care of kids) to not having this demarcation anymore (i.e., gender equality, etc). So at least with regards to gender roles, these societies have evolved from being modular to being integrated. As a general rule, I tend to believe that modularity is important for allowing innovation and adaptation, which are important in a changing environment, whereas integration is good for efficiency. So, the question here, for example, is whether these societies have reached a certain level of "stability" such that modularity is no longer important. Aside from this example, people have shown that bacteria that live in changing environments tend to be modular, whereas those that live in a stable environment tend to be more integrated. Furthermore, organizations (e.g., business firms) also tend to become more integrated/tightly coupled as they mature.

* [[Roozbeh Daneshvar]]: Steven, we have a complexity landscape here that imposes where the system should stay. That is normally somewhere between order and disorder that gives the system the highest capabilities. I also associated order with modularity and disorder with dis-modularity ([[Wendy Ham]] seemed to agree with this!). Now the amount (and perhaps form) of modularity has changed. So, my intuition is that the complexity landscape (which determines the future behaviors of the system) is changed. This is what I meant by change in "behavior of complexity". I meant that the dynamics of that complex system is changed and hence, the equilibrium is somewhere that did not use to be equilibrium before this (there were some topics related to this area on Monday June 15 lectures).

* [[Gustavo Lacerda]]: Watson, Kolmogorov Complexity is a very general concept. Do you mean "motif discovery"?

* [[Mauricio Gonzalez-Forero]]: I would like to hear more about this project. Can we meet sometime?

===Evolving nanomachines===

Take the evolving motors animation we saw at the end of Olaf Sporn's talk, but instead put nanoscale physics, i.e. overdamped motion with Brownian noise, into the simulation. Perhaps put some basic chemistry in too. Evolve possible designs for nanomotors! What we get may include existing biological molecular motors. Or even more crazy idea: put in the physics of quantum mechanics. [[Steven Lade]] but with credits to Lilliana!

* [[Roozbeh Daneshvar]]: I am interested in this. Although I am curious to know what methods do you want to pursue for this matter? ABM? By the way, I deeply believe that this is the kind of research which determines the future of robotics!

===Credit Market Simulation===
Money is loaned every day on the bond and money markets between banks, corporations, and individuals. It usually works very efficiently, but, ultimately, it is driven by humans. An agent simulation could provide us with insight into what behavior patterns give rise to the booms and busts that we have been experiencing. My guess is that it boils down to how individuals estimate risk and future reward. Nathan Collins suggested a learning model for how people get habituated to reward, expecting more and more for satisfaction. However, what happens to our estimates of risk in the face of increasing rewards? When the two are out of sync, we would likely see interesting dynamics. We've come up with a few ideas for how to implement this. [[Nathan Hodas]]
* [[Jacopo Tagliabue]]: It could be interesting to embed insights on risk-seeking and risk-averse behaviour from prospect theory and behavioural economics. I am also interested in agent-based simulations of a simple economy, where agents may use different heuristics (rational decision theory, Simon's model, Kahneman and Tversky theory, etc) to decide what to do. It is often said that in the market "errors cancel each other out", leaving a optimal or quasi-optimal global outcome: but is it true? And what's the relationship between individual strategies and this dynamics?

*[[john paul]]: I'd like to throw my weight in with this one to see how this is addressed. Mr. Hodas and I have been talking about real-world risk associated with credit and defaults as noise in a system, and directed flows of current cash, credit and derivatives as three possible visualizations. Ideally we can pull out some real-world credit data and begin to construct a scale market of one economy (or sector of an economy, like government spending) and then hopefully either scale that up or adjust as needed to other data.

* [[Wendy Ham]] Do you guys consider credit default swaps (CDS) as a special kind of financial instrument - one that almost completely lacks inhibitory mechanisms and thus is able to grow indefinitely? (Analogy to cancer cells?)

===Creative Process===
This is a very preliminary attempt to analyze the creative process in order to identify how we come up with ideas.

Creation of ideas as a process of random combination of concepts and connections taking place in the subconscious. Most of these ideas are filtered before reaching the conscious. Those ideas that rise above the conscious are new to the individual, some of which may also be new to the world. We generally classify the latter ideas as creative. Furthermore, the creativity literature refers to ideas as creative only when they are immediately useful in solving some problem or condition.

The existing concepts and connections can be considered as nodes or agents. A new idea can be a combination of at least 2 concepts + a connection or two connections, or some superposition of them. The following rules obey at the subconscious level:

1. The random process is taking place all the time with a single combination at one time

2. Each idea (which is a newly created concept or connection) attempts to pass through a filter. It either passes through or it doesn’t. If it does pass through, the idea is recognized and the coupling between the concepts/connections is raised. Each increase is by a factor of 0.1 (starting from 0) of the existing coupling until it reaches a maximum of 1. If it doesn't pass through, it ceases to exist (however, it may reappear later and given a change in the characteristics of the filter, they may be allowed to pass through).

The rules that define the ideas that pass through are:

1. The database of filters (individual’s understanding of the external environment, self control, etc.) defined in terms of what concept and connection associations are allowed to pass through as well as 20% deviation in them. [Ques: How can the deviation of a concept be evaluated numerically?]

Using complexity theory:

1. Agent based modeling can be used to identify how newer ideas rise to the level of consciousness, how the filters affect them

2. The network analysis can be used to understand how the coupling affects the creation of new ideas (concepts/connections)

[[Murad Mithani]]

[[Wendy Ham]]: Hi Murad, there are definitely some overlaps in our interests.

===The Biological Evolution and Social Learning of Cooperation===
Both evolutionary biologists and social scientists have convincingly shown that cooperation can emerge and persist in human society. Although the two have employed the same methods (game theory and agent-based modeling), they have proposed different mechanisms: on the one hand, biological evolution based on kin selection, group selection, the “green-beard” effect or reciprocity and on the other, socio-cultural adaptation due to social learning. The two mechanisms act on different time scales and make different assumptions on the agents’ behavior (fixed vs adaptive) and the underlying dynamics (reproduction vs imitation). I think it will be interesting to combine the two mechanisms in a single agent-based model and to explore how they relate to each other. Following standard practice, the model will consist of agents on a spatial grid or a(n evolving) network who play a game such as the Prisoner’s Dilemma or Hawk-Dove. [[Milena Tsvetkova]]

Nice. Indeed, one can reinterpret things to some extent and understand cultural and biological evolution in similar veins. In both sorts of evolutionary processes, individuals can be assigned fitness. In the biological case fitness refers to ability to leave offspring, while in the cultural case fitness might refer to ability to be imitated by others. So, reproduction can be understood as genetic or cultural. Mainstream evolutionary biologists use these interpretations, but I wonder if they break in some cases. [[Mauricio Gonzalez-Forero]]

[[Mauricio Gonzalez-Forero]]: Mareen, Varsha and I have sketched a potential agent-based model for the evolution of division of labor. It needs more thought, and the input from social sciences people would be very valuable. The model considers two labors performed by agents and a cooperative trait. Given spatial structure and dispersal restriction, we expect the cooperative trait to allow for the division in labor to evolve. It should be straightforward to implement in NetLogo. After an analysis of the simulations, it would be neat to synthesize the model analytically. Interested people are certainly welcome to help!

[[Gustavo Lacerda]]: Mauricio, this sounds interesting.

===The Emergence of Meaning and the Evolution of Language===

There are several attempts in the philosophical and psychological literature (see [http://en.wikipedia.org/wiki/David_Lewis_(philosopher) Lewis’ work] on convention and [http://en.wikipedia.org/wiki/Paul_Grice Grice’s] analysis of meaning) to analyze the emergence of meaning. Most accounts (it not all) make extensive use of meta-representations, that is, the ability we have to understand other people intentions and “read” the content of their mental states. There are two problems with these theories: first, they are developed in a static fashion, while it may well be the case that the emergence of meaning is the result of a continuous, adaptive process; second, they seem to be plainly false, at least if we are willing to say that people affected by autism – and thus unable to read others mind – understand and produce meaning (see this recent paper by [http://people.su.se/~ppagin/papers/Autism5D.pdf Gluer and Pagin]).
Brian Skyrms and others used evolutionary game theory to evolve proto-languages, so-called “signaling games”, to understand how meaning dynamically emerges without meta-representations (it turns out that meaning can be understood as a form of equilibrium in these evolutionary dynamics). It could be interesting to further develop these insights, adding more realistic features to AB models:

* adding noise
* explore the same game in different topologies and see if the emergent behaviour depends in some way on constraints on how agents move
* see if it is possible to evolve language with a proto-grammar

These are just some preliminary considerations. Let me know what you think! [[Jacopo Tagliabue]]

* [[Gustavo Lacerda]]: Jacopo, I'm a fan of Simon Kirby's work.

=== Biological Pathways ===

Loosely defined, biological pathways are networks of molecular interactions that achieve a specific biological function. I'm interested in using the information we already have about them in the analysis of microarray data. I have a bunch of half-baked ideas; here are two.

* [[Steven Lade]] I'm interested in one or both of these.
* [[Gustavo Lacerda]]: Me too! I'm interested in statistics in the "small n, large d" setting, sparse regression, and incorporating structural knowledge through e.g. strong Bayesian priors.

==== Many hits vs. critical hits ====

[[Rosemary Braun]]

Microarrays assay 10^5-10^6 biological markers per sample. The most basic analysis is to ask whether each marker, individually, is disease-associated; common multi-marker approach is to sort the markers based on the magnitude of their association with disease, and then ask whether the high-scoring markers are over-represented in some pathways (biological interaction networks). By systematically performing an enrichment analysis on all known pathways, it is possible to elucidate which ones may play a role in disease. (cf [http://www.ncbi.nlm.nih.gov/pubmed/16199517 GSEA].)

On the other hand, it is well known that the centrality of a molecule in the biological pathway is strongly correlated with its biological importance -- the lethality of knocking out a gene is related to its centrality (eg [http://www.ncbi.nlm.nih.gov/pubmed/11333967 Jeong 2001]). This finding has been used to study individual markers 'within' a given pathway to predict which ones would be the most biologically relevant (eg by ranking the markers based on centrality, ([http://www.ncbi.nlm.nih.gov/pubmed/18586725 Ozgur 2008]).

One of the drawbacks of GSEA-type enrichment approaches is that they do ''not'' consider the centrality of each marker, ie, they are pathway-topology-ignorant. To the best of my knowledge, while centrality has been looked at to examine the importance of individual genes to a given function, it has not been incorporated in enrichment analyses. I would like to answer the question "is a pathway more ''critically'' hit with disease-associate alterations than would be expected by chance alone" using a centrality-aware scoring function.

One very naive way to do this would be to simply scale the single-marker association statistic used in GSEA by the centrality of the gene in the network. This raises a question of its own, however: to what degree do the results depend on the severity of the scaling?

Anyway, that's one half-baked idea. [Resources available: tons of data; adjacency matrices for pathways represented in KEGG, BioCarta, Reactome, and the NCI/Nature pathway database; useful ancillary functions in R; a cluster for permutation testing/exploring the parameter space.]

==== Gene expression time-course spectra ====

[[Rosemary Braun]]

Consider all the genes involved in a given pathway. Consider, also, a set of data that gives us the expression values for each gene at a handful of timepoints, eg, before (t=t0) and after (t=tf) an environmental exposure.

Next, suppose we describe the activity of that pathway by completely connected directed graph, for which the weight of the edge from gene_i to gene_j is given by MI(gene_i(t=t0),gene_j(t=tf)) (in the case of multiple timepoints, we could extend this -- eg transfer enropy). That is, the weight of each directed edge from gene_i to gene_j would tell us how well gene_i at t=t0 predicts gene_j at t=tf.

(I suggest the complete graph, rather than using the known pathway topology, because in practice the time differences tf-t0 may result in multiple "hops" -- so we may have correlations between next-next-neighbors rather than nearest neighbors, etc.)

So, we now have a description of signal propagation through the pathway over the time t0->tf, which we could summarize using the eigenvectors of the Laplacian. If we have two classes, eg cells which do/don't respond to the exposure, will we see statistically significant differences in the spectra for certain pathways, and thus infer that those pathways are involved in the response?

Possible pitfall: most time-course experiments only have a handful of samples for each timepoint.

=== Network structure of personality ===

[[Sean Brocklebank | Sean]] is interested in using the methods [http://www.santafe.edu/events/workshops/index.php/CSSS_2009_Santa_Fe-Readings#Scott_Pauls:__Partition_Decoupling_for_Roll_Call_Data presented] by Scott Pauls at SFI on Wednesday to analyze the structure of personality as revealed by personality psychology's canonical test, the NEO PI-R, and it's freeware version, the IPIP NEO.

These surveys consist of 240 and 300 questions, respectively, and have been analyzed using traditional factor analysis to reveal the Five Factor Model of personality (FFM, see [http://en.wikipedia.org/wiki/Five_Factor_Model Wikipedia article]). But there is much debate within personality psychology about the exact structure of the factors, and particularly the higher order correlations among them. Traditional factor analysis is not much use in resolving these disputes, but that is just about the only method which has been used so far. I've spoken to Scott Pauls about this already, and he says that his method might be useful to help to resolve the issue (see his comments below).

I've got a dataset of about 1000 responses to the NEO-PI-R and 21,000 responses to the IPIP NEO, and I can get access to a smaller dataset which also includes some info on FMRI imaging and some other personality tests if necessary.

This is not a subject which I was originally planning on pursuing when I came to the CSSS, but I think that the central importance of this test to personality psychology means that the project will have a reasonable chance of getting published regardless of the results, and anyone working on it should learn some cool data analysis techniques along the way.

If you'd like more information about what I've written here, note that I will be talking about the subject over lunch on Tuesday the 16th. Just find my table (or avoid it, depending on your preferences).

I'm in. [[Marek Kwiatkowski]]

[[Murad Mithani]]: I would like to know more about this.

I'd like to talk more. [[Casey Helgeson | Casey ]]

[[Scott Pauls]]: Some comments on this idea.

I think this is a very interesting application of the PDM or some variant of it). One of the aspects of the "Five Factor model" is the controversy around the selection of the factors and their putative independence (they are not). The collection of tools we use will allow for a data driven extraction of factors on multiple scales. I suspect, although it is not a given, that the top layer of factors will reflect to some extent the "five factors" already used. However, it will give detailed information on the relationships between the pieces. Moreover, the multi-scale decomposition should yield a very textured description of the personality factors and their interactions.

