1. Self-organised social systems of animals
Mini Course Italy Day 1 Hour 1
Charlotte K. Hemelrijk,
Theoretical Biology
Centre for Ecological and Evolutionary Studies
University of Groningen
The Netherlands

2. Complex Social Phenomena
Fish
Birds
Primates

3. ‚Self-organisation‘ models
Simple behavioural rules of individuals
Complex patterns at a group level
Self-organisation
‚Understanding by building‘
(Pfeifer & Scheier, 1999)

4. This Mini Course: Two Examples
Models
Day 1: Moving groups (Fish and birds)
Coordination
Shape
Density variation in school
Day 2: Social organisation (Primates)
Competition and affiliation
Type of society: egalitarian vs despotic

5. Moving Groups Coordinate in: Heterogeneous environment (e.g. primates)
E.g. Follow specific food sources (orang utans ,
te Boekhorst & Hogeweg, 1994)
Homogeneous environments (e.g. fish, birds)
E.g. In air and water
With a preferred direction (e.g. toward reproduction area)
Without preferred direction (coordination by self-organisation)
This Course

6. Coordinating groups
Starlings (C. Carere)
Without chemical

7. Coordination In Moving Groups Of Fish, Birds
Mechanism
No currents, chemics, light, etc.
No leader
Using sensory information:
Fish
Eyes
Lateral system
Birds
Self-organised system

8. Simple physical model Model of self-propelled particles (SPP): Result:
Vicsek et al 1995
Model of self-propelled particles (SPP):
Random movement
Alignment with closeby neighbours
Fixed velocity, v
Angle, 
Result:
Alignment of the whole population at high density
Average direction
-1, 1 = complete alignment
N=3 N=11 N=47
Time (min)

9. Marching Cockroaches Need certain density for collective marching
Buhl et al 2006
Need certain density for collective marching
Experimetal set up:
Ring shaped arena
8 h observation of position and orientation
Result:
At high density: alignment
Movie
-1, 1 = complete alignment
N= N=12 N=47
Time (min)

10. Cockroaches & Model are similar Mean number of moving locusts
Number of locusts
are similar

11. Real animals Density differs between species (0.3 – 3 BodyLength)
Question: how do they stay in groups and aligned?
Models
2D, 3D
Alignment
Attraction and repulsion

12. Flocking by local rules Reynolds (1987)
Global Y
Global Z
Global X
MODEL
‚World‘
Boids:
Behavioural Rules
Global target
Velocity matching
(heading and speed)
Priority
and
Weighted
average
Dead angle
A boid‘s
neighbourhood

13. Behavioural Rules of Boids
All Boids Have the Same Rules
Collision avoidance
(steer away from flockmates)
Aligning: steer towards
the average heading of local
flockmates
Priority
and
Weighted
average
Flock centering (try to be close to centroid of approx. 3 neighbours)

14. Flocking Reynolds Flock-like behaviour
Coordinating group splitting and merging when avoiding collision with large objects (‘houses’)
‚Conceptual model‘

15. Schools without a goal (Huth and Wissel 1992; based on Aoki 1982)
MODEL:
2-D Environment
N=8 identical fish (no leader):
initially random location and orientation
Fish have
a position, xi,
orientation v0i,
speed vi
Speed: fixed with error
Gamma distribution with certain average value, independent of other fish
New position & orientation:
Depends on position and orientation of neighbours and vi
Other groupmembers !....

16. Schools without a goal (Huth and Wissel 1992)
Reaction if one neighbour is
at a distance that is:
Close
Repulsion: moveAwayUnder 90°
with least effort
Medium
Paralel: orientateParalel
Medium-Far
Attraction: moveTowards
Far
Search: TurnSearchAngle(±180°)
Search
Attraction r3
Paralel r2
Repulsion r1
Dead Angle
Turning angle αi with random noise:
Normal distribution around target angle βi
Several individuals

17. Influence of Several Neighbours on Alignment
priorityDir b2
neighbour2
neighbour1
AverageDir b1 b2
Move To
Averaging Model
Decision-Priority Model
distance
Front-central, etcetera
Behaviour?

