Three Behavioral Zones • Zone of repulsion • Zone of orientation • Zone of attraction • Blind Region a Adapted from Inada, 2002
The Logic of the Model Ifany neighbors in zone of repulsion (“Dude, quit riding my tail!”). Get away--repulsion has highest priority. Else If all neighbors are in the zone of orientation: Orient to their (average) heading If all neighbors are in the zone of attraction: Come closer to their (average) position If neighbors exist in both orientation and attraction zones: Then orient and get closer, in proper proportion Otherwise fish is lost Turn around 180 degrees and start heading back
The Three “Laws of Orientation” Desired direction for individual i. i = 1, 2, …, N Repulsion Rule Attraction Rule Orientation Rule
Model Implementation: Compute Desired Heading Ifany neighbors in zone of repulsion (repulsion has highest priority!): Else If all neighbors are in the zone of orientation: If all neighbors are in the zone of attraction: If neighbors exist in both orientation and attraction zones: Otherwise fish is lost, turn 180 degrees -
Model Implementation: Update Current Heading Desired turning angle: If f(t) < wt (Desired turn can be achieved in one time step) Else (Desired turn cannot be achieved in one time step, turn as much as possible toward desired heading) Fraction defines how much of desired turn is actually achieved.
Quantifying group coherence Polarization Angular Momentum Moment Arm Centroid Average heading
Couzin Model Results Emergent collective behavior: all fish pointed the same direction Circulating fish school—rare! Random/disorganized group behavior
Predator Attack! • What rules do you obey? • Move away from predator? • Or stay with the school? Obey your thirst!
Run (errr, swim) for Your Lives!: The Predator Escape Rule Pure predator escape rule Rpred If predator is within the ‘danger zone’ (defined by Rpred) Predator escape with obedience to the school Obedience parameter (range = 0-1) h = 1: Fully obedient to the school h = 0: Ignore the school, move only to get away from predator
Predator Attack: Further Considerations And what about ratio of school size to number of predators? What about multiple predators?
References • I.D. Couzin et al. Collective Memory and Spatial Sorting in Animal Groups, J. theor. Biol(2002) 218, 1-11 • Y. Inada and K. Kawachi. Order and Flexibility in Motion of Fish Schools, J. theor. Biol(2002), 214, 371-387 • AdiShklarsh, Gil Ariel, EladSchneidman, Eshel Ben-Jacob. Smart Swarms of Bacteria-Inspired Agents with Performance Adaptable Interactions. PLoS Computational Biology, 2011; 7 (9): e1002177 DOI: 10.1371/journal.pcbi.1002177