A couple of technical points - given the length of the data series (200-300 questions), I would probably limit the analysis to roughly 150 respondents at a time. The wealth of data available means that one can do multiple experiments using ~150 members allowing for a good analysis of the robustness of the factor results.
[[Guimei Zhu]] interested in it, i am also curious on persons.

===Music Rhythm Pattern Generation with Hierarchies and Dynamics (PROGRAMMERS WANTED!)===

Western based music comes in boring measures. 4 beats, 16 beats and then repeat plus a little modification. Boring!

Even exotic music from India or Bali sticks to one particular measure ... even if it's some bizarre integer, a prime number say, like 17. But what if we introduce hierarchies of measures?

So lets say a measure is one minute long. Between every beat of your 4 measure I introduce 7 beats. And between the first four of those I introduce 2 beats; between the 2nd 5 beats and between the third and fourth 3 beats each. What does that music sound like!?

Clearly there is synchrony every x beats between different patterns but in between there is something which bears some relationship over time but takes a little listening to understand.

What music is most pleasing? What do you want to hear more of? What is too complicated/random and what is too boring?

I have worked previously on such a system written in Java called the [http://mf.media.mit.edu/pubs/conference/EmonicReport.pdf Emonic Environment]. But this was many years ago and I have learned much about much since then.

What can we create now?

A few people have exhuberated interest including Murad and Casey but I need at least one or two other people who are capable of contributing to the implementation before we can go ahead with the project.

Do you find yourself fascinated by your own attraction to different sorts of rhythm? Do you sense that this summer school could be a pathway for reigniting your own passion for creativity and expression, while maintaining some connection to science? Both Liz Bradley and Peter Dodds encouraged us to nurse the flame fueled by playfulness and creation, to keep ourselves engaged by having fun and staying curious. If a group of us got together and really inspired one another with our ideas and passion, maybe we could make something compelling and bring out the curious 5-year-old latent in all of us.

What are interesting ways to create hierarchies and change them dynamically? What sort of dependence should one structural or functional parameter have on others in order to create sequences of sounds that aren't just random but rich in some sense?

[[watson]]

*[[Massimo Mastrangeli]]: I guess Watson is referring to polyrithm(ics), which is a way of layering musical compositions with parts having each its own signature/tempo. This is traditional in some african cultures, and is anyway sometime used also in western modern music (e.g. Strawinski's "Rite of spring"; also, those who know of metal bands like Meshugga, Pain of Salvation and similar can have an immediate idea). Odd time signatures are also quite common in muzak/klezmer tradition (and progressive rock!). They bring an overall impression of dynamism and energy, given that the beat patterns can be richer and more unpredictable than in common 4 beat time signatures. I like quite a lot this type of music (you had doubt still? :) ), I could contribute to the project with my musical experience. It can be a nice occasion also to learn about new tools. The project may have some substantial physiological/esthetic components to it.

*[[watson]]: hmmm ... yes. this is exactly what I am talking about. very cool to hear you have some experience with this Massimo. right now i am leaning on going ahead with this project. i think we have serious potential to make impact, elucidate new relationships and phenomena and educate in the process. and i think it could be a ton of fun. here are a couple of links i have found which could be of use:
**[http://fusionanomaly.net/polyrhythms.html this] page talks about history, theory and even mentions chaos.
**[http://web.mit.edu/cjoye/www/music/tabla/ this] is a good source for tabla samples. tabla is one of the simpler devices that has some melodic structure as well as rhythmic structure to it. we could work with others as well... one thought is even just a drum kit of different sounds (rock style).

===Rebellion===
The results of Iran's recently held presidential election (June 12, 2009) is very controversial. Demonstrations are being held across Iran and some have turned violent with a few fatalities reported. Demonstrations are also being held in major cities across the world. It is reminiscent of the Iran's revolution about 30 years ago. So, here is an idea for an agent-based modeling of a rebellion; what does it take to tip the balance to successfully influence the election process for a possible re-election? What kind of networks to model the rebellious groups? Or, to take it to the extreme, what does it take to have another revolution?
[[Mahyar Malekpour]]

[[David Brooks]] This seems to be the same problem as the Gossip suggestion from above. Perhaps we could combine the two adding factors such as participation hesitation to represent the stability that must be overcome to induce action (participation in gossip or revolution). Perhaps we could get together with the gossip model team to discuss the potential.

[[Scott Pauls]] There are interesting discussions in the political science literature concerning revolutions in relatively authoritarian regimes. [http://fds.duke.edu/db/aas/PoliticalScience/faculty/t.kuran/publications T. Kuran] has spent most of his career on such models. One of his first papers on this is T. Kuran, Now out of never: The element of surprise in the East European Revolution of 1989, World Politics, vol. 44 (October, 1991), pp. 7-48.

===Mesoscopic self-assembly of passive functional components===
Self-assembly is being recognized in the field of microelectronics as a viable way to assemble multifunctional systems in a cheap and efficient way. Beside speeding up the assembly procedures that are now standard (e.g. pick-and-place), self-assembly is enabling the construction of unique systems which could otherwise be not possible. This is particularly important and promising for devices whose size ranges from microns to millimeters, i.e. devices which are too large to be assembled by supramolecular assembly and also too small to be assembled by robotic assembly.

This project would aim at designing ensembles of electronic components (i.e. devices endowed with electromechanical interconnecting structures which constraint the possible arrangements) and the constraints on the physical environment that would result in the autonomous formation of standalone and functional systems. It is a type of static self-assembly, where the energy is dissipated only while the system is reaching its thermodynamical minimum energy state. I propose agent-based models which should encode physical forces among components and/or templates (e.g. gravity, capillarity, electromagnetic fields, chemical forces), and should bring about a plausible dynamics and parameter space for successful assemblies.

[[Massimo Mastrangeli]]

===Guns, Germs and Steel: Modeling the fates of human societies===
In his hugely influential book ''Guns, Germs and Steel'' J. Diamond tries to answer a question once posed to him by his field assistnat: "Why is it that you white people developed so much cargo and brough it to New Guinea, but we black peope had little cargo of our own?" The book is a verbal model, suggests that the fate of human society is a product of the locally available resources, such as which crops could be domesticated, and the geographic configuration of regions, which then allowed these resources to be transmitted. The book has many intriguing and testable elements. In effect, Diamond describes a network model, where success is determined by connectedness and information transfer. The ideas of GGS can be tested by taking the underlying patterns of resource distribution and feeding them into an explicitly specified the information transfer networks. You can even permute various parts of the system and see whether you would still get the same historical dynamics. [[Alexander Mikheyev | Sasha]]

[[Randy Haas]] Sasha, I have lots of thoughts on this, and it is similar to a problem I've considered posting. I can certainly contribute an anthropoloigcal perspective on the problem, and the archaeology of agricultural origins is an area of specialty for me. let's talk about it.

[[Alhaji Cherif]] There is a nice book by Peter Turchin Historical dynamics where he studies cliodynamics and has looked at some of these questions from both empirical and mathematical models. He has written some papers too on the subjects, too. His papers might be a good starting point.

[[Nathan Hodas]] I'd like to be in on this. I've pondered a good deal about this since reading the book. Maybe we should contact Jared Diamond?

===Regional language differentiation===
The goal of the [http://dare.wisc.edu/?q=node/1 Dictionary of American Regional English] is to capture how colloquial expressions vary across the United States, based on interviews conducted in the mid-20th century. Check out this [http://dare.wisc.edu/?q=node/4 sample entry]. There is also a collection of recordings where >800 people from various regions read the [http://dare.wisc.edu/?q=node/44 same text]. I am not exactly sure what one can do with this resource, but I maybe someone can come up with a good idea. [[Alexander Mikheyev | Sasha]]

===Deconstructing CSSS09===
One fun and easy application of network theory would be to look at ourselves at the end of the course, using an anonymous survey. What was the social interaction network? How frequently was there ''discussion'' between disciplines and did that lead to productive final projects? Is there a link between the social and final product networks? In prinicple, these data can potentially be linked to those collected by SFI at the beginning of the summer school. This could be an interesting way to see how the summer school (and more broadly interdisciplinary interactions) actually works. These data mihgt also be useful for planning the structure/composition of future classes. [[Alexander Mikheyev | Sasha]]

[[Wendy Ham]]: I agree Sasha, would love to help out with designing surveys, etc.

[[Margreth Keiler]]: Murad and I had the same idea yesterday, but we thought to make each week a surveys to see how the network change over time and to add also after CSSS surveys. Should we discuss our draft tomorrow at SFI?

===Biodiversity, evolution, modularity--ideas from Doug Erwin's lecture===
Here is a list of ideas mostly inspired by Doug Erwin’s lecture. I haven’t written anything very in depth due to lack of time but I think it would be fun to think about how to model any of these topics. Many of the topics are highly interrelated. I would recommend looking at Doug’s 2007 article on the readings page if interested.

How to model biodiversity.
Why would greater bio diversity rise out of extinction?
Does evolution reach sort of a stability point when all the niches are ‘full’ and is there is a lot of competition?
Does lack of competition (due to extinction or whatever) create the opportunity to diversify more?
Why does biodiversity cluster?
Two models in the paper:
Genetic or developmental hypothesis: mutation driven model of change. Corresponds to ‘supply driven’ innovation in economics
Ecospace hypot: variations in ecological opportunity control the success of major new morphologies. Corresponds to
‘demand driven’ innovation.
Genetic kernels
How are they developed?
Why did they all develop at the same time after extinction?
Why did animals develop kernels and not plants?
Modularity. http://en.wikipedia.org/wiki/Modularity_(biology)
Why do biological organisms develop modules?
How many components make up one module?
Is there a difference in the modularity of ‘higher’ versus ‘lower’ level organisms? (There is well studied modularity
in the central nervous systems of long swimming organisms such as leeches or electric eels).
Why do nonvertebrates develop locomotion modules (repeating, identical body part segments hooked together in some way to
allow motion) but vertebrates do not (only have 2 or 4 legs).
[[Corinne Teeter]]

===Economic Geography in the Lake Titicaca Basin===

See summary in the final projects section below.
Group working page: [http://www.santafe.edu/events/workshops/index.php/Economic_Geography_and_State_Emergence Economic Geography and State Emergence]

===“Let it rain” - Simulating flood events by Agent-Based Modeling and GIS===

How much rain is required to flood the Grand Canyon?

The idea is to build an Agent-Based Model to simulate the impact of increased rainfall on flow dynamics of a specific river network of the Grand Canyon region. The agent for the ABM is the water flow (=runoff) moving from cell to cell, dependent upon topography (=slope/gradients of the neighboring cells).
The flow dynamics are therefore directly related to the Digital Elevation Model (DEM) of the region and indirectly to environmental parameters such as soil/substrate (e.g. stratigraphical units) and land cover/use (e.g. bare soil, shrubs, forest, settlement). The latter parameters could be integrated into the ABM by assuming a possible range of values influencing flow dynamics in relation to e.g. infiltration (if the soil is saturated, runoff occurs) and vegetation cover (high vegetation cover leads to high interception, less runoff).
The different data layers can be integrated into the ABM by GIS (Geographical Information Systems).

[[Image:Theoretical_framework.jpg|480px|thumb|Theoretical_framework]]

What is the relationship between rainfall pattern and runoff/ flooding?

What effects do topographical/environmental parameters (e.g. slope gradients, substrate, vegetation cover) have on runoff/flooding?

Are there non-linearities related to the dynamical flow network?

What are possible feedback mechanisms? (e.g. positive feedback mechanism: increased rainfall → increased runoff → erosion and hence deepening of channels → steeper slope gradients → increased runoff)

Looking forward to exchanging ideas!

[[Steven Lade]] Hi Almut, As I've said, I think this is well suited to modelling with differential equations. Particularly if, as I assume to be the case, the GIS data comes already in a rectangular grid. Having said that, there are some complementary aspects for which ABM would be well-suited. For instance, following agents as they form streams, or if you were to have a localised thunderstorm. We could possibly do this in parallel and see if they match and/or use each method's particular advantages.

You may be interested in this paper, which I found through the SFI library database: [http://pubs.usgs.gov/sir/2007/5009/pdf/sir_2007-5009.pdf]. I think this one is more complicated though, because they need to consider a three-dimensional water table. More generally, what sort of modelling (if any) do people usually do in these sorts of topics?

[[Karen Simpson]] I am interested in this project! I have studied these concepts in many of my classes. Through past research, I've looked at storm/rain events, and how a large runoff from stormwater causes high contaminant concentrations in streams and rivers. This research was done for urban, forest, and agricultural landuse types.(I will try to find the results of this research soon). Another thing to think about is the time between rain events. A long timespan between rainfall events will cause the soil to become unsaturated, and the next rainfall may have little effect on the stream. I also will not be around much this weekend, so would it be possible to meet sometime tomorrow (Thursday 6/18)?

===Scalable (parallel) Spatial Agent-Based Models===

This project idea is an exploration of what happens to agent-based models “in the large?” For example,
* As the number of interacting agents in a model increases, what happens to the dynamics of the model?
* What happens as the size of the agents’ domain increases (e.g. simulating a neighborhood versus simulating a city or country)
* How do the properties of the model change? Are there scaling laws in effect ?

In order to investigate these issues, we need a scalable simulation, i.e. a parallel implementation of the model that allows us to introduce arbitrarily large numbers of agents. There are many approaches to doing this [lit review needed here!], but for this project, I would like to focus on spatial agent-based models: models where there are N agents who exist in a geographical domain and possess “vision,” where vision can be optical/eye-based, local communications (audible or electromagnetic line of site).
A couple such models which can serve as starting points include the flocking model (aka “boids”) and Epstein’s model of civil violence (or its derivative “Rebellion” model).

