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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