Agent-based models
of animal behaviour
From micro to macro
and back.
Ellen Evers, Behavioural Biology, University Utrecht.
Outline
... - genome – cell – organism – group – population – ecosystem - ...
Organization, structure, patterns
(spatial, temporal, social, ...)
Behaviour of animal groups
(coordination)
Self-organization
(complexity arises from simple rules)
Tool to understand and study:
Agent-based Models (ABM)
Flocking
Examples real:
Starlings, ants (movie), fish
Collective motion
Bird flocks (starlings), insect swarms (flies),
mammal herds (wildebeest), fish schools (herring)
Fish schooling
School level:
Locomotion:
Simultaneous change of direction
Defense:
Flash expansion, fountain effect, aggregation
No disorganized crowd, but coordinated behaviour
between members of the group!
HOW to get structure, patterns, organization in a system?
Organization
Leader:
Well informed (top-down)
Provides everyone with instructions
No! Fish change position within school
Blueprint, Recipe, Template:
Plan or procedure
Fixed, not very flexible
No! Unlikely in big groups
Fish schooling
Individual level:
Vision (location of neighbours)
Lateral line (orientation of neighbours)
Coordination only with nearest neighbours, whole
swarm locomotion through:
SELF-ORGANIZATION!
Self-Organization
... process in which a pattern at the global level of a
system emerges solely from numerous interactions
among the lower-level components of the system.
(Camezine et al, 2001)
No external, centralized control (no leader)
Local information, simple rules (no global plan, overview)
ORGANIZATION! (bottom-up)
FISH SCHOOLING? COLLECTIVE MOTION?
Fish schooling
Self-Organization Hypothesis:
Few simple rules in response to local information from
neighbouring fish generate schooling patterns
without directly coding for them. (Huth & Wissel, 1992)
Schooling rules:
1. Cohesion
2. Separation
3. Alignment
Fish schooling
Self-Organization Hypothesis:
Few simple rules in response to local information from
neighbouring fish generate schooling patterns
without directly coding for them. (Huth & Wissel, 1992)
To test hypothesis and understand mechanism:
Models?!
Agent-Based Models (ABM)
Models
What is a model?
Models
Models
Models
Models
Models
Definition:
Representation of a system of entities,
phenomena, or processes
to simplify, visualize, simulate, manipulate and
gain intuition about the entity, phenomenon or
process being represented.
Simplified Realistic Understandable Predictive Explaining Precise
Simplification
versus
Realism
www.wikipedia.org
Collective motion
Model rules:
1. Cohesion
2. Separation
3. Alignment
Craig Reynolds 1987: bird flocking (BOIDS)
Huth & Wissel 1992: fish schooling
Hooper, 1999: predator avoidance (cool school)
Collective motion
Conclusions from the model:
Simple rules can account for complex pattern
No leader, no external cue nessecary
Schools could be self-organizing
No proof of real mechanism
Proven: possible explanation works
2nd part
Scientific models
Spatial
dynamical
ordinary differential equations
deterministic
stochastic
(ABM)
CA
nonlinear
AGENT-BASED MODELS
IBM
monte carlo simulation
IOM
partial differential equations
agent-based models
complex systems
static probabalistic
ORDINARY
DIFFERENTIAL EQUATIONS
ABM
(ODE)
difference equation
cellular automata
ODE
PDE
linear
Predator-prey system
+
-
sheep
wolves
+
a) data:
sheep
wolves
b) model:
sheep
wolves
-
+ sheep
+
wolves -
-
+ sheep
+
wolves -
ODE:
ABM:
Population densities
Discrete indiviuals
sheep
wolves
-
+ sheep
+
wolves -
ODE:
ABM:
Equations
Rules
dS/dt
dW/dt
= bS – pSW
= pSW - dW
Sheep
=
+ birth*Sheep
– pred.*Sheep*Wolves
Wolves =
+ pred.*Sheep*Wolves
– death*Wolves
(if-then, loop,
scheduling)
SHEEP:
If I meet wolve: die!
With chance = birthrate: Reproduce!
WOLVES:
If I meet sheep: energy +1
If energy (from sheep) = 0: die!
With chance = birthrate: Reproduce!