The idea is to decompose the spatial domain into independent subdomains, distribute those subdomains to nodes on a compute cluster, amalgamate the results, wash-rinse-repeat. One possible approach is to use an adaptive mesh refinement (AMR) such as those used by engineers for finite element analysis or by physicists in hydrodynamics simulations. One concrete example, using a quad-tree decomposition to keep agent density constant on each processor (and thereby keeping computational load balanced), is as follows:

[[Image:Particle.PNG|thumb|left|An example showing decomposition of a particle system using a quad-tree. Each resulting square has (roughly) the same number of particles in it. Can this approach be used for parallelizing spatial agent-based models ?]]
I have a cluster available for implementation, along with the MPI libraries for parallel programming. Other suggested areas of expertise that would greatly benefit the project include:
Someone interested in evaluating simulation results, who can help ensure that we don’t break the model by decomposing it.
Someone interested in analysis, for exploring the effects of scaling on the model.
Someone interested in high-performance computing, to help with programming (probably c/c++ with MPI)

From talking to folks in our class, some other benefits of the approach include
* improving running time for very-long-running simulations
* aerospace applications—decomposing the National Air Space into computationally tractable subdomains for modeling or real-world purposes.
* Applying the decomposition technique to other model domains. For example, can a similar technique be used to decompose a social network, especially if a single model has both geographic spatial domains and also network domains?

Other approaches suggested by classmates have included implementation on GPUs (graphics processors used for general purpose computation) and sticking to an SMP implementation (multicore workstations with shared memory--simpler implementation/perhaps not as scalable), versus a distributed-memory cluster. I welcome further ideas that might help kick-start this zany scheme.

[[Steven Lade]] What I'm about to say seems kind of obvious, and I'm not sure it helps you at all, but I can't help but say that if your 'averaged behaviour' converges for very large numbers of agents, you'd in effect be modelling some partial differential equation.

[[Matt McMahon]] Thanks, Steven. Not obvious to me though ... Can you elucidate?

[[Steven Lade]] It seems that as you reach a large number of agents, and your grid becomes small, you'd most likely reach some partial differential equation in the density of agents. Say a diffusion equation. Or a Navier-Stokes (fluid flow) equation. Not sure how easy it would be to derive, but this would be my intuition. It would be easiest for local interactions only (i.e. some radius which you could let approach zero) but non-local interactions might be possible too. It would of course all depend on the agent rules you use. If you're lucky one might even be able to derive some analytical results for special cases. If you want to chat more, find me in person. (Anyone: does this allnmake sense?)

=== Resilience to invaders in social systems ===

A piece of anecdata from my organizing days: the effect of an external organizer coming to help on a local campaign had one of two -- very different -- effects: either further coalescing the local campaign, or fragmenting it.

I'm curious how well social structures tolerate interlopers and what drives their resilience.

Possible metaphors/methods which could be useful:
* An agent-based models of the connectivity of the underlying social structure & reaction to interloper?
* Analogizing to food-web/ecology with the interloper as an invasive species?
* Analogizing the interloper to a crystal defect?

BUT I have no idea 1) how to parameterize this and 2) whether there are data (of any sort -- eg resilience to colonists/prophets/carpetbaggers) to which the model could be compared for sanity-checking.

I know '''nothing''' about sociology & related fields, so maybe this is a well-studied problem. Or an ill-posed problem. Or maybe it's not a problem at all. In any event, I'd be curious to hear other's thoughts.

==Final Projects==

Please place your final project ideas here: details should include clear and objective outlines.

===The Effect of Gossip on Social Networks===
In this project we look at the effects of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about an individual C who is not present, which has the potential to affect the strengths of all three relationships A-B, B-C, and A-C. This work is novel in two respects: first, there is no theoretical work on how network structure changes when information passing through a network has the potential to affect edges not in the direct path, and second while past studies have looked at how network structure affects gossip spread, there is no work done on how gossip spread affects network structure.

Page: [[Modeling gossip networks]]

Members:
* [[Allison Shaw]]
* [[Chang Yu]]
* [[Dave Brooks]]
* [[Milena Tsvetkova]]
* [[Roozbeh Daneshvar ]]

===1,2,3, language!===

In a nutshell:
In this project we will make use of information theoretic measures of similarity between data sets, such as mutual information
or more specifically some global allignment methods coming from evolutionary biology to build up a distance matrix between languages.
The data under study are simply the numbers 1,2,3...,10, for which we have access to a massive dataset that enumerates the spelling of the first ten numbers in more than 4,000 languages. We will finally derive the phylogenetic tree of languages, and compare it with the state of the art.

Members:
* [[Andrew Berdahl]]
* [[Lucas Lacasa]]

===Social mitosis in group conversations: a cooperative phenomenon approach===

In a nutshell:
When you participate in a conversation, you typically expect to (i) actively participate and (ii) be confortable in it. These arguments somewhat put some constraints in the number of persons attending the same conversation. In other words, when people are forced to stay in the same confined space, they tend to undertake a conversation, however if too many people are present, the conversation rapidly splits in two, three... some nucleation phenomenon takes place. In this project we approach this subject from a complex systems point of view and want to understand if the 'conversation mitosis' is a collective phenomenon, much in the vein of a symmetry-breaking phenomenon in statistical physics. We will develop an agent based model that captures the essential mechanisms of conversation dynamics and will characterize such behaviors. Analytical developments will also be addressed. Finally, we will compare our analytical/numerical results with empirical data gathered through e-mail surveys.

Members:
* [[Massimo Mastrangeli]]
* [[Martin Schmidt]]
* [[Lucas Lacasa]]

===Modeling mesoscopic sequential self-assembly===

One of the reasons for the huge success of microelectronics is the ability to produce very large amounts of devices at very small price. Anyway, a large part of the final price of electronic devices is due to assembly and packaging issues. The standard procedure to package microdevices is by robotic or even manual manipulation, which while satisfactory for large sizes becomes inefficient and even practically incontrollable below the millimeter scale. Moreover, when dealing with very large amounts of components the task becomes time-consuming and this expensive.

Self-assembly techniques have the potential to boost electronic assembly by their intrinsic massive parallelism and advantageous scaling properties. Particularly, self-assembly performed in liquid environment has gained momentum by showing interesting performance. Anyway, the analytic modeling of the dynamics of this process is still limited and not capable of capturing the details of the stochastic dynamics of self-assembly. In this project, I want to simulate the dynamics 2D and 3D sequential self-assembly with agent-based models. This framework, never so far applied to this task, may help sheding light on the role of important parameters of the process such as dimensions of the assembly space, redundance of components, viscosity of the fluid carrier.

[[Massimo Mastrangeli]]

===Percolation-like phenomenon in the Google search engine===

In a nutshell:
Type a (short) random string of letters in Google. This mimics the effect of mispelling words, 'typos'. Surprisingly, you will find a non-null amount of results: the probability of finding such a word, even if it's a random string without a semantic meaning, is non-null, since (i) someone could have already 'invented it' (acronym or so), (ii) someone could have mispelled a word (committed a typographic error) in his/her website/blog etc. But repeat the procedure with larger strings, and look how the number of results rapidly drops to zero... Is this a phase transition? Can we characterize such phenomenon? What are the relations between language-like properties and this behavior? What information can we extract? In this project we will endeavor such questions, programming automatic queries to google of randomly-generated strings and relating the system's behavior to some collective phenomena such as Percolation.

Members:
* [[Jacopo Tagliabue]]
* [[Andrew Berdahl]]
* [[Lucas Lacasa]]

===Competitive spatial network growth===
Many large-scale aggregate networks are actually composed of several essentially independent subnetworks, each of which takes into account the other agents' actions. While traditional optimization methods yield insight into the most efficient network structures to satisfy a fixed objective, the presence of several overlapping and evolving networks may change the optimal strategy or create niches for otherwise suboptimal strategies. In this project we develop an agent-based network growth model to simulate competitive airline network growth, studying the effects of the demand distribution, entry time, and number of agents on the success and network structure of the agents.

[[Interacting distribution networks]]

Members:
* [[Brendan Colloran]]
* [[Caroline Farrior]]
* [[Daniel Wuellner]]
* [[Michael Schultz]]

===Spectral clustering of gene expression===

1. Can we differentiate between genes involved in separate biological functions (ie pathways) using spectral clustering?

2. If so, can we use this method to detect the genes activated in cancer?

Members:
* [[Rosemary Braun]]
* [[Corinne Teeter]]
* [[Elliot Martin]]
* [[Eric Kasper]]

===Foraging on the move===
Many animals (e.g. caribou, wildebeest) forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and migration in a certain direction. While there is a vast literature on both flocking and optimal foraging, there has been no work done to understand how animals should trade off the decision to flock or forage (since it is difficult to do both simultaneously) during migration. We develop an individual-based model to address this, and implement a genetic algorithm to find the best decision-rule for switching between foraging and flocking, under a variety of conditions.

Page: [[Foraging on the move]]

Members:
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

===“Let it rain” - Simulating flood events by Agent-Based Modeling and GIS===

How much rain is required to flood the Grand Canyon?

The idea is to build an Agent-Based Model to simulate the impact of increased rainfall on flow dynamics of a specific river network of the Grand Canyon region. The agent for the ABM is the water flow (=runoff) moving from cell to cell, dependent upon topography (=slope/gradients of the neighboring cells).
The flow dynamics are therefore directly related to the Digital Elevation Model (DEM) of the region and indirectly to environmental parameters such as soil/substrate (e.g. stratigraphical units) and land cover/use (e.g. bare soil, shrubs, forest, settlement). The latter parameters could be integrated into the ABM by assuming a possible range of values influencing flow dynamics in relation to e.g. infiltration (if the soil is saturated, runoff occurs) and vegetation cover (high vegetation cover leads to high interception, less runoff).
The different data layers can be integrated into the ABM by GIS (Geographical Information Systems).

What is the relationship between rainfall pattern and runoff/ flooding?

What effects do topographical/environmental parameters (e.g. slope gradients, substrate, vegetation cover) have on runoff/flooding?

Are there non-linearities related to the dynamical flow network?

What are possible feedback mechanisms? (e.g. positive feedback mechanism: increased rainfall → increased runoff → erosion and hence deepening of channels → steeper slope gradients → increased runoff)

Members:
* [[Steven Lade]]
* [[Karen Simpson]]
* [[Almut Brunner]]

Update and own page following soon!

===Creative Process===
The project attempts to model the generation of ideas in the subconscious as a random combination of existing concepts (reflected as words) and their selection (reflected as variance). The selection filter determines the quality and quantity of ideas that rise to the conscious. Although the complete model may not be in place by the end of the week, the presentation will display a basic version of the final (and hopefully publishable) paper.

* [[Murad Mithani]]

===A Markov Model of Elite Factionalization===

Authoritarian regimes fracture when elites within the ruling coalition, which buttresses the dictator, defect. Consequently, regime change crucially depends on elite competition and coordination. Previous work has explored this topic through conventional formal models that make exacting informational and cognitive demands on agents. In contrast, this model will attempt to replicate these findings, while exploring additional dynamics and emergent behavior, by embedding boundedly rational agents in a Markovian system. Rather than assume hyper rational actors, capable of solving difficult dynamic programming problems, I assume that elites use relatively simple heuristics to navigate a stochastic environment.

* [[Trevor Johnston]]

===Radicalization Network (RadNet): Spread Mechanisms and Control===
Spread of radical ideologies is a key source of terrorist activities. Coordination and management of resources for preemptive control of such activities require network models that enable predictive identification of areas and agents before occurrence of terrorist action. Our RadNet project develops a layered network model where the dynamics of radicalization are used to define an evolving radical network layer that exploit an underlying social network layer. We develop quantitative models for change of state of nodes (representative of individuals in the social network) that capture progress of radicalization through intermediate stages of general, susceptible, indoctrinated, and radical. We analyze the model and its robustness to control actions by modeling in netlogo. The models developed and analyzed in RadNet, builds on insights from the contagion model, and introduces novel modular layered network approach to capture exploitation of social network for spread of ideology and control networks for monitoring and preemptive actions on the evolving radicalization network.

Members:
* [[Alhaji Cherif]]
* [[Prasanta Bose]]
* [[Hirotoshi Yoshioka]]
* [[Wei Ni]]
See [[Radicalization]]

===Guns, Germs and Steel: A Simulation===
[[Image:GGSscreencapture.jpg|400px|thumb|hunter-gatherer behavior of early humans]]
We intend to model the spread of early human populations. In his popular work--Guns Germs, and Steel--Jared Diamond argues that the differential concentration of wealth and people in geographic space is a result of geographic and historical contingencies. Using net logo we will model the dynamics of hunter-gatherer spread and the emergence of early agriculture. Global bioproductivity maps will be used to quantitatively represent resource habitats.

Members:
* [[Randy Haas]]
* [[Nathan Hodas]]
* [[Alexander Mikheyev]]

===Spiking Networks on the Cusp of Chaos===

The objective of this project is to investigate what small networks of idealized spiking neurons look and behave like at the edge of chaos. Specifically "edge of chaos" here means that special boundary area between the regions where we observe orderly periodic behavior on one side and chaotic non-periodic behavior on the other. (both have been observed previously in this dynamical system)

More details here: [[Spiking Networks on the Cusp of Chaos]]

===Game theoretic strategies in bike racing ===

Cooperation is often a paradoxical component of human groups. Seemingly altruistic behavior can often be explained by selfish strategies. The cultivation of cooperation in humans is crucial for solving the world's pressing problems such as climate change and international disputes. Apparent cooperation often shows up naturally in sports and is often attributed to social norms. Here we intend to set up the basic elements of a bike race where each individual is motivated to win, but can benefit through cooperation with other riders. Each rider will be given a set of skills and a cooperation strategy. The analysis will include competition among different strategies and an understanding of the emergent level of cooperation from only race environment (no social norms). We hope that the differences in qualitative properties between the modeled race and real races might teach us about the presence of social norms even in these competitive environments.