18. Measures Centre of mass Path of group = path of group‘s centre of mass
Confusion/Polarization = mean of angle deviation of each fish to swimming direction of the group (= summed orientations of all) t2 t1
MeanDir

19. Priority versus Averaging reaction to neighbours
D-Priority
Path of centre of
mass of group
Polarization
Average deviation of group direction
D-Priority:
(Polarization)
Confusion 60°
Averaging :
(Pol. )
Conf. 10°

20. Example Why averaging works better than prioirity Time Priority
Nearest Nb
Averaging
Why averaging works better than prioirity

21. Number of neighbours 3 neighbours are enough Expanse
Surface:
Expanse
BLU
degrees
(Polarization) Confusion
neighbours
3 neighbours are enough

22. Moving group Coordination by self-organisation No leader
Collision avoidance
Alignment
Attraction
No leader

23. Group behaviour: polarization (Couzin et al 2002)
Model after Aoki (1982), Reynolds (1987), Huth & Wissel (1992)
3 Dimensional space
Fixed speed, attraction, alignment, avoidance
Questions:
What happens for different radii of attraction and alignment

24. Size of Zone of attraction, orientation and avoidance
‘milling’
angular momentum
Barracuda, tuna, jack
Swarm
Feeding
midges
Attr medium
Align low
Attr high
Align low
‘highly parallel group’
polarized
Attr high
Align high
Attr medium
Align medium
Milling of fish….

25. Milling Depends also on speed and area of vision and ..former state..
Parrish & Edelstein-Keshet 1999
jack
Depends also on speed and area of vision and ..former state..

26. Transition Between States Due To Area Of Alignment r0
Measure:
Polarisation
Angular momentum (degree of rotation of group around group centre)
Momentum M is force times distance, M = F * l
ric is radius of individual i to centre of gravity

27. Hysteresis Couzin et al 2002
polarized
config
Polarization
Radius-attraction is fixed, very high;
Increasing and decreasing
range of orientation
(or alignment):
collective state depends on history
milling
swarm
aligning zone
milling
polarized
config
Angular momentum
swarm
aligning

28. Summary Small changes in micro-patterns large ones in macro-patterns;
Fast changes possible.
Collective memory

29. Oblong School Form And Frontal Density
Adaptive traits:
Predator attack at front
Highest danger at front
Individuals hide behind others
(Bumann, Krause, Rubenstein1997)
Mechanisms?
compare density in different parts of school?
react to the changing distribution of others?
Side-effect of coordination →

30. Density Highest Density at Front Oblong Form Side-effect of Behaviour
From Coordination Rules
Hemelrijk & Kunz (2004)
BUT:
Critique of former models →
Unrealistic Assumptions !

31. Critique by Parrish & Viscido 2005
Our new Implementation
Cruise speed, V0,
(after deviations return to it),
Adaptable view (increase at low density, decrease at high density)
Group size (up to 2000)
3D (Couzin et al 2002; Huth and Wissel 1994)
Fixed speed (Couzin et al 2002) with random error (Huth and Wissel 1992)
Almost global view
Group size (up to 128)
2D (Huth and Wissel 1992)

32. Methods Hemelrijk & Hildenbrandt 2008 Fish In 3-dimensional Space
ri = position vector
N = 100 r1 r2
etcetera ez ex ey
Avoidance
Alignment
Attraction
Blind angle
Overlapping zones
Slice through perception volumes

33. Rules Of Individuals If the other is Nearby: Avoid/Repulse/Separate
Scaled by distance
At Medium Distance: Align
Further Away: Approach/Cohere
Actual behaviour:
attraction
avoidance
random
acceleration
alignment

34. Model: Parameters Weights: Wc = 9, Wa = 5, Ws = 10
attr
align
avoid
Weights: Wc = 9, Wa = 5, Ws = 10
No milling, no splitting (Hemelrijk, Hildenbrandt, 2008)
Two Speeds
Group Size
Mullet 4BL/s
Silverside 2BL/s

35. Results
DEMO

36. Model: Frontal Density and School Form
A slice through the school:
High
Low
Densest 10% = Core
Movement
Movement
Backwards 25% = Tail
Fast Slow
N=600
Density Highest At The Front
And Form Is Oblong !
Robust phenomenon !

