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

“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 - normalizing B - 1/T

SPP Model - Results Order Parameter, m - average velocity Sharp Transition, Disorder --> Order Depends on density

Locusts!! Swarms - Can cover up to 1200 sq. km billion locusts per sq. km Can travel 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 = low m = low + & - little o Text “Torus” p = low m = high small Ro large Ra “Dynamic Parallel Group” p = high m = low medium Ro medium Ra “Highly Parallel Group” p=very high m = low large 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, Couzin, 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, 1-11 Csahok, Z. & Vicsek, T. (1995). Lattice gas model for collective biological motion Physical Review E Vol. 52 No. 5 Reynolds, C. W. (1987). Flocks, herds, and schools: a distributed behavioral model Computer Graphics Vol. 21 No. 4 Sources