Members:
* [[Rhonda Hoenigman]]
* [[Joslyn Barnhart]]
* [[Caroline Farrior]]

===Study of Sustainability of the Companies, Cities and Societies: Towards the Theory of Social Organizations.===

=======BOEING AS A CASE STUDY===========
The first phase of this quantitative study will commence by analyzing Boeing as a complex adaptive system but with a view to start building a broad fundamental, quantitative, predictive theory of social organizations, with the help of the successful body of work that has already begun at SFI. A major component is to understand the role of innovation and adaptability in shaping the growth and sustainability of cities to corporations.
Why Boeing? Boeing itself is largely a structure facilitating and integrating the flow of information through the complex organization network consisting from its many divisions and its multi-tiered multi-national suppliers chains. Boeing’s outstanding longevity (has thrived for 100 years while others failed), outstanding complexity, high propensity for innovation and the availability of the data recommend the company as the perfect case study, from which in the future a bridge can be build towards developing some universal laws of sustainability.
The study will attempt to identify the reasons for the system’s longevity, to quantifiably measure its robustness to perturbations and to define the strategy for its optimization and sustainability as a complex network.
The study will attempt to look at this complex network’s topology and at the dynamics of the information flow across the network, studying the impact this dynamics has on technologies and speed of innovation within the company. The study will look at the efficiency of the company’s internal communication and especially try to determine the ways of the optimization of the information flow from the bottom up, with the goal to increase the speed of innovation and economic productivity.
The study will attempt to answer some specific questions, such as for example: how the number of internal patents has been growing with the growth of the company’s size? Can out of this data some dynamic laws be derived and what are the strategic implications and innovation expectations for a company of a certain size?
The study will especially focus on those areas of the system’s landscape where the knowledge spillover occur and will especially try to determine in quantifiable terms the rates of technological improvement due to the knowledge transform.
The analyses of the data on learning curves, design structure matrices and patents (preferably all of the above for several different models) could be very useful in further investigating questions surrounding how technology characteristics (such as modularity) affect rates of technological improvement.

Members:
* [[Michael Richey]]
* [[Lara Danilova-Burdess]]

===Leverage in Equities Markets===

When people get excited about their prospects on the stock market, they borrow money from the bank to invest. This leverage effectively couples the bank to the stock market. Thus, interest rates determine demand for stock, and demand for stock can determine interest rates. Does this interplay cause traders to naturally find a stable balance of leverage and aggressiveness? How do the behavioral traits of traders influence the stability of these interactions? Are there regulatory behaviors, such as limiting leverage or slowing margin calls, that would contribute to the overall health of the market?

Members:
*[[Nathan Hodas]]
*[[Jacopo Tagliabue]]
*[[Martin Schmidt]]
*[[Jeremy Barofsky]]
*[[John Paul Gonzales]]
(provisionally [[Corinne Teeter]])

===Deconstructing CSSS09 Social Network===
CSSS09 is a group of people interested in complex systems who are randomly chosen to attend the one month summer school. The international and interdisciplinary group spends four weeks together learning, discussing and working on projects related to complex systems. We are interested in understanding the following questions:

- What is the social interaction network?

- How does the network change over time?

- What other factors influence the evolution of the network?

- How frequently was there discussion between disciplines and did that lead to productive final projects?

- Is there a link between the social and final product networks?

Status

Stage 1: First survey (profile, social contacts, future collaboration) – after 2nd weeks

Stage 2: Second survey (language, social activities, social contacts, future collaboration) – end of 3rd week

Stage 3: Network visualisation in NetLogo (proto type) & discussion on approaches for further analysis of data

Stage 4: Survey at the end of 4th week and one month after summer school

Members
*[[Margreth Keiler]]
*[[Murad Mithani]]
*[[Roozbeh Daneshvar]]
*[[Wendy Ham]]

===Acupuncture points networks===

Background and description

_Acupuncture is a technique of inserting and manipulating fine filiform needles into specific points on the body to relieve pain or for therapeutic purposes. The word acupuncture comes from the Latin acus, "needle", and pungere, "to prick". In -_Standard Mandarin, 針砭 (zhēn biān) (a related word, 針灸 (zhēn jiǔ), refers to acupuncture together with moxibustion).
According to traditional Chinese medical theory, acupuncture points are situated on meridians along which qi, the vital energy, flows. There is no known anatomical or histological basis for the existence of acupuncture points or meridians. Modern acupuncture texts present them as ideas that are useful in clinical practice. According to the NIH consensus statement on acupuncture, these traditional Chinese medical concepts "are difficult to reconcile with contemporary biomedical information but continue to play an important role in the evaluation of patients and the formulation of treatment in acupuncture."

Objective

_We want to construct a acupuncture complex network of the whole body depending on different kinds of illness to do the research on interactions between acupuncture points, organics, and muscles. To investigate the global dynamical properties and stabilities of such networks. With the use of a simple dynamical model, we want to find the body stationary state, to find the global attractor points of the dynamics. These results suggest that the acupuncture points networks are robustly designed for their functions.

Members
*[[Guimei Zhu]]
*[[Brian Hollar]]
*[[Dave Brooks]]
*[[Massimo Mastrangeli]]

Aacknowledgments:

*[[Van Savage]]
*[[Karen Simpson]]
*[[Jacopo Tagliabue]]
*[[Corinne Teeter]]

===Analyzing Contagion in Networks===
Using the real-life data for the flu shots "contagion", and generating an agent based model, the project intends to analize contagion in a network in which all the nodes have various levels of threshold for changing. The project intends to investigate if the thresholds are various, can that lead to new behaviors in group level?

*[[Roozbeh Daneshvar]]
*[[Lara Danilova-Burdess]]
*[[Karen Simpson]]
*[[Jeremy Barofsky]]
*[[Varsha Kulkarni]]

===Water: A critical resource in a dynamical world===

Background and description

Water is often considered a critical resource. The starting point of our discussion was the conflict in the Middle East where we assumed that the supply of water is an underlying factor for the conflict in this region. Also, in the Southwestern United States, the distribution of water is a pertinent topic, which will become more important in the future. The Colorado River is a good example regarding the interaction between the resource and the human system.
Both of these geographical systems can be seen as complex systems and represents a coupling between water and humans, with lot of feedback loops (direct and indirect) in and between the systems and also exhibits non-linear, dynamical behaviour. Climate change has an influence on the amount, pattern and intensity of precipitation as well as the atmospheric and water temperature. Thus affecting hydrological processes such as runoff and storage of groundwater. According to the National Resources Defense Council, the Colorado Basin will continue to get warmer and more arid (http://www.nrdc.org/globalwarming/west/fwest.pdf). Due to human impact such as dams and irrigation techniques, the Colorado River no longer drains to the Gulf of California. The micro-climate is also heavily influenced which in turn increases the rate of evaporation from large water surfaces (including reservoirs, wetlands, swimming pools).
The human system consists of heterogeneous groups with different interests regarding water distribution. Social and economic dynamics can create also ‘economic’ and/or ‘political’ water shortage without any changes in the ‘natural’ systems. However, any shortage of water will put stress on the human systems and therefore re-organisation is necessary (i.e. equal distribution or ‘the winner takes it all’ approach).

Another factor to consider is the quality of water that is being distributed to the people, especially for consumption purposes. Many times, the quality of water is strongly affected by anthropogenic sources (human activities). It may be necessary to sanitize and treat the water before allowing humans to drink it through procedures such as filtration, disinfection and deionization. Depending on the degree of treatment, the price of producing clean water increases thereby also increasing the amount of stress on policy makers and consumers.

Objective

The objective of the project is to model the coupled human-water systems using heterogeneous agents employing prediction models to determine actions to represent the non-linear behaviour of economic and political systems and water processes.
We work on an agent-based-model focusing on interactions and feedback loops of hydrologic and human systems to gain more insight of the dynamic of this coupled system.
The further objective of the project is to observe the behaviour of the model, mainly by tracing utility measures, changing policies, or subjecting the system to shocks like economic crisis, significant droughts, sewer overflows, etc.

Members

*[[Hamid Benbrahim]]
*[[Jennifer Terpstra]]
*[[Karen Simpson]]
*[[Margreth Keiler]]
*Greta ?

===Economic Geography and State Emergence===
Economic geography models advanced by Paul Krugman explain how core-periphery distributions of material-production and people can arise endogenously in industrial societies. His new trade theory posits that consumer preference for product diversity drives regional manufacturers to specialize in brands of goods rather than a given type of good. From this model comes his model of economic geography in which economies of scale drive unequal distribution of populations and wealth.

Although Krugman's models seem to explain the heterogenous spatial distribution of production and people in wage economies, it is curious that such spatial heterogeneity is also evident in non-industrial, non-wage economies in prehistory. Accordingly, the goal of our study is to explore the degree to which economic geography can be applied to prehistoric economies that show similar patterns of nucleation. To this end, we are exploring the more salient rules of Krugman's models and applying them in an agent-based model that attempts to predict the geographic distribution population clusters. We will validate this model on the geographic landscape of the Titicaca Basin with the goal of reproducing empirical settlement patterns observed for the Tiwanaku Empire, which rose from a relatively homogeneous and dispersed settlement distribution at 2000 B.C. to a hierarchically nested settlement system by A.D. 1000.

For more information, see our working page at [[Economic Geography and State Emergence]].

Members
*[[Jeremy Barofsky]]
*[[Randy Haas]]
*[[Jacopo Tagliabue]]

===Modeling behaviors between students and teachers ===
Background

In the project, we study the impact of teacher's quality (in term of qualification (proxy by salary), and sets of activities s/he organizes) on minority/marginalized students. Under Chinese elite educational system, there is a large group of marginalized high school students who have been ignored due to the emphasis on exam-oriented results. As a result, teachers have primarily paid more attention to good students since number of good students produced by a teacher is used as a promotion marker which is in turn used as a salary increase index. This practice has unattended consequences on various socio-economic factors, drop-out rates and crime rates.

Objectives

The study was motivated by previous empirical investigations on two secondary vocational schools in China. From this study, it was observed that teachers’ attitudes and behaviors (proxy for various activities they organized) are significant factors that motivate these students to tuned down their personalities and behaviors (note: these students are troubled students). It was thus recommended that improvement of students’ personality and behaviors should served as the prime index in teacher’s salary. Only in this matter can teachers be motivated to devote ample of time in exploring various educational methods on these students. According to the previous research and data analysis from the questionnaires, we will model the bidirectional interactions between students and teachers in NetLogo to investigate some of the assumptions made in the above statements.

Members

* [[Chang Yu]]
* [[Alhaji Cherif]]

Update and Details about this project, please click here ! [http://www.santafe.edu/events/workshops/index.php/Modeling_behaviors_student&teacher Modeling behaviors between students and teachers]

===Network Models of Rebellion===

Recent events in Iran have demonstrated the inability of autocratic regimes to readily suppress civil demonstrations, cascading into national protests. In this project, we explore this phenomenon through a series of networks (e.g. small world, lattice). Revolutionary fervor spreads through the network like a contagion, but depends on the revolutionary thresholds and grievance levels of each node. Additionally, we provide for nodal removal and rewiring to better capture the underlying dynamics that drive revolutions, and thus endogenize regime legitimacy. Finally, our model deviates from existing work insofar as we arrange actors along a continuum, allowing for counter-revolutionaries and police to eventually be coopted into the revolution. This is a crucial condition for successful revolutions, which is too often overlooked.

Members:
*[[Elliot Martin]]
*[[Andrew Berdahl]]
*[[Eric Kasper]]
*[[Mahyar Malekpour]]
*[[Trevor Johnston]]

===Modeling maternal effects on the division of labor===
Division of labor in animal societies has been typically studied by means of the evolution of cooperation, where some members of the group relinquish their reproduction in order to help group mates. The evolution of this behavior is justified when the Hamilton's rule is satisfied (c/b > r, where c is the cost of cooperation, b is the benefit provided to others, and r is the relatedness between the actors). In contrast, an alternative to this view is the evolution of labor by means of parental manipulation. In this view, a mother can manipulate its offspring so that it does not reproduce and instead invest its efforts on raising its sisters. This can happen via zigotic gene expression, or by maternal behavioral manipulation (e.g., the mother eats the eggs laid by its offspring, so offspring is left with raising the mother's eggs).

Objectives

We attempt to build an agent-based model of maternal manipulation. The model includes niche construction, which is allowed by the division of labor. This feature is expected to provide stability to division of labor, especially when niche monopolization occurs. The basic objective is to gain intuition about the different processes involved (maternal effects, niche construction, and kin selection). We aim to explore the possible advantages of maternal manipulation over more standard explanations of division of labor.

Members

* [[Mareen Hofmann]]
* [[Varsha Kulkarni]]
* [[Angela Onslow]]
* [[Mauricio Gonzalez-Forero]]

===Marriage, Monkeys, and Problem Solving===

Our project consists of three sub-projects involving search: 1) marriage markets (men and women searching for each other); 2) monkeys foraging (monkeys searching for food sources); and 3) problem solving (problems and solutions searching for each other).

[[Image:Bjh_gender_imbalance.png|200px|right]]'''1) Gender-Imbalanced Marriage Markets:''' The basic concept is to try to model the effects of "marriage markets" with more men in them than women or vice-versa. Examples of social groups which experience a gender imbalances in marriage markets include: most religious groups, college campuses, some large cities (such as New York and Washington, DC), the African-American community, and some nations (notably China). I am interested in how these gender imbalances affect social norms, marriage and divorce rates, and dating/matching behavior in each of these various groups. [[Brian Hollar]]

'''2) Monkeys Foraging:'''
There is evidence from the field that groups of animals share their search space with other groups, creating a contact network of overlapping home ranges. Despite a vast literature describing the statistical patterns of home range usage, very little research has addressed the behavioral mechanisms through which home range patterns emerge. Here, we are developing a spatially explicit foraging model using primates as a model system to understand patterns of space use driven by individual foraging decisions. [[Liliana Salvador]]

'''3) Problem Solving:''' We have created a Netlogo model representing a population of problems and solutions that are searching for each other. In our model, each problem may have several components, each of which requires a solution. (In other words, a problem may require the combination of several solutions in order to get solved). Problems and solutions are represented using bitstrings, which can vary in length. There are several key features of problem solving that we include in our model thus far:
* Solutions do not always have to match perfectly with the problem that they are solving. To reflect this, the match level between problems and solutions may be adjusted.
* Once a problem is solved, the solutions may replicate. In the real world, when a solution is known to work, people usually adopt it and spread its use.
* The replication of a solution may not be glitch-free. As solutions get replicated, their fidelity may decay over time.
* Similarly, problems and solutions may evolve or mutate spontaneously as time goes by as there is no guarantee of persistent fidelity.
* When problems are connected via links (which may represent cognitive association as well as social network), they may engage in the exchange of solutions. The same goes for solutions that are linked to one another. We are interested in seeing how the presence of links may alter the rate of problem solving in a population of problems and solutions.
* On the other hand, problems and solutions may also travel via simple diffusion (as opposed to networks), which represents broadcasting in the real world.
* When a group of solutions has solved a problem (or problems) repeatedly, it may become interdependent over time such it can now only 'travel' together as a group, which may subsequently reduce its effectiveness in finding suitable problems.