37. Development of Shape and Core26 24 22 20 18 16 14 12
Width
Length
Core location
Length, Width
N = 600
Start ball-shaped school
t=1 A A
t=2
t=3 A
Collision Avoidance → usually Slow Down & Move Inwards → Lengthening of Swarm and the Tail
More evidence

38. Group Size and Density
Shortens Nearest Neighbour Distance (conform real fish, Partridge et al 1980; Partridge, 1980;Nursall, 1973; Keenleyside, 1955; Breder, 1954)

39. Group Size and Frontal Density
→ School Size
Fast
Core location
Distance to back / length
0.6
0.5
0.4
0.3
0.2
0.1
Slow
Length
Distance to back
Group size
Density
Larger Groups Have
Core More At The Front (Empirical Data Absent)
Due To Longer Tail, Because More Individuals Fall Back, Because Denser

40. Group Size, Speed And Oblong Shape
Larger Groups Are More Oblong (Herring: Axelsen et al., 2001)
→ School Size
Fast
Length / Width
2.5
1.5
1.0
Slow
Slower Schools are More Oblong (Partridge et al (1980): Herring vs Saithe vs Cod, for optimal vision or different hydrodynamics at different speeds; Contrary to Breder (1959); Radakov (1973): elastic)
In model ?

41. Slower Schools Are Turning More Slow Curvature K Path: Slow School
Fast
School Size
Path: Fast School
Turning More

42. Slower Schools Are
School Size 1
0.995
0.99
0.985
Fast
Polarisation
Slow
Turning More  Are Less Polarised (real fish: Viscido et al 2004)
More Collision Avoidance Falling Back  More Oblong

43. Speed and Density Faster Schools: Denser Core, And Loser Tail,
0.6
0.5
0.4
0.3
0.2
0.1
School Size
Density
#Individuals / BLU3
Core
School
Tail
Fast
Densest 10%
Slow
25% backwards
Slow
Fast
Faster Schools: Denser Core, And Loser Tail,
Because Less Fall Back
Contrary to Breder (1959); Radakov (1973)

44. Frontal Density and Oblong Form
Arises as a side-effect of coordination!
Due to falling back to avoid collision
Attraction at the sides

45. Robust Two models 2D-Fixed speed, group size 20-100:
3 Body shapes (Kunz &Hemelrijk 2003)
Different % 2 body sizes Hemelrijk & Kunz 2005)
Mixed groups with extra rules (avoidance, preference)
3D speed & interaction range are adaptable, N=
Two velocities (Hemelrijk & Hildenbrandt, 2008)

46. Conclusion: Zone-based model of schooling
Through coordination and movement
Side-effect !
Oblong Shape and High Frontal Density
Model-based Hypotheses

47. Model-based Hypotheses Empirical data
Group
Size
a. larger groups are denser
(Partridge, 1980; Nursall, 1973; Keenleyside, 1955; Breder, 1954) (Partridge et al., 1980).
b. they are less polarised
n.a.
c. larger groups are more oblong
(Axelsen et al., 2001)
d. their densest core is located more forward
Cruise
Speed
a. Slower groups are less polarised
(Viscido et al., 2004)
b. they are more oblong
(Partridge et al., 1980)
c. their path is more curved

48. Shape of School of Real Fish
Two problems with shape as a side effect
Insufficient empirical data:
Group sizes < 20
No systematic study
Empirical data in tank
Our model: free swimming fish
Tank may disturb process to produce oblong shape
Collect own data in tank and adapt model
Next hour !