-
+ sheep
+
wolves -
ODE:
ABM:
Deterministic
Stochasticity
(pseudo-random numbers)
sheep
wolves
... to represent
variability of processes
that cannot or need not
to be modelled
deterministically
After Grimm 2005
-
+ sheep
+
wolves -
ODE:
ABM:
Non-spatial
Homogenity
Well mixed
Explicitly spatial
Heterogenity
Local interactions
(bottom-up, adaptive)
Patterns
-
+ sheep
+
wolves -
ODE:
ABM:
Homogeneous
population
Individual variation
(age, colour, knowledge, spatial
position, size, sex, ...)
Agent-based Models
= Agent-based Models
(ABM)
= Individual-based Models
(IBM)
= Individual-oriented Models (IOM)
... describe behaviour, variability and
interactions of autonomous individuals.
After Grimm 2005
Collective foraging
Ants: Trail formation, transporter recruitment,
efficient path finding, PHEROMONES!
Collective foraging
Collective decision of colony:
Selection of richest of two foods
Selection of shortest path
Hyp 1: directed by leader (queen?)
Hyp 2: Self-organization
Global pattern emerges
from simple rules
and local information
Collective foraging
Foraging rules:
Execute random walk
or follow strongest pheromone trail
Food found:
walk home & leave pheromone trace
Resnick, M. (1994)
Collective foraging
Self-organization:
Simple rules
No global knowledge, local information
Self-reinforcing phermone trails
Feedback via environment
Emergence of accurate (not perfect!) collective decision:
efficient path selection.
Self-organization
Mechanism:
Information from neighbours
Information from local environment
(stigmergy)
Feedback from emerging structure
(control, signal)
Emergent properties
... arise out of interactions between lower-level
entities, yet are novel and irreducible to them.
(Stanford Encyclopedia of Philosophy)
Emergent property:
Order, organization,
pattern on group level
Entities:
Individuals without
global knowledge,
plan or intent
Emergence
Self-organization
Complex Systems
physical and chemical systems (liquid)
biological systems (cell, brain)
social systems and organizations (stock market, social structures)
Complex system patterns often
emerge through self-organization.
Complex Systems
Multiple levels of organization!
Individual < subgroup < population
Interconnected, interdependent
Higher level affects lower one
Higher level has “behaviour” on its own
Emergent property: Substrate to evolution
3rd part
ABM in science?
Criticism:
Too complex to be understood
Impossible to include everything in a model
Too many parameters unknown
Hard to test
Parameters can tweak everything
“Gaming”
After Grimm 2005
Modelling cycle
After Grimm 2005
Modelling cycle
Formulate the question:
Filter for essential
processes
Not model per se,
but for specific purpose
After Grimm 2005
Modelling cycle
Assemble hypotheses:
Starting point: conceptual
model (drawing)
Based on empirical data,
experience, theory,
gut feeling
What do we expect to see?
PATTERNS (at multiple levels)
After Grimm 2005
Modelling cycle
Chose model structure:
Which entities?
Which processes?
How to model/represent
processes?
After Grimm 2005
Modelling cycle
Implement model:
Write program code
(if-then rules, loops)
After Grimm 2005
Modelling cycle
Analyze the model I:
Controlled simulation
experiments
(visual debugging, process understanding,
extreme tests)
Design and analysis just
as with “real” experiments
(statistics on program generated data)
After Grimm 2005
Modelling cycle
Analyze the model II:
Much freedom and control
in experimental setup
(upscale numbers and time,
hypothetical thought experiments)
Can the model reproduce
PATTERNS?
(at multiple levels!!!)
After Grimm 2005
Modelling cycle
Analyze the model IIIa:
Change parameter/rule:
Group
Group
Same
Effect on system behaviour?
