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

Prior hypotheses 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).

Wave-like Front in Wildebeest Migration

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.).

Wildebeest ModelThe lag compensation rules cause small perturbations to be

amplified over time in simulations

http://www.youtube.com/watch?v=uIH-p1OSRZwSimilar model might be used for oscillations in single-file line:

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

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.

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.

Feedback loops with the environment

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

Human Swarms: architecture, pedestrians and emergencies

Craig Reynold’s 1987 simulation “boids” remains one of the clearest examples of self-organization. 3 parameters:

Boids of a feather flock together: nearest neighbors

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.

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

Couzins extends Reynold’s model

A. ‘‘Swarm’’: low P and low M

B. Torus: Low P high M

C. Dynamic parallel: higher P, low M

D. Highly parallel: highest P, low M

Couzins extends Reynold’s model

P = Group polarization -- how much of group is aligned M = Group angular momentum -- how much of group rotates about center

Hysteresis: as you increase zone of orientation (ro) you get a torus, and then parallel flock.

As you decrease ro from the parallel flock it does not generate a torus

It has memory!

Couzins extends Reynold’s model