Collective Animal Behavior

Ariana Strandburg-Peshkin

Boids - Craig Reynolds (1986)Separation - Steer to avoid

collisions

Alignment - Steer towards average heading of flockmates

Cohesion - Steer towards average position of flockmates

Boids

Neighborhood: Distance and Angle

QuickTime™ and aCinepak decompressor

are needed to see this picture.

“Self-Propelled Particle” Model (Vicsek & Csahok)

Triangular Lattice - L x L sites, periodic boundary conditions, N particles

Particles have position and velocity, updated at each time step

Multiple particles can occupy one lattice point

SPP Model - Rules

Choose new velocity based on sum of nearby neighbors

If multiple particles at one spot, one follows rule above, others choose a random velocity (to reduce effects of multiple occupancy - diffuse away)

All particles advance one lattice unit in direction of velocity

Z - normalizingB - 1/T

SPP Model - ResultsOrder Parameter, m - average velocity

Sharp Transition, Disorder --> OrderDepends on density

Locusts!!

Swarms - Can cover up to 1200 sq. km40 - 80 billion locusts per sq. kmCan travel 100 - 200 km per day

Solitary --> Gregarious --> Hopping “bands” --> flying “swarms”

Locusts - Empirical Study (Buhl et. al.)

Effect of density on alignment (order) of locusts

Filmed locusts in ring-shaped arena (for 8 hours!) and tracked position and orientation

Compared to a related SPP model

Locust Model vs. Empirical

D = 1.2 D = 4.5 D = 19.1

D = 1.4 D = 4.9 D = 19.2

Couzin - “Swarming” Model

zor > zoo = zoa

“Desired direction”

Turning rate

Noise

Parameters and Measurements

Group Polarization (Alignment)

Angular Momentum (Rotation about the center)

“Swarm”p = lowm = low

+ & -little o

Text

“Torus”p = low

m = highsmall Rolarge Ra

“DynamicParallelGroup”

p = highm = low

medium Romedium Ra

“HighlyParallelGroup”p=very

highm = lowlarge Ro

medium Ra

Individual Variations Affect Location in

Group

A Collective Memory?

Buhl, J., Sumpter, D.J.T., Couzin, I.D., Hale, J., Despland, E., Miller, E. & Simpson, S.J. (2006) From disorder to order in marching locusts Science 312, 1402-1406Couzin, I.D., Krause, J., James, R., Ruxton, G.D. &

Franks, N.R. (2002) Collective memory and spatial sorting in animal groups Journal of Theoretical Biology 218, 1-11Csahok, Z. & Vicsek, T. (1995). Lattice gas model

for collective biological motion Physical Review E Vol. 52 No. 5Reynolds, C. W. (1987). Flocks, herds, and

schools: a distributed behavioral model Computer Graphics Vol. 21 No. 4

Sources