parameter
(knockout, sufficient & neccessary)
setting:
Individual Individual
Changing
parameter
setting:
Group
Group
Individual
Individual
Group
Group
Group
Group
Individual
Individual
Individual
Individual
After Grimm 2005
Modelling cycle
Analyze the model IIIb:
Multiple runs, same
parameter set
(account for stochasticity)
Same
parameter
setting:
Group
Group
Group
Group
Individual
Individual
Individual
Individual
After Grimm 2005
Modelling cycle
Communicate the model:
Materials & Methods
Reproducability of results
After Grimm 2005
ABM – a scientific method
Model validation:
New hypotheses from the model
Not built into the model beforehand
Can be tested in “real” system
After Grimm 2005
Primate social cognition
Social structure: dominance hierachy
Spatial structure: centrality of dominants
Primate social cognition
DOMWORLD (Hemelrijk 1999, Hogeweg1988)
Simple rules > complex behaviour
1. Grouping rules:
Max view
Near view
Personal space
Primate social cognition
Dom-value: rank
(initially all the same)
2. Interaction rules:
Prediction
(mental simulation)
Dominance contest:
Win chance ~ rank
Loser flees, winner chases
Dom-value update according to expected outcome
(winner-loser effect)
Primate social cognition
Dominance hierarchy
(differentiation from initially equal individuals)
(individual variation!!!)
Emergence of spatial structure
(centrality of dominant individuals as
unintentional side-effect)
Hemelrijk, 1998
Stabilizing feedback from spatial structure
on social structure:
neighbors of similar rank
no unexpected outcomes
no big updates of dom-value
Primate social cognition
INSIGHTS:
No centripetal instinct necessary for spatial structure
From side effect to evolutionary substrate
Emerging spatial structure feeds back on social structure
ABM internship: http://bio.uu.nl/behaviour/people/Evers/index.html
Evolution in silico
Evolution ingredients:
Mutations:
Inheritence of traits (to offspring)
Chance of changing traits
Selection:
Define fitness measure
Explicit selection
(once in a while: take out 100 best and reproduce)
Reproduction/death
(dependent on fitness measure)
Conclusions
Biological systems:
Organisation / patterns
Several possibilities:
Central, fixed control
(leader, blueprint, ...)
Self-organisation
Interactions between individuals
Emergence of pattern on group level
Conclusions
ABM: useful tool to study / understand
Multiple connected levels
Behavioural rules
(individual, group)
Explicit spatiality:
Locality
Heterogenous space
Individual variation
(hierarchy, evolution)
Heraklit: You never enter the same river twice.
Conclusions
Models are useful:
Development: Explicit formulation of processes
Simplification: Identify essential (sufficient & nessecary)
processes
Scientific research tool:
Controlled experiments (knockout, change parameter/rule)
Series of runs (variation)
Statistics on generated data
Material & methods
Reproduced results: validation
Group
Group
Group
Individual
Individual
Individual
Conclusions
Models advantages:
Freedom in experimental setup
Little time, money, animals, facilities needed
No ethical objections
Generate new hypotheses
Reveal general and unexpected properties of a
system
Help understanding a system
Change way of thinking about a system
Proust: The real voyage of discovery lies not in
finding new landscapes, but in having new eyes.
Sources
Modelling, general
J. J. Bryson,
Bryson Y. Ando, and H. Lehmann, “Agent-based modelling as scientific method: a case study analysing primate social behaviour,”
Philosophical Transactions of the Royal Society B: Biological Sciences 362, no. 1485 (2007): 1685-1698.
D. L. DeAngelis and W. M. Mooij, Individual-based modeling of ecological and evolutionary processes. Annual Reviews in Ecology, Evolution
and Systematics 36: 147-168.
V. Grimm,
Grimm “Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future?,” Ecological
Modelling 115, no. 2 (1999): 129-148.
V. Grimm and S. F. Railsback, Individual-based Modeling and Ecology (Princeton University Press, 2005).
V. Grimm et al., “Pattern-Oriented Modeling of Agent-Based Complex Systems: Lessons from Ecology,” Science 310, no. 5750 (November 11,
2005): 987-99.
J. W. Haefner,
Haefner Modeling Biological Systems: Principles and Applications, 2nd ed. (Springer, 2005).
C. K. Hemelrijk,
Hemelrijk “Understanding Social Behaviour with the Help of Complexity Science (Invited Article),” Ethology 108, no. 8 (2002): 655-671.
P. Hogeweg,
Hogeweg “MIRROR beyond MIRROR, Puddles of LIFE,” Artificial Life (1989): 297–316.
