Foraging on the move

Project Description

Introduction

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.

Background

• Benefits of group living include lower predation (dilution effect), shared information, and easy of finding mates and find resources
• Costs of group living include an increased attraction of predators, transmission of diseases, and competition for resources
• In theory, group size is determined by the payoff to members: at equilibrium (with groups of size N), the benefit to joining a group should be equal that of being loner individual
• An individuals position within the group can have significant fitness consequences (see Krause 1994)

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).

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), a result we should see with our model. [CHECK FOR THIS] Additionally, we expect to see individual position within the group change over time, as individuals change their preference for different group locations as their conditions (e.g. energy reserves) change (Parrish 1999). [CHECK FOR THIS]

Add:

• migration models
• details of caribou and wildebeest systems
• more on collective behavior?

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

• Barta, Z. 1997. Geometry for a selfish foraging group: a genetic algorithm approach. Proceedings of the Royal Society B: Biological Sciences, 264, 1233-1238.
• 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.
• Fretwell, S. & Lucas, H. 1969. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor, 19, 16-36.
• 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.
• 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.
• Schoener, T. 1971. Theory of feeding strategies. Annual Review Of Ecology And Systematics, 2, 369-404.

• Couzin, I. D., Krause, J., Franks, N. & Levin, S. A. (2005). 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). "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). "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). "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

• 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 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. SteveLade 04:17, 24 June 2009 (UTC)

• how to prevent flock from wrapping around across the boundary?
  • Currently not a problem -- flock not long enough
• 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 SteveLade 04:59, 25 June 2009 (UTC)
  • yeah, this was a due to a bug in how I sent initial conditions -Allison

MODEL DEVELOPMENT (MORE INVOLVED)

• develop/implement metrics to describe group
  • flock density
  • average flock speed (Done 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 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 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
• Kate Behrman
• Liliana Salvador
• Steven Lade

Original Discussion

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 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).