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

Complex Social Phenomena Fish Birds Primates

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

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

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

Coordinating groups Starlings (C. Carere) Without chemical

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

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)

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=3 N=12 N=47 Time (min)

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

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

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

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)

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

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 !....

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

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?

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

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°

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

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

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

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

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….

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..

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

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 0 0.5 1 1.5 2 2.5 3 3.5 aligning zone milling polarized config Angular momentum swarm 0 0.5 1 1.5 2 2.5 3 3.5 aligning

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

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 →

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

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)

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

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

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 3 - 2000 Mullet 4BL/s Silverside 2BL/s

Results DEMO

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 !

Development of Shape and Core 26 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

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

Group Size and Frontal Density 10 30 100 300 2000 → 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

Group Size, Speed And Oblong Shape Larger Groups Are More Oblong (Herring: Axelsen et al., 2001) 10 30 100 300 2000 → 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 ?

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

Slower Schools Are 10 100 2000 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

Speed and Density Faster Schools: Denser Core, And Loser Tail, 0.6 0.5 0.4 0.3 0.2 0.1 10 20 30 60 100 200 300 600 1000 2000 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)

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

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= 20-2000 Two velocities (Hemelrijk & Hildenbrandt, 2008)

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

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

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 !