We have several other ideas which we plan to develop in the future. They can be viewed them on our previous project page: [[Problem_solving]]

Members:
* [[Brian Hollar]]
* [[Liliana Salvador]]
* [[Wendy Ham]]
* [[Guimei Zhu]]
* [[David Brooks]]
* [[Nathan Hodas]]

===Synchronizing A Network===
There is a vast literature on synchronization phenomenon as exhibited by humans, animals, and even inanimate objects. Synchronization of fireflies, in particular, has been studied for a number of years. There even exists an agent-based model for the fireflies. However, the existing models do not always result in synchrony. In this project, we explore the synchronization phenomenon using a variety of networks (e.g. fully connected, lattice, random) and implementing various strategies for synchronizing a group of entities communicating through the network.

Members:
* [[Mahyar Malekpour]]

===Testing Panarchy===
The panarchy theory describes transformations in complex adaptive systems by distinguishing 4 typical dynamic phases: exploitation, conservation, release, reorganization. It also incorporates feedbacks between different interacting hierarchical levels, i.e. lower levels with faster, and higher levels with slower dynamics. The theory often inspired adaptive management plans, but has not been quantitatively analysed so far. We will build simple models to test some hypotheses of the theory, e.g. the connection between increased specialization and rigidity, and the coupling between fast and slow systems. To increase the practical value of the theory, we will consider metrics for distinguishing the dynamic phases.

Members:
* [[Andrew Noble]]
* [[Barbara Bauer]]
* [[Damian Winters]]

===Determining spatial contact networks for pathogen transmission===
According to Grenfell et. al., "Understanding the spatial contact network for parasite transmission is a holy grail because it will allow prediction about the spread of emerging pathogens and ultimately guide public health and veterinary intervention programs." Our goal is formalize a method for determining spatial contact networks from time series data of disease transmission. We have weekly measles outbreak reports from 60 urban cities in England and Wales dating from 1944 to 1967. It appears that several cities may act as pathogen sources from which the disease spreads to surrounding cities. We plan to reconstruct this spatial contact network for the measles data and, in doing so, introduce a method for inferring such networks for other disease outbreaks.

Members:
* [[Sasha Mikheyev]]
* [[Kate Behrman]]
* [[Erin Taylor]]

Foraging on the move

2009-06-29T14:35:34Z

Kbehrman: /* Parameter Settings from Literature */

Foraging on the move

2009-06-26T22:37:26Z

Kbehrman: /* Parameter Settings from Literature */

== Project Description ==

=== Introduction ===
Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction.

Individual members of a species group together for a variety of reasons, and for many of these the largest benefit is gained from being at the center of the group (e.g. Hamilton). However, when foraging, individuals gain the most benefit from being at the edge of the group, since those in the center likely experience the most competition [ref]. One possible solution to this problem is for individuals to change location within the group over time.

In instances where organisms are continually moving in a direction (migrating) instead of staying within a homerange, this can appear as though the group is 'flowing' through an area (see caribou video).

Our goal is to develop a combined foraging/flocking agent-based-model with simple rules to model this behavior, where individuals will simultaneously balance three demands:
# foraging (finding enough resources)
# flocking (maintaining group cohesion)
# migrating (continually moving in a certain direction)

=== Background ===
'''[add more here]'''

=== Parameter Settings from Literature ===
'''[add more here]'''
# Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
# de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
# Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
# Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
# Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
# Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
# Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
# Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).

=== Model Details ===
'''INPUTS/ASSUMPTIONS:'''
* simple NetLogo flocking model (flocking.nlogo) where individuals move based on two rules: 1) "separate" (if other agents are too close, move away from them), and 2) "align" and "cohere" (otherwise move in the same direction as nearby agents, and move towards them)
* add in foraging element: agents have energy reserves that deplete slowly as they move, and increase if they stop to forage
* agents have behavioral rules to decide when to forage and when to flock (only one can be done at at time)
* agents die if they fail to forage (starve) or fail to flock (are subject to predation)
* agents are constantly moving, i.e. not everyone can just stop and forage (to match concept that migrating organisms are moving under time constraints)

'''OUTPUTS:'''
* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* adaptive dynamics -- what is the ideal balance between foraging and flocking activities?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?

'''EXTENSIONS:'''
* evolve flocking vs foraging decision rule
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== References ===
* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* Hamilton, W.D. (1971). [http://www.ecfs.org/projects/prepole/ANIMAL%20Behavior%2007/HW%20Articles%5Cgeometry.pdf "Geometry for the Selfish Herd."] ''JTB.'' 31 (2): 295-311.
:: individuals can benefit from flocking behavior -- center of group is often safest from predation

* Reynolds, Craig W. (1987). [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
:: original Boids model

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Tasks ===

'''LITERATURE'''
* migration models lit review (Allison)
* basic description of wildebeest & caribou migration cycles (Allison)
* appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana)
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC)
* how to prevent flock from wrapping around across the boundary?
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* ''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* adaptive dynamics framework to evolve parameters (Andrew & Steve)
* design behavior rules to determine when to forage and when to flock (Steve & Andrew)
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-06-26T22:36:49Z

Kbehrman: /* Parameter Settings from Literature */

== Project Description ==

=== Introduction ===
Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction.

Individual members of a species group together for a variety of reasons, and for many of these the largest benefit is gained from being at the center of the group (e.g. Hamilton). However, when foraging, individuals gain the most benefit from being at the edge of the group, since those in the center likely experience the most competition [ref]. One possible solution to this problem is for individuals to change location within the group over time.

In instances where organisms are continually moving in a direction (migrating) instead of staying within a homerange, this can appear as though the group is 'flowing' through an area (see caribou video).

Our goal is to develop a combined foraging/flocking agent-based-model with simple rules to model this behavior, where individuals will simultaneously balance three demands:
# foraging (finding enough resources)
# flocking (maintaining group cohesion)
# migrating (continually moving in a certain direction)

=== Background ===
'''[add more here]'''

=== Parameter Settings from Literature ===
'''[add more here]'''
## Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
## de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
## Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
## Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
## Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
## Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
## Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
## Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).

=== Model Details ===
'''INPUTS/ASSUMPTIONS:'''
* simple NetLogo flocking model (flocking.nlogo) where individuals move based on two rules: 1) "separate" (if other agents are too close, move away from them), and 2) "align" and "cohere" (otherwise move in the same direction as nearby agents, and move towards them)
* add in foraging element: agents have energy reserves that deplete slowly as they move, and increase if they stop to forage
* agents have behavioral rules to decide when to forage and when to flock (only one can be done at at time)
* agents die if they fail to forage (starve) or fail to flock (are subject to predation)
* agents are constantly moving, i.e. not everyone can just stop and forage (to match concept that migrating organisms are moving under time constraints)

'''OUTPUTS:'''
* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* adaptive dynamics -- what is the ideal balance between foraging and flocking activities?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?

'''EXTENSIONS:'''
* evolve flocking vs foraging decision rule
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== References ===
* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* Hamilton, W.D. (1971). [http://www.ecfs.org/projects/prepole/ANIMAL%20Behavior%2007/HW%20Articles%5Cgeometry.pdf "Geometry for the Selfish Herd."] ''JTB.'' 31 (2): 295-311.
:: individuals can benefit from flocking behavior -- center of group is often safest from predation

* Reynolds, Craig W. (1987). [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
:: original Boids model

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Tasks ===

'''LITERATURE'''
* migration models lit review (Allison)
* basic description of wildebeest & caribou migration cycles (Allison)
* appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana)
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC)
* how to prevent flock from wrapping around across the boundary?
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* ''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* adaptive dynamics framework to evolve parameters (Andrew & Steve)
* design behavior rules to determine when to forage and when to flock (Steve & Andrew)
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Foraging on the move

2009-06-26T22:34:56Z

Kbehrman: /* Parameter Settings from Literature */

== Project Description ==

=== Introduction ===
Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction.

Individual members of a species group together for a variety of reasons, and for many of these the largest benefit is gained from being at the center of the group (e.g. Hamilton). However, when foraging, individuals gain the most benefit from being at the edge of the group, since those in the center likely experience the most competition [ref]. One possible solution to this problem is for individuals to change location within the group over time.

In instances where organisms are continually moving in a direction (migrating) instead of staying within a homerange, this can appear as though the group is 'flowing' through an area (see caribou video).

Our goal is to develop a combined foraging/flocking agent-based-model with simple rules to model this behavior, where individuals will simultaneously balance three demands:
# foraging (finding enough resources)
# flocking (maintaining group cohesion)
# migrating (continually moving in a certain direction)

=== Background ===
'''[add more here]'''

=== Parameter Settings from Literature ===
'''[add more here]'''
1.Creel, S. & Winnie, J.A. Responses of elk herd size to fine-scale spatial and temporal variation in the risk of predation by wolves. Animal Behaviour 69, 1181-1189(2005).
2.de Knegt, H.J. et al. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology (2007).
3.Focardi, S. & Pecchioli, E. Social cohesion and foraging decrease with group size in fallow deer (Dama dama). Behavioral Ecology and Sociobiology 59, 84-91(2005).
4.Focardi, S., Marcellini, P. & Montanaro, P. Do ungulates exhibit a food density threshold? A field study of optimal foraging and movement patterns. Journal of Animal Ecology 606-620(1996).
5.Frair, J.L. et al. Scales of movement by elk (Cervus elaphus) in response to heterogeneity in forage resources and predation risk. Landscape Ecology 20, 273-287(2005).
6.Fryxell, J.M. et al. Landscape scale, heterogeneity, and the viability of Serengeti grazers. Ecology Letters 8, 328-335(2005).
7.Johnson, C.J. et al. Movement parameters of ungulates and scale-specific responses to the environment. Journal of Animal Ecology 225-235(2002).
8.Mueller, T. et al. In search of forage: predicting dynamic habitats of Mongolian gazelles using satellite-based estimates of vegetation productivity. Journal of Applied Ecology 45, 649-658(2008).

=== Model Details ===
'''INPUTS/ASSUMPTIONS:'''
* simple NetLogo flocking model (flocking.nlogo) where individuals move based on two rules: 1) "separate" (if other agents are too close, move away from them), and 2) "align" and "cohere" (otherwise move in the same direction as nearby agents, and move towards them)
* add in foraging element: agents have energy reserves that deplete slowly as they move, and increase if they stop to forage
* agents have behavioral rules to decide when to forage and when to flock (only one can be done at at time)
* agents die if they fail to forage (starve) or fail to flock (are subject to predation)
* agents are constantly moving, i.e. not everyone can just stop and forage (to match concept that migrating organisms are moving under time constraints)

'''OUTPUTS:'''
* group metrics -- how does adding foraging behavior compare to just flocking?
* how are stopping time / group size / migration rate interrelated?
* adaptive dynamics -- what is the ideal balance between foraging and flocking activities?
* do we get different movement patterns under different parameter settings -- e.g. stringy 'wildebeest' movement vs 'flowing' caribou movement?

'''EXTENSIONS:'''
* evolve flocking vs foraging decision rule
* build in interaction with the environment (local depletion of resources)
* look at how habitat structure affects group movement

=== References ===
* Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). [http://www.nature.com/nature/journal/v433/n7025/abs/nature03236.html Effective leadership and decision-making in animal groups on the move.] Nature, 433, 513-516.
:: 3-radius flocking model where individual movement is a weighted combination of the direction they inherently want to go and the influence of individuals around them

* Holdo, Ricardo M., Robert D. Holt and John M. Fryxell. (2009). [http://www.journals.uchicago.edu/doi/abs/10.1086/597229 "Opposing Rainfall and Plant Nutritional Gradients Best Explain the Wildebeest Migration in the Serengeti."] ''American Naturalist.'' 173: 431-445.
:: wildebeest migration clearly driven by rainfall gradient
:: model suggests that wildebeest are maximizing green grass intake (rate of intake of high-quality food)

* Hamilton, W.D. (1971). [http://www.ecfs.org/projects/prepole/ANIMAL%20Behavior%2007/HW%20Articles%5Cgeometry.pdf "Geometry for the Selfish Herd."] ''JTB.'' 31 (2): 295-311.
:: individuals can benefit from flocking behavior -- center of group is often safest from predation

* Reynolds, Craig W. (1987). [http://portal.acm.org/citation.cfm?id=37401.37406&type=series "Flocks, herds and schools: A distributed behavioral model."] ''Proceedings of the 14th annual conference on Computer graphics and interactive techniques.'' 21: 25-34.
:: original Boids model

* [http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html Planet Earth: Plains: Following the Caribou]
:: video of caribou migration

== Participation ==

=== Tasks ===

'''LITERATURE'''
* migration models lit review (Allison)
* basic description of wildebeest & caribou migration cycles (Allison)
* appropriate foraging parameters / energy function for ungulates: "energy-forage" and "energy-move" in NetLogo model, also probability of forage as a function of energy (Liliana)
* appropriate flocking parameters / flocking lit review: "minimum-separation", "max-align-turn", "max-cohere-turn", "max-separate-turn", and "vision" in NetLogo model (Kate)
* collective behavior lit review
* foraging lit review (Liliana)
* look for flocking metrics -- e.g. group 'coherence' or group structure/dynamics

'''MODEL TWEAKING (SIMPLE)'''
* how to initially distribute agents?
: currently are all started in roughly same area and orientation
: alternative would be to give them all the same preferred direction (a la Couzin et al 2005)
* how to step model forward (appropriate time step)? ("stepsize" and "steprepeats" in NetLogo model)
** Have just stepsize = 1 and steprepeats (which was only smoothing) now removed [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* problem: why do agents die from bad-foraging but do not die from bad-flocking? (or have we just not found those parameter settings?)
** ''note: starvation rate depends on relative values of "energy-forage" and "energy-move"''
: maybe have agents die from bad-flocking when too few individuals in their sight radius (instead of none)
: Your sigmoidal forage-probability curve has threshold at 0.5 energy units. If energy-move is large compared to this value (and you currently have it at 0.3 by default), it will take only a couple of steps to go from 'stomach full' to 'dead'. Why there are no flocking deaths I don't know. [[User:SteveLade|SteveLade]] 04:17, 24 June 2009 (UTC)
* how to prevent flock from wrapping around across the boundary?
* should we stick with 2-zone model or change to 3-zone one (a la Couzin et al 2005)?
* ''NOTE: energy levels become synchronized over time and move like a wave through the population''
** ''only happens for high "vision" values''
** ''depends on "energy-move" values''
** Doesn't seem to happen any more [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)

''' MODEL DEVELOPMENT (MORE INVOLVED)'''
* develop/implement metrics to describe group
** flock density
** average flock speed (Done [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** average fraction of time individual spends foraging (This is just from the ratio of energies received/spent from flocking/foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC))
** group size stability threshold (below which group fails to flock/survive)
** group 'coherence' (check literature)
** group structure/dynamics (check lit)
* adaptive dynamics framework to evolve parameters (Andrew & Steve)
* design behavior rules to determine when to forage and when to flock (Steve & Andrew)
: should decision to forage be independent at each time step or are foraging individuals more likely to keep foraging than to start flocking?
: Have behaviour rules but currently no hysteresis for foraging [[User:SteveLade|SteveLade]] 04:59, 25 June 2009 (UTC)
* couple foraging to changes in resource distribution -- e.g. a patch is depleted by a foraging agent and must grow back after some time
* design different landscape resource distributions to have agents moving across

=== Members ===
* [[Allison Shaw]]
* [[Andrew Berdahl]]
* [[Kathrine Behrman|Kate Behrman]]
* [[Liliana Salvador]]
* [[Steven Lade]]

== Original Discussion ==
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

* [[Roozbeh Daneshvar]]: Daniel, I am absolutely in for such a preview. Can you upload it in After Hours so that we all watch it together?

