Foraging on the move

Project Description

Motivation

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:

1. foraging (finding enough resources)
2. flocking (maintaining group cohesion)
3. migrating (continually moving in a certain direction)

Model Framework

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

Relevant Literature

• 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)
• 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)

• 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

MODEL DEVELOPMENT (MORE INVOLVED)

• develop/implement metrics to describe group
  • flock density
  • average flock speed
  • average fraction of time individual spends foraging
  • 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?

• 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).