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
If any 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
Unit direction vector of fish i wrt its “local coordinates”

6. The Three “Laws of Motion”
Repulsion Rule
Attraction Rule
Orientation Rule
Image credit:

7. Model Implementation: Compute Desired Heading
If any 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
Gaussian noise term: Imprecision/error
“cruising speed”, assumed constant over time
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,
Adi Shklarsh, Gil Ariel, Elad Schneidman, Eshel Ben-Jacob. Smart Swarms of Bacteria-Inspired Agents with Performance Adaptable Interactions. PLoS Computational Biology, 2011; 7 (9): e DOI: /journal.pcbi