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Birds flock, fishes school: Modeling Emergent Collective Behavior

Birds flock, fishes school: Modeling Emergent Collective Behavior. Breaking news…. Three Behavioral Zones. Zone of repulsion Zone of orientation Zone of attraction Blind Region. R o. a. Adapted from Inada, 2002. The Logic of the Model.

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Birds flock, fishes school: Modeling Emergent Collective Behavior

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  1. Birds flock, fishes school:Modeling Emergent Collective Behavior

  2. Breaking news….

  3. Three Behavioral Zones • Zone of repulsion • Zone of orientation • Zone of attraction • Blind Region Ro a Adapted from Inada, 2002

  4. 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

  5. Definition of Coordinate System y Unit direction vector of fish iwrt its “local coordinates”

  6. The Three “Laws of Motion” Repulsion Rule Attraction Rule Orientation Rule Image credit: http://www.red3d.com/cwr/boids/

  7. 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: r: orient/attract priority parameter. Range = [0-1] Otherwise fish is lost, turn 180 degrees

  8. Model Implementation: Update 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.

  9. Add a little noise; update position “cruising speed”, assumed constant over time Gaussian noise term: Imprecision/error vi(t+t) vi(t)

  10. Quantifying Group Behavior Polarization Angular Momentum Moment Arm Centroid

  11. Couzin Model Results Emergent collective behavior: all fish pointed the same direction Circulating fish school—rare! Random/disorganized group behavior

  12. Predator Attack! • What rules do you obey? • Move away from predator? • Or stay with the school? Obey your thirst!

  13. 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

  14. Predator Attack: Further Considerations And what about ratio of school size to number of predators? What about multiple predators?

  15. Simulation Software (FishSim)

  16. 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

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