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

[[Murad Mithani]]: It sounds similar to what happens when the cognitive processes are focused on a particular problem to come up with ideas. The initiation of problem solving is a conscious mechanism that flourishes when that initial push is taken away. If you guys are planning to model this in some way, count me in.

[[Steven Lade]]: I like the sound of this too. Dare I suggest a meeting, perhaps one lunchtime, to flesh out plans a little more? Allison, since it was your idea, would you like to call it?

[[Allison Shaw]]: Sure, that would be great! How about lunch tomorrow (Tuesday the 16th)? Let's try to synchronize sitting together. I talked to JP about doing a Planet Earth showing and he said we could use the projector for the lectures, but we'd need to get a decent set of speakers (as far as I know there isn't a working TV/DVD combination in any of the lounges and we'd have to pay to use the more advanced media system in the lecture room).

Kathrine Behrman

2009-06-17T14:15:26Z

Kbehrman:

Email: behrmank@gmail.com

I am a third year Ph.D student at the University of Texas in ecology and evolution. I completed my under graduate degrees in biology and mathematics at University of California Santa Barbara.

Answers to Dan's Questions:

1. What are your main interests? Feel free to include a "pie in the sky" big idea!
Most of my thesis work focuses on understanding species ranges both from an evolutionary and ecological point of view. I am particularly interested in (1) how species' ranges form and (2) how species' ranges may change in time and space as organisms adapt (or fail to adapt) to new environmental conditions. I am also interested in how the scale at which environmental variables act create present spatial patterns.

2. What sorts of expertise can you bring to the group?
My background as a graduate student is in ecology and evolution, I also have an undergraduate degree in Mathematics. I have currently been using lots of simulations, numerical, and statical techniques for my thesis work. I can bring a unique perspective about to tackle problems from both and evolutionary and ecological point of view.

3. What do you hope to get out of the CSSS?
I would like to get a sense for techniques I am not familiar with to study complex systems, brush up on the mathematics used to study nonlinear dynamics, learn about the techniques used by economists and social scientists that have the potential to be applied to ecological and evolutionary questions, and meets lots of new scientists.

4. Do you have any possible projects in mind for the CSSS?
I don't have any projects currently in mind.

In my free time I enjoy kayaking, running, hiking, yoga, and making jewelery.

I am looking forward to meeting you all in June! -Kate

CSSS 2009 Santa Fe-Projects & Working Groups

2009-06-14T18:54:02Z

Kbehrman: /* Foraging on the move */

{{CSSS 2009 Santa Fe}}
==Brainstorming==
===Disease ecology of media hype===
How much and event gets covered in the news often appears to depends on how much it is already covered in the news. Often this distorts reality. For example, the number of searches for "swine flu" (a proxy for media hype), do not reflect the patterns of disease spread over the same period.
[[Image:Flu_trends.png|thumb|Google searches for "swine flu"|left]]
[[Image:Flu_cases.png |thumb|Actual number of swine flu cases over the same period|left]]
While the number of flu cases increased, the searches died off, as interest in the topic waned. It would be interesting to follow the origin, spread and extinction of media hype, maybe applying models commonly used to study the spread of disease. [[Alexander Mikheyev]] 

You could look at the dynamics from agent-based (ABM) perspective. There is a recent paper by Epstein and colleague that focuses on the impact of fear on disease from agent-based perspective, but does not capture this dynamics. However, my collaborator and I are currently writing a paper on the same problem you just outline from mathematical epidemiological perspective. Our results show some interesting dynamics. I think its extension in ABM might provide richer dynamics.
Another relevant paper: S. Funk, E. Gilad, C. Watkins and V.A.A Jansen (2009) the spread of awareness and its impact on epidemic outbreaks. PNAS early edition
[[Alhaji Cherif]]

===Housing prices.===
[[Image:Phoenix.jpg|thumb|Change in Phoenix home prices. Source: NYT|left]]
The New York Times has a set of [http://www.nytimes.com/interactive/2007/08/25/business/20070826_HOUSING_GRAPHIC.html?scp=3&sq=home%20prices%20graphic&st=cse dramatic graphs] showing the rise and fall of home prices in select cities. Again these graphs reminded me a bit of those produced by [http://www.math.duke.edu/education/ccp/materials/postcalc/sir/sir2.html susceptible-infected-recovered] models of disease spread. Maybe there is something to it? Or maybe this phenomenon is already well understood by economists? [[Alexander Mikheyev]] 

===Movie Turnouts===
Which would be the more popular movie -- a combination of Steven Spielberg, Eddie Murphy and Gwyneth Paltrow, or Woody Allen, Dwayne 'the rock' Johnson, and Tom Cruise? Using the adaptation and turnout models presented by Nathan Collins, could we construct a prediction for gross movie receipts or even movie ratings? [[Nathan Hodas]]

===Climate network model.===
''Requires someone with climatology knowledge.'' Lenton et al. recently published a [http://www.pnas.org/content/105/6/1786 paper] listing 'policy-relevant' 'tipping elements' in the Earth's climate system and the temperature tipping points required to initiate them. (Basically, the tipping elements are components of the climate system where a bifurcation leading to a different stable state can be induced. The tipping point is the temperature at the bifurcation.) Surely, many of these tipping elements would have feedback effects on other tipping elements or the climate system as a whole. I would like to make a network model of these tipping elements and look at the tipping (or other) dynamics of the whole system. But Lenton et al. don't discuss these feedbacks much in their model, so we need some expert knowledge. [[Steven Lade]]

===Synchronised magma oscillations===
''Requires someone with geological knowledge'' In a recent [http://www.springerlink.com/content/n76781712g2q3578/?p=ec0c1ffe588f473a8dbe9637a3822ebf&pi=2 paper], which was also [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WY-4WBRC9H-G&_user=554534&_coverDate=05%2F20%2F2009&_alid=931681330&_rdoc=1&_fmt=high&_orig=search&_cdi=33799&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000028338&_version=1&_urlVersion=0&_userid=554534&md5=5dc46c822607723e06f9b72fb16d1463 reported] by New Scientist, Mjelde and Faleide report on seismological measurements that allowed them to infer past rates of magma flow in the plume generally though to rise beneath Iceland. When the plume is strong it thickens the Earth's crust at this point. They found the crust thickened approximately every 15 million years, and inferred that the magma plume must also have pulsed with this period. These pulsations have also been observed in the crust under Hawaii, with almost exactly the same period! Mjelde and Faleide hypothesise that there must be some giant heating oscillation in the Earth's core which drives these two oscillations at very different parts of the Earth. But other geologists are skeptical because of the huge energy required and lack of other evidence of such oscillations. But all this reminds me of the synchronisation phenomenon, where coupled oscillators, even if only weakly coupled, tend to synchronise. So the oscillations under Hawaii and Iceland may be generated independently, but have some weak coupling that has led them to synchronise. We can make coupled oscillator models, that's easy, but someone to provide more context on possible forms of coupling and their parameterisation is more what we need. They only observe about three periods of this oscillation and the data is quite imprecise so we can't do much direct data analysis, unfortunately. [[Steven Lade]]

===Implementing Synchronization using NetLogo===
Since I just learned about NetLogo, I look forward to the tutorial sessions and would like to implement a synchronization scheme of a group of entities. If I find out how the fireflies synchronize themselves, then that would be an option. Of course, I'll be surprised if this has not been done before in NetLogo. I'll welcome any help and suggestions.[[Mahyar Malekpour]]

===The Global Spread of Cricket===
No I'm not actually intending to study this particular topic. But there is one interesting article published in 2005 (Kaufman and Patterson, American Sociological Review) that examined why cricket continues to be popular in many British-influenced societies while it is not in the U.S. and Canada. This is interesting given the fact that cricket was very popular in the two countries and that the first official international cricket match took place between the two countries in the mid-19th century. So, not only how cultures, ideas, technologies, etc. diffuse across nations, populations, and so on, but also mechanisms that influence the retention after the initial adoption merit serious attention I think. One possible topic include is modern contraceptive use in developing countries. I guess modeling such mechanisms would require taking into account the models presented by Nathan Collins and Peter Dodds, in addition to signed networks (Doreian). One difficulty of modeling this kind of mechanism is that both structural and individual factors should be considered [[Hirotoshi Yoshioka]].

===Contagion in Networks===
[[Peter Dodds]] discussed contagion in a simplified network in which all the nodes have certain amount of threshold for changing. I thought that if the thresholds are various, that can lead to new behaviors in group level. For instance, people in different cities might have different resistances against inputs. Hence, we might see that an epidemic issue spreads in one city but not in the other. Consider the cities as nodes in a higher level network. This means that we might see the same patterns in this higher level. Different nodes (cities) react differently to external inputs. This also seems to be a more realistic model of the real world. Any comments, suggestions or discussions, even in the order of minutes are appreciated!
[[Roozbeh Daneshvar]]

Perhaps this concept could be related to ecological food webs and the success of invasive species. The "epidemic" would be an introduced species, and the "spreading of the disease" would be how successful the alien species is within that food web. There are plenty of journal articles attempting to study the success of biological invasion, and I think in addition to looking at the food web networks, generating an agent based model would be ideal! It could be related to your idea, Roozbeh, in that the cities represent "habitats", and the "epidemics" represent the introduction of an alien species.

Introducing Agent-Based Modeling:
Several concepts (external and internal inputs) have been discussed that are said to contribute to whether or not a species succeeds in it's novel environment. These include: how many individuals are in the founding population, the "strength" of any competing organisms (this would be 0 is there are no competitors), the amount resources available, the ability of organism to adapt to the new environment, physiological advantages of new species over native species (i.e. defense mechanisms), and many more. I think we could find properties of ecological foodwebs, and then introduce a species (or epidemic) into the network and see what happens based on these inputs.

Let me know your thoughts. [[Karen Simpson]]

===Linking topology to dynamic response in small networks===
Imagine a small (3-7 nodes) network where every node represents a protein species, and every (directed) edge the activation relation between the proteins (i.e. A ---> B means that the protein A can react with B and activate it). Furthermore,
assume that there are two numbers associated with every node: the total number of protein molecules of the given type and the fraction of the active forms. Finally, let two nodes, R and E, be special and call them the Receptor and the Effector. What you have is a crude model of intracellular signalling.

This [http://www.cosbi.eu/templates/cosbi/php/get_paper.php?id=147 paper] considers such models and exhaustively classifies all the possible topologies (i.e. wirings) with respect to the activation pattern of the Effector in response to a standardized signal sent by the Receptor. The goal of our project would be to do the same experiment using different tools, and potentially obtain different results. The main difference would be to use stochastic (rather than deterministic) dynamics to determine the response. As the signalling systems operate with relatively low numbers of molecules, stochastic effects may be important. If we do this and have time left, we can try pushing it further and consider the issues of robustness and evolvability of these networks.

To put a nasty spin on the project, I propose that we use an obscure computational technique called [http://en.wikipedia.org/wiki/Model_checking model checking] to get the response profile of a network; partly just because we can, but partly also because it nicely deals away with the need of explicitely simulating and averaging of stochastic models.

Now, a couple of final remarks:
* Don't think of it as a network project. All networks involved will be rather trivial.
* The project group should include a biologist (to do sanity checks) and somebody familiar with parallel computing.
* Model checking is (very) expensive computationally, we will probably need a cluster.
* I have all the original results from the paper mentioned.
* The tool to use would probably be [http://www.prismmodelchecker.org/ PRISM].
[[Marek Kwiatkowski]]

: Marek, this dovetails nicely with my interests & I'd like to talk more about it with you. I have experience with -- and access to! -- a parallel cluster. No experience with prism, however. [[Rosemary Braun]]
: OK then, I am going to start a [[From Topology to Response]] project page. '''We still need a biologist.''' [[Marek Kwiatkowski]]

===Pattern Generation in Dynamic Networks: Elucidating Structure-to-Behavior Relationships===
Many sorts of networks produce patterns when dynamics are active on them. The brain is a great example. In fact, the patterns generated in your head are not only interesting and perhaps beautiful, but crucial to your success in surviving and thriving in the world. Gene or protein networks are another example. Change a few genes around and suddenly your stuck with a nasty disease.

One question we can ask is: how do the patterns of behavior (or "function" if you want to presume as much) change when we change the structural connections in the dynamic network from which they emerge? Alternatively, for a given type of behavior (set of similar patterns), is there a class of networks which all exhibit this behavior? What is common between all of those networks? What is the underlying mechanistic explanation for how they all behave this way?

Some potential topics:
* Genetics - what patterns of proteins emerge depending on what genes are where on a genome? (maybe other questions ... I'm not a geneticist!)
* Spiking neural networks - I have a lot of experience with this.
* Kauffman-like Boolean networks
* Population biology / food webs?
* Economics?

