Self-Organization in Vertebrate Collective Behavior ( Couzins and Krause 2003)

1. Self-Organization in Vertebrate Collective Behavior (Couzins and Krause 2003)

2. Birds turning almost instantaneously due to ‘‘thought transference’’ (Selous, 1931) Generation by muscles of an electromagnetic field that could be detected by other group members (Presman, 1970). A ‘‘leader’’ must coordinate the motion of such groups (Heppner and Haffner, 1974). Prior hypotheses

3. Wave-like Front in Wildebeest Migration

4. Wildebeest Model 1. If a gap reaches a specified maximum distance, individuals lagging will speed up to reduce the gap. 2. Those ahead of neighbors can continue until the gap reaches a specified maximum distance, and then they slow down. 3. Small random perturbations (some individuals are speedy, someone trips, etc.).

5. Wildebeest Model The lag compensation rules cause small perturbations to be amplified over time in simulations Similar model might be used for oscillations in single-file line: http://www.youtube.com/watch?v=uIH-p1OSRZw

6. Feedback loops with the environment 1. Individuals will choose path of least resistance: where prior travel broke bushes, packed snow, etc.2. Positive feedback: the more individuals taking this path, the more comfortable/attractive 3. Memory fades: if the spring dries up, fallen tree blocks path etc. the plants will regrow

7. Feedback loops with the environment A) Individuals move between points 1 and 2, an obstacle in between. B) Individuals randomly select either direction around the obstacle. C) If individuals make multiple trips, and take the same route each time, the shortest route can be selected collectively.

8. Feedback loops with the environment A) Individuals move between points 1 and 2, an obstacle in between. B) Individuals randomly select either direction around the obstacle. C) If individuals make multiple trips, and take the same route each time, the shortest route can be selected collectively.

9. Human Swarms: architecture, pedestrians and emergencies A) In this example, “pressure” builds until one side allows others to pass. B)In emergencies, the pressure can be physical, enough to bring down walls and shatter glass.http://www.trafficforum.org/somsstuff/pedapplets/Door.html

10. Boids of a feather flock together: nearest neighbors Craig Reynold’s 1987 simulation “boids” remains one of the clearest examples of self-organization. 3 parameters: • Separation: Steer to avoid crowding birds of the same color. • Alignment: Steer towards the average heading of birds of the same color. • Cohesion: Steer to move toward the av. position of birds of the same color.

11. Couzins extends Reynold’s model Zone of repulsion, zone of orientation, and zone of attraction. These change:Group polarization increases as the degree of alignment of group members increases.Group angular momentum measures the degree of rotation of a group about the group center

12. Couzins extends Reynold’s model A. ‘‘Swarm’’: low P and low MB. Torus: Low P high MC. Dynamic parallel: higher P, low MD. Highly parallel: highest P, low M P = Group polarization -- how much of group is aligned M = Group angular momentum -- how much of group rotates about center

13. Couzins extends Reynold’s model Hysteresis: as you increase zone of orientation (ro) you get a torus, and then parallel flock.As you decrease rofrom the parallel flock it does not generate a torusIt has memory!