T. J. Prescott,
Prescott J. J. Bryson, and A. K. Seth, “Introduction. Modelling natural action selection,” Philosophical Transactions of the Royal Society
B: Biological Sciences 362, no. 1485 (2007): 1521-1529.
http://www.swarm.org/index.php/Main_Page
http://ccl.northwestern.edu/netlogo/
http://www.abmsystemsbiology.info
Complexity, Emergence and SelfSelf-organization, general
http://www.santafe.edu/
http://www.vs.uni-kassel.de/systems/index.php/Emergence
http://www.pbs.org/wgbh/nova/sciencenow/3410/03.html
http://www.cna.org/isaac/Glossb.htm
Biological examples of emergence and selfself-organization
J. Buck,
Buck “Synchronous Rhythmic Flashing of Fireflies. II.,” The Quarterly Review of Biology 63, no. 3 (1988): 265.
S. Camazine et al., Self-Organization in Biological Systems: (Princeton University Press, 2003).
http://mute-net.sourceforge.net/howAnts.shtml
Sources
AgentAgent-based models of animal behaviour
R. Axelrod,
Axelrod The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration (Princeton University Press, 1997).
R. Axelrod and W. D. Hamilton, “The evolution of cooperation,” Science 211, no. 4489 (1981): 1390-1396.
H. de Vries and J. C. Biesmeijer, “Modelling collective foraging by means of individual behaviour rules in honey-bees,” Behavioral Ecology and
Sociobiology 44, no. 2 (1998): 109-124.
H. de Vries and J. C. Biesmeijer, “Self-organization in collective honeybee foraging: emergence of symmetry breaking, cross inhibition and
equal harvest-rate distribution,” Behavioral Ecology and Sociobiology 51, no. 6 (2002): 557-569.
C. K. Hemelrijk,
Hemelrijk “Towards the integration of social dominance and spatial structure,” Animal Behaviour 59, no. 5 (May 2000): 1035-1048,
doi:10.1006/anbe.2000.1400.
C. K. Hemelrijk,
Hemelrijk “Social phenomena emerging by self-organisation in a competitive, virtual world (‘DomWorld’),” 1st International Conference
of the European Society for Social Simulation (ESSA 2003), Groningen, September (2003).
P. Hogeweg,
Hogeweg “MIRROR beyond MIRROR, Puddles of LIFE,” Artificial Life (1989): 297–316.
P. Hogeweg and B. Hesper, “The ontogeny of the interaction structure in bumble bee colonies: A MIRROR model,” Behavioral Ecology and
Sociobiology 12, no. 4 (1983): 271-283.
C. Honk and P. Hogeweg, “The ontogeny of the social structure in a captive Bombus terrestris colony,” Behavioral Ecology and Sociobiology
9, no. 2 (1981): 111-119.
H. Lehmann,
Lehmann J. Wang, and J. J. Bryson, “Tolerance and Sexual Attraction in Despotic Societies: A Replication and Analysis of Hemelrijk
(2002),” Modelling Natural Action Selecton: Proceedings of an International Workshop, Edinburgh. The Society for the Study of Artificial
Intelligence and the Simulation of Behaviour (AISB) (2005).
S. C. Pratt et al., “An agent-based model of collective nest choice by the ant Temnothorax albipennis,” Animal Behaviour 70, no. 5 (2005):
1023-1036.
M. Resnick,
Resnick Turtles, Termites, and Traffic Jams: Explorations in Massively Parallel Microworlds (MIT Press, 1994).
C. W. Reynolds,
Reynolds “Flocks, Herds, and Schools: A Distributed Behavioral Model,” Computer Graphics 21, no. 4 (1987): 25-34.
W. I. Sellers,
Sellers R. A. Hill, and B. S. Logan, “An agent-based model of group decision making in baboons,” Philosophical Transactions of the
Royal Society B: Biological Sciences 362, no. 1485 (2007): 1699-1710.
D. J. van der Post and P. Hogeweg, “Resource distributions and diet development by trial-and-error learning,” Behavioral Ecology and
Sociobiology 61, no. 1 (2006): 65-80.
D. J. van der Post and P. Hogeweg, “Diet traditions and cumulative cultural processes as side-effects of grouping,” Animal Behaviour 75, no. 1
(2008): 133-144.
http://www.red3d.com/cwr/boids/