We might even think of embedding this in some physical space. Perhaps neural nets drive the 'muscle' movements of creatures (a la the [http://www.karlsims.com/evolved-virtual-creatures.html Karl Sims 'Creatures'] video we saw in Olaf Sporn's lecture) or the motors of [http://people.cs.uchicago.edu/~wiseman/vehicles/test-run.html vehicles].

I have experience in Python, Java, Matlab and a few other languages and am open to working with whatever (NetLogo?). I also have experience with Information Theory, which could come in handy in digesting and analyzing the patterns.

Clearly this project could go multiple directions. Feel free to add ideas/comments here...

[[watson]]

* [[Jacopo Tagliabue]]: Premise: I don't know if it makes sense at all, and even if it fits the project. I was thinking that just not the fact that some areas are connected makes a difference, but also the way they are connected. For example, the synchronization of neurons plays a pivotal role in the proper behaviour of the brain: when some disease (such as [http://en.wikipedia.org/wiki/Multiple_sclerosis multiple sclerosis]) leads to [http://en.wikipedia.org/wiki/Demyelinating_disease demyelination], the signals in the axioms can no more be processed at the right speed. The upshot is progressive cognitive and physical disability. Can we use agend-base models and/or network analysis to better understand what happens (and why, for example, multiple sclerosis may evolve in four different ways)? If someone with some neuroscience background would like to talk about this (or just explain why this doesn't make sense at all),I'd be glad to learn!

[[Karen Simpson]]: This is interesting to me, especially in the case of food webs merely because that is what I am most familiar with. Within an ecological community, there are certain links that depict the dynamics within that community. If we remove a link (or change it somehow, maybe by redirecting it through another organism), the community is stressed. The community may be resilient and the underlying dynamics may shift back to equilibrium. On the other hand, it may lead to the extinction of certain organisms.
One way that these links are changed is by introducing another node into the system, this node representing an introduced species. The success of this species depends largely on its position in the food web and its connecting links. My question (from an ecological perspective) is: Does introducing a non-native species result in different underlying dynamics and patterns? My intuition says yes, but it largely depends on the ability of the non-native organism to succeed in it's new environment. (See my thoughts under "Contagion in Networks" for more on this topic)

=== All sorts of (mostly US-centric) data===
For fun, brainstorming, and sanity-checking:
[http://www.data.gov/ data.gov] has tons of data collected by the US Gov't.

===Problem solving and mating - are they similar?===
I was intrigued by Tom's model of mating and began to wonder whether we can think of problem solving in a similar way. If we were to model problem solving, how would we do it? I'd like to think that problems and solutions are components that combine to generate an emergent property. (After a problem meets a solution--or a solution meets a problem--something new is allowed to emerge. While one instance of problem solving does not exactly create a complex system, many instances may.) That said, there are several questions/considerations to think about before/while we create a proper model of problem solving:

* What is the difference between problems and solutions anyway?
* What makes certain kinds of problems and solutions "hang out" in a cluster or neighboring clusters? Is this primarily due to path-dependence?
* When there is a difficult problem (tentatively defined as a problem for which there is no nearby solutions), how can we tell which clusters have the greatest probability of containing the solution(s)? (Can some of the network stuff we learned be of help here?)
* It is of course important to remember that a problem can have many solutions, and a solution can solve many problems, but that they may have different degrees of affinity (just like a ligand-receptor interaction in molecular biology). Also, occasionally a problem needs a combination of several solutions ("AND" as opposed to "OR").

I would love to hear your thoughts and comments, and I'm hoping that someone may actually share some of my interests in figuring out the answers to the questions above! [[Wendy Ham]]

===Modularity in complex systems - why is it there and what does it do?===
Evolving systems often switch from being highly modular to highly integrated, and vice versa. Why is this so and how does it happen? [[Wendy Ham]] and [[Roozbeh Daneshvar]].

* [[Roozbeh Daneshvar]]: Today in a slide of [[Olaf Sporns]] presentation, I noticed a graph showing the relation between order/disorder and complexity. When the system becomes too much ordered or too much disordered, in both cases complexity reduces. There is somewhere in between that we have the most amount of complexity. I was thinking that the emergence of modules are also a movement towards orderliness. But, complex systems do not go beyond a limit and still keep some non-modularity. So, Wendy, we have contrasting views on modularity. But maybe we will meet somewhere in between, where we have the most amount of complexity!
** '''Question''': Why modularity changed in human societies? Did the behavior of complexity change?
* [[Steven Lade]] Wendy, can you give some examples for evolving systems moving from "highly modular to highly integrated"? Also Roozbeh I don't understand what you mean by "behavior of complexity". Maybe we should talk.

===Evolving nanomachines===
Take the evolving motors animation we saw at the end of Olaf Sporn's talk, but instead put nanoscale physics, i.e. overdamped motion with Brownian noise, into the simulation. Perhaps put some basic chemistry in too. Evolve possible designs for nanomotors! What we get may include existing biological molecular motors. Or even more crazy idea: put in the physics of quantum mechanics. [[Steven Lade]] but with credits to Lilliana!

===Credit Market Simulation===
Money is loaned every day on the bond and money markets between banks, corporations, and individuals. It usually works very efficiently, but, ultimately, it is driven by humans. An agent simulation could provide us with insight into what behavior patterns give rise to the booms and busts that we have been experiencing. My guess is that it boils down to how individuals estimate risk and future reward. Nathan Collins suggested a learning model for how people get habituated to reward, expecting more and more for satisfaction. However, what happens to our estimates of risk in the face of increasing rewards? When the two are out of sync, we would likely see interesting dynamics. We've come up with a few ideas for how to implement this. [[Nathan Hodas]]
* [[Jacopo Tagliabue]]: It could be interesting to embed insights on risk-seeking and risk-averse behaviour from prospect theory and behavioural economics. I am also interested in agent-based simulations of a simple economy, where agents may use different heuristics (rational decision theory, Simon's model, Kahneman and Tversky theory, etc) to decide what to do. It is often said that in the market "errors cancel each other out", leaving a optimal or quasi-optimal global outcome: but is it true? And what's the relationship between individual strategies and this dynamics?

===Creative Process===
This is a very preliminary attempt to analyze the creative process in order to identify how we come up with ideas.

Creation of ideas as a process of random combination of concepts and connections taking place in the subconscious. Most of these ideas are filtered before reaching the conscious. Those ideas that rise above the conscious are new to the individual, some of which may also be new to the world. We generally classify the latter ideas as creative. Furthermore, the creativity literature refers to ideas as creative only when they are immediately useful in solving some problem or condition.

The existing concepts and connections can be considered as nodes or agents. A new idea can be a combination of at least 2 concepts + a connection or two connections, or some superposition of them. The following rules obey at the subconscious level:

1. The random process is taking place all the time with a single combination at one time

2. Each idea (which is a newly created concept or connection) attempts to pass through a filter. It either passes through or it doesn’t. If it does pass through, the idea is recognized and the coupling between the concepts/connections is raised. Each increase is by a factor of 0.1 (starting from 0) of the existing coupling until it reaches a maximum of 1. If it doesn't pass through, it ceases to exist (however, it may reappear later and given a change in the characteristics of the filter, they may be allowed to pass through).

The rules that define the ideas that pass through are:

1. The database of filters (individual’s understanding of the external environment, self control, etc.) defined in terms of what concept and connection associations are allowed to pass through as well as 20% deviation in them. [Ques: How can the deviation of a concept be evaluated numerically?]

Using complexity theory:

1. Agent based modeling can be used to identify how newer ideas rise to the level of consciousness, how the filters affect them

2. The network analysis can be used to understand how the coupling affects the creation of new ideas (concepts/connections)

[[Murad Mithani]]

===The Biological Evolution and Social Learning of Cooperation===
Both evolutionary biologists and social scientists have convincingly shown that cooperation can emerge and persist in human society. Although the two have employed the same methods (game theory and agent-based modeling), they have proposed different mechanisms: on the one hand, biological evolution based on kin selection, group selection, the “green-beard” effect or reciprocity and on the other, socio-cultural adaptation due to social learning. The two mechanisms act on different time scales and make different assumptions on the agents’ behavior (fixed vs adaptive) and the underlying dynamics (reproduction vs imitation). I think it will be interesting to combine the two mechanisms in a single agent-based model and to explore how they relate to each other. Following standard practice, the model will consist of agents on a spatial grid or a(n evolving) network who play a game such as the Prisoner’s Dilemma or Hawk-Dove. [[Milena Tsvetkova]]

===Foraging on the move===
[[Image:Caribou.jpg|250px|thumb|left|Snapshot of caribou migration.]]
[[Allison Shaw]]: Many animals forage in groups while moving from one location to another. This means individuals have to simultaneously balance several demands: finding the best resources, maintaining the cohesion of the group, and in some cases moving in a certain direction. Can we develop an agent-based model with a simple set of individual movement rules that would allow for all these demands to be met?

This was inspired by a piece of Planet Earth footage on caribou: go to http://dsc.discovery.com/convergence/planet-earth/video-player/video-player.html, scroll down in the video clips to "Planet Earth: Plains: Following the Caribou" and watch the dynamics at about 1:30-2:00. (If anyone has a hard copy of this segment or knows how to get one, please let me know!). In this case each individual caribou pauses to eat along the way but the group never fragments and in fact it seems to almost 'flow' through an area. My guess is that one of the physicists could provide some interesting insight on how to model this.

[[Daniel Wuellner]]: Cool idea. Most importantly: I actually brought the Planet Earth DVDs with me which I'll happily lend; maybe we can organize a viewing w/ a projector somewhere.

I think there's some swarm literature out there for ideas on rules you could extend to incorporate foraging (or any other caribouish behavior). The one I know is [http://portal.acm.org/citation.cfm?id=37401.37406&type=series Flocks, herds and schools: A distributed behavioral model] (this actually might be the 'original' swarm paper).

[[Kate Behrman]]: I also interested in this. One possible extension could be to consider how the structure of the landscape between the two locations affects the movement of the group.

===Modeling Gossip Networks===

It could be neat to develop a model of gossip networks. If you define gossip as information passed between 2 individuals (call them A and B) about a third party (C), then the act of gossiping has the potential to change the status/connection strength of all parties involved (e.g. maybe strength A-B, and weaken A-C and B-C bonds). Essentially passing information along a path in the network changes the value of BOTH edges in the direct pathway as well as other edges in the network. These are just preliminary ideas, but perhaps we could model how gossip tendency/frequency influences the structure of a network. Also, is it possible for individuals to influence their location in a network (e.g. increase centrality) by changing their gossiping frequency? (Although this is potentially a complicated rather than complex model idea...) Let me know what you guys think! [[Allison Shaw]]
* [[Milena Tsvetkova]]: This is a very interesting idea from sociological point of view. The effect of networks on the spread of gossip is well understood: some of the social dynamics at play include biases in the selection of trusted third parties (one draws a sample of information consistent with one’s predisposition), the reinforcement of opinions in dyads due to an etiquette mechanism, the exaggeration of information in triads due to echo effects. However, I am not aware of any studies that investigate how the spread of gossip affects network structure. My work is on the coevolution of behavior and social networks so we should talk!

===The Emergence of Meaning and the Evolution of Language===

There are several attempts in the philosophical and psychological literature (see [http://en.wikipedia.org/wiki/David_Lewis_(philosopher) Lewis’ work] on convention and [http://en.wikipedia.org/wiki/Paul_Grice Grice’s] analysis of meaning) to analyze the emergence of meaning. Most accounts (it not all) make extensive use of meta-representations, that is, the ability we have to understand other people intentions and “read” the content of their mental states. There are two problems with these theories: first, they are developed in a static fashion, while it may well be the case that the emergence of meaning is the result of a continuous, adaptive process; second, they seem to be plainly false, at least if we are willing to say that people affected by autism – and thus unable to read others mind – understand and produce meaning (see this recent paper by [http://people.su.se/~ppagin/papers/Autism5D.pdf Gluer and Pagin]).
Brian Skyrms and others used evolutionary game theory to evolve proto-languages, so-called “signaling games”, to understand how meaning dynamically emerges without meta-representations (it turns out that meaning can be understood as a form of equilibrium in these evolutionary dynamics). It could be interesting to further develop these insights, adding more realistic features to AB models:

* adding noise
* explore the same game in different topologies and see if the emergent behaviour depends in some way on constraints on how agents move
* see if it is possible to evolve language with a proto-grammar

These are just some preliminary considerations. Let me know what you think! [[Jacopo Tagliabue]]

=== Biological Pathways ===

Loosely defined, biological pathways are networks of molecular interactions that achieve a specific biological function. I'm interested in using the information we already have about them in the analysis of microarray data. I have a bunch of half-baked ideas; here are two.

==== Many hits vs. critical hits ====

[[Rosemary Braun]]

Microarrays assay 10^5-10^6 biological markers per sample. The most basic analysis is to ask whether each marker, individually, is disease-associated; common multi-marker approach is to sort the markers based on the magnitude of their association with disease, and then ask whether the high-scoring markers are over-represented in some pathways (biological interaction networks). By systematically performing an enrichment analysis on all known pathways, it is possible to elucidate which ones may play a role in disease. (cf [http://www.ncbi.nlm.nih.gov/pubmed/16199517 GSEA].)

On the other hand, it is well known that the centrality of a molecule in the biological pathway is strongly correlated with its biological importance -- the lethality of knocking out a gene is related to its centrality (eg [http://www.ncbi.nlm.nih.gov/pubmed/11333967 Jeong 2001]). This finding has been used to study individual markers 'within' a given pathway to predict which ones would be the most biologically relevant (eg by ranking the markers based on centrality, ([http://www.ncbi.nlm.nih.gov/pubmed/18586725 Ozgur 2008]).

One of the drawbacks of GSEA-type enrichment approaches is that they do ''not'' consider the centrality of each marker, ie, they are pathway-topology-ignorant. To the best of my knowledge, while centrality has been looked at to examine the importance of individual genes to a given function, it has not been incorporated in enrichment analyses. I would like to answer the question "is a pathway more ''critically'' hit with disease-associate alterations than would be expected by chance alone" using a centrality-aware scoring function.

One very naive way to do this would be to simply scale the single-marker association statistic used in GSEA by the centrality of the gene in the network. This raises a question of its own, however: to what degree do the results depend on the severity of the scaling?

Anyway, that's one half-baked idea. [Resources available: tons of data; adjacency matrices for pathways represented in KEGG, BioCarta, Reactome, and the NCI/Nature pathway database; useful ancillary functions in R; a cluster for permutation testing/exploring the parameter space.]

==== Gene expression time-course spectra ====

[[Rosemary Braun]]

Consider all the genes involved in a given pathway. Consider, also, a set of data that gives us the expression values for each gene at a handful of timepoints, eg, before (t=t0) and after (t=tf) an environmental exposure.

Next, suppose we describe the activity of that pathway by completely connected directed graph, for which the weight of the edge from gene_i to gene_j is given by MI(gene_i(t=t0),gene_j(t=tf)) (in the case of multiple timepoints, we could extend this -- eg transfer enropy). That is, the weight of each directed edge from gene_i to gene_j would tell us how well gene_i at t=t0 predicts gene_j at t=tf.

(I suggest the complete graph, rather than using the known pathway topology, because in practice the time differences tf-t0 may result in multiple "hops" -- so we may have correlations between next-next-neighbors rather than nearest neighbors, etc.)

So, we now have a description of signal propagation through the pathway over the time t0->tf, which we could summarize using the eigenvectors of the Laplacian. If we have two classes, eg cells which do/don't respond to the exposure, will we see statistically significant differences in the spectra for certain pathways, and thus infer that those pathways are involved in the response?

Possible pitfall: most time-course experiments only have a handful of samples for each timepoint.

=== Interacting distribution networks ===

I'm interested in thinking about evolving, interacting (re)distribution networks. Many large-scale aggregate networks are actually composed of several essentially independent subnetworks (e.g. individual airline carriers, local utility distribution companies), each of which takes into account the other agents' actions. While there may be interesting structure in the aggregate view, we know that the system followed an evolutionary path affected by interactions and should expect evidence of that process in the network structure. In other words: let's think of an agent-based model where each agent is a subnetwork maximizing some objective in a shared environment with constrained resources. I know there is some work on creating networks using games, but the agents are typically single nodes - see [http://portal.acm.org/citation.cfm?id=872035.872088 On a network creation game]

There may be some reasonable biological applications (for example, competing fungal hyphae networks; there was a recent work which modeled individual fungal growth - see [http://rspb.royalsocietypublishing.org/content/274/1623/2307.abstract Biological solutions to transport network design], possibly root structures, functional neural modules?) or social applications (competing idea networks). At the moment I'd love to think about anything other than airline networks.

There are many directions to take this depending on the system in question. Off the top of my head:

* Under what conditions (i.e. which games) can competing entities coexist? In this case, do they all form similar network structures, or do different structures allow them to occupy noncompeting niches?

* How does the game structure affect equilibrium network structure?

* Apparently certain environments support different size networks (small-scale regional carriers, large-scale national/international carriers) - is this realizable with an identical objective function for all agents?

I know basically nothing about game theory, and I'd love to take this in a biological direction. I'm also happy to go off in another direction if this inspires a tangential idea. [[Daniel Wuellner]]

Alfred Hubler's Nonlinear Dynamics Lab

2009-06-11T13:40:00Z

Kbehrman: /* Thursday June 18 7:00 p.m. */

{{CSSS 2009 Santa Fe}}

Alfred will be hosting a lab where students get to play around with a few concepts from nonlinearity and complexity science.

Class size is limited to 12 students.

===Tuesday June 16, 7:00 p.m.===
1 [[Erin Taylor]] 
2 [[Roozbeh Daneshvar]] 
3 [[Allison Shaw]] 
4 [[Matt_McMahon]] 
5 [[Nathan Hodas]] 
6 [[Steven Lade]] 
7 [[Daniel Wuellner]] 
8 [[Karen Simpson]] 
9 [[Mauricio Gonzalez-Forero]] 
10 [[Margreth Keiler]] 
11 [[Chang Yu]] 
12 [[Hirotoshi Yoshioka]] 

===Wednesday June 17, 8:30 a.m.===
1 [[Rosemary Braun]] 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

===Thursday June 18 7:00 p.m.===
1 Caroline Farrior 
2 Kate Behrman 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

[[Erin Taylor]] will be there for Tuesday the 16th's lab

[[Allison Shaw]] will be there for lab on the 16th too

CSSS 2009 Santa Fe-Tutorials

2009-06-11T12:52:09Z

Kbehrman: /* Maximum Entropy (and maybe maximum entropy production) */

{{CSSS 2009 Santa Fe}}

Feel free to organize your own tutorials. 
Post tutorial schedules here.

== Maximum Entropy (and maybe maximum entropy production) ==
[[Steven Lade]]: Well, nobody responded to my request so perhaps I'll do it myself :) I learnt a little at another summer school, so maybe I'm the best qualified, I was just hoping I wasn't. :)

Maximum entropy comes out of information theory (which I'm not expert in, so if there's someone knowledgeable to help me there, that would be great). It states simply that the most likely state of a system is the one which maximises its (information-theoretic) entropy. The entropy of statistical mechanics comes naturally from it: indeed, stat mech can be viewed as a subset of information theory from this perspective. But you can apply it to any sort of system, not just physics. For instance, you can easily obtain scaling laws in ecological systems. It's the closest thing to a 'theory of complex systems' that I've seen!

Tentative time: 7PM, Monday June 15. Add your name if interested.

* I am interested and will happily wear the skeptic hat: essentially if the entropy is sensitive to your parametrization, it loses much of its meaning. I think this is why some people (such as Amari) like to do "coordinate-free statistics". -Gustavo Lacerda

* I'm no expert, but I do have information theory basics under my belt... and more importantly, I happen to have some introductory info. theo. latex slides for a talk I recently gave. So I can offer help with the background, and then sit back & listen to the higher level, post-Shannon applications :) -[[Rosemary Braun]]
** On edit: I just noticed Lucas & Roozbeh requested an info theo tutorial -- shall we just roll it all together? -[[Rosemary Braun]]

*[[Lucas Lacasa]] Great, I'm in. Steve, with the Max-ent stuff you mean Jaynes? I've seen Jaynes formalism two or three times but never saw the difference with a merely Lagrange multiplier optimization, so great to hear about that. Rosemary, I would also be glad to learn some information theory stuff. I know the ultra-basics (Shannon entropy, mutual information, and not much more...).

[[Angela Onslow]]: I'd like to come along to this

[[Roozbeh Daneshvar]]: FYI, We have ABM tutorial on Monday, June 15th starting at 04:30 PM. I assume that it is finished by 07:00 PM.

[[Kate Behrman]]: I also do not claim to be an expert, but have gone over a lot of the theory that is commonly used in biology. I would like to know what physicists think. Count me in!

== MATLAB / Mathematica ==
[[Steven Lade]]: Hiro, I will happily give a tutorial on the basics of these languages (but only the basics, I don't use any of the fancy bits). Anyone here know if the labs here run MATLAB/Mathematica?

If there is anyone else interested (leave your name) I'll arrange a time, otherwise I'll talk directly with you Hiro.

[[Karen Simpson]]: I would also like a tutorial on MATLAB. I know some things about it, but never really learned the basics so it takes me a long time to do things. The computer labs should be equipped with MATLAB. I also have a fairly updated version on my laptop.

[[Lucas Lacasa]]I'm also interested! Also know some basics but I usually program in Fortran so I'd love to learn it.

Steven, many thanks! I think that the computers in the lab have MATLAB. If not, we can access it through my school's server as long as the internet connection is stable. [[Hirotoshi Yoshioka]]/lakiaypayaska

[[Brian Hollar]] I'm also very interested! I've never used these languages, but have some basic knowledge of Java, NetLogo, and FORTRAN. I'd appreciate the help and would love to learn.

[[Milena Tsvetkova]] Count me in! Steve, what is a good time for you?

[[Wei Ni]]: Hi ppl. Could I join in? I know MATLAB and I would like to further polish my MATLAB skills. Meanwhile I want to learn Mathematica.

Thanks for coordinating the tutorial and for 'setting up' the facilities, Steve and Lucas.

[[Chang Yu]]:Hello,I'm here! Thank you guys for this tutorial.I'm a kid in MATLAB and very courious about it.I know M is a giant in Mathematics,Statistic Analysis,Images and Genetic Algorithm and really want to learn more about that.By the way, I have the installation of Matlab 7.0 and I'll take it in my flash drive.If you have updated version, that would be better.

== Statistical physics: applications to complex systems ==
[[Lucas Lacasa]]:Statistical physics is a rather huge field, so I'm thinking on building a tutorial that focus on some specific topics related to complexity science in a chat-like level, namely:

- Fundamentals of statistical mechanics: ensembles, partition function and associated thermodynamic quantities (free energy, entropy) and some other basic stuff.

- Critical phenomena: Phase transitions in physical, social, and algorithmic systems. Self-organized criticality as the counterpart of a critical phase transition. Relation between phase transitions and local bifurcations of dynamical systems.

- Monte Carlo simulations, ergodic theorem

- Specific example gathering all of the above: Ising model

- Other related topics that you may like to listen to

Maybe we could schedule it for next week, something like next wednesday (17) at 7pm? (provided that no PRIORITY things such as basketball or soccer games are scheduled). If anyone else is interested please leave your name. Depending on the 'audience' we can fix one place or another...

*[[Steven Lade]] Fantastic, I'm in. But there is the 'Music on the Hill' 6-8pm Wednesdays. Is 8pm getting too late for 'work'? Or I miss an hour of the music. (Tuesday and thursdays there's the nonlinear dynamics labs)

*[[Lucas Lacasa]] You're right. What about friday 19 after lunch?

*[[Roozbeh Daneshvar]] I'd like to join this one.

*[[Corinne Teeter]] I'd also like to come.

*[[Barbara Bauer]] I'm interested too.

== Tutorial requests! ==
Either a formal 'lecture' or a casual 'chat' is fine!
* Time series analysis (requested by Steve Lade)
* Maximum entropy / Maximum entropy production (requested by Steve Lade)
* Mathematical modelling in ecology (requested by Steve Lade)
* Some physics stuff: statistical mechanics; mean field theory; self-organized criticality and phase transitions; Ising model and the like (requested by Mareen Hofmann and Roozbeh Daneshvar)
** [[Lucas Lacasa]] I can talk you about phase transitions, Ising model, SOC and general stat phys...
** [[Steven Lade]] I'd like to hear about this too; can you schedule a tutorial?
* Evolutionary game theory (requested by Mareen Hofmann and Roozbeh Daneshvar)
* Ergodic theory (requested by Roozbeh Daneshvar)
* Information theory (requested by Roozbeh Daneshvar and Lucas Lacasa)
* Spectral graph theory (requested by Lucas Lacasa)
* Spin glass theory: Replica method (requested by Lucas Lacasa)

*If somebody can give a tutorial on Matlab and/or Mathematica, that would be nice. I'm also interested in the difference between the two programs (e.g., what each program is good at). Thanks in advance! Hiro/lakiaypayaska

*Fitting high dimensional data with functions--is there such thing as 4D maximum likelihood estimation (MLE)? Also how to tell if two 'blobs' of high dimensional data are statistically the same or different.[[Corinne Teeter]]

Kathrine Behrman

2009-05-26T13:34:30Z

Kbehrman:

I am a third year Ph.D student at the University of Texas in ecology and evolution. I completed my under graduate degrees in biology and mathematics at University of California Santa Barbara.

Answers to Dan's Questions:

1. What are your main interests? Feel free to include a "pie in the sky" big idea!
Most of my thesis work focuses on understanding species ranges both from an evolutionary and ecological point of view. I am particularly interested in (1) how species' ranges form and (2) how species' ranges may change in time and space as organisms adapt (or fail to adapt) to new environmental conditions. I am also interested in how the scale at which environmental variables act create present spatial patterns.

2. What sorts of expertise can you bring to the group?
My background as a graduate student is in ecology and evolution, I also have an undergraduate degree in Mathematics. I have currently been using lots of simulations, numerical, and statical techniques for my thesis work. I can bring a unique perspective about to tackle problems from both and evolutionary and ecological point of view.

3. What do you hope to get out of the CSSS?
I would like to get a sense for techniques I am not familiar with to study complex systems, brush up on the mathematics used to study nonlinear dynamics, learn about the techniques used by economists and social scientists that have the potential to be applied to ecological and evolutionary questions, and meets lots of new scientists.

4. Do you have any possible projects in mind for the CSSS?
I don't have any projects currently in mind.

In my free time I enjoy kayaking, running, hiking, yoga, and making jewelery.

I am looking forward to meeting you all in June! -Kate

Kathrine Behrman

2009-05-26T13:33:56Z

Kbehrman: New page: I am a third year Ph.D student at the University of Texas in ecology and evolution. I am completed my under graduate degrees in biology and mathematics at University of California Santa Ba...

I am a third year Ph.D student at the University of Texas in ecology and evolution. I am completed my under graduate degrees in biology and mathematics at University of California Santa Barbara.

Answers to Dan's Questions:

1. What are your main interests? Feel free to include a "pie in the sky" big idea!
Most of my thesis work focuses on understanding species ranges both from an evolutionary and ecological point of view. I am particularly interested in (1) how species' ranges form and (2) how species' ranges may change in time and space as organisms adapt (or fail to adapt) to new environmental conditions. I am also interested in how the scale at which environmental variables act create present spatial patterns.

2. What sorts of expertise can you bring to the group?
My background as a graduate student is in ecology and evolution, I also have an undergraduate degree in Mathematics. I have currently been using lots of simulations, numerical, and statical techniques for my thesis work. I can bring a unique perspective about to tackle problems from both and evolutionary and ecological point of view.

3. What do you hope to get out of the CSSS?
I would like to get a sense for techniques I am not familiar with to study complex systems, brush up on the mathematics used to study nonlinear dynamics, learn about the techniques used by economists and social scientists that have the potential to be applied to ecological and evolutionary questions, and meets lots of new scientists.

4. Do you have any possible projects in mind for the CSSS?
I don't have any projects currently in mind.

In my free time I enjoy kayaking, running, hiking, yoga, and making jewelery.

I am looking forward to meeting you all in June! -Kate