Agent-Based Modeling
PSC 120
Jeff Schank
Agent-Based Modeling
• What Phenomena are Agent-Based
Models Good for?
• What is Agent-Based Modeling (ABM)?
• What are the uses of ABM?
• Model Assumptions
• Analyzing Models
• Comparing Models to Data
What are they good for?
• Complex systems
• Emergent phenomena
• When we understand the parts better
than the whole
• When we seek mechanistic
explanations
• When we are faced with multiple levels
of organization
What is ABM?
• ABM is a general Style of modeling that focuses on individuals
– Agents can represent people, animals, or entities at different levels of
organization
– The modeling of agents typically require the specification of rules for
agent behavior and interactions
• ABM is a style of modeling that has features of both
experimental and mathematical styles of thinking
– When designing an ABM it is often useful to think like an
experimentalist
• What behaviors and properties do/should agents have?
• How should the environment be designed and controlled?
• How should experiments be designed?
– Most ABMs have probabilistic elements, so each simulation experiment
may differ considerably even for the same parameter values
– Thus, a large number of simulated experiments are often required to
analyze an ABM for a given set of parameters
– From a mathematical style of thinking, the emphasis should be on
investigating the entire parameter space or regions of interest in more
complex models
What are the uses of ABM?
• To model complex systems in which individual behavior and
properties are better understood than the behavior and
properties of the system
–
–
–
–
Molecular and cellular biology
Ecology
Anthropology and other social sciences
Animal behavior
• Exploratory modeling
– Artificial life
– Evolutionary game theory
• Investigating the robustness of analytical results
– Evolutionary game theory
– Ecology
– Evolutionary Biology
Analysis of Models
• Parameter sweeps
– Systematically vary one or move parameters of a model
– The limitations are on the number of parameters
• If there are two parameters and you want to look at 5 values
for each parameter, then you must conduct 5 × 5 = 25 sets
of simulations
• As you can see, the number of sets of simulations to be
conducted increases exponentially with the number of
parameters to be swept
• Another approach is to use genetic algorithms to
evolve models that either fit some set of goals or
data of interest
• I’ll discuss an example of both approaches
Ovarian-Cycle Synchrony
• Does ovarian-cycle synchrony exist in
mammals?
• The problem of cycle variability
• Ovarian cycles and female mate choice
– The cost of synchrony
Synchrony?
• Studies have reported synchrony in
– Women
– Norway rats
– Golden hamsters
– Golden lion tamarins
– Chimpanzees
• All are fundamentally flawed and more
recent studies have found no effects
The Cost of Synchrony
• There are two types of fitness costs for
synchronized females
– Male quality
– Mating opportunities
• To explore these costs, I built an ABM,
based on J. B. Calhoun’s study: The
Ecology and Sociology of The Norway
Rat
Calhoun’s Rats ABM
• Aims and Design
– Ecologically realistic
– Based on data
– 5 to 10 reproductive females at a given
time
– 61 adult males (7 high, 12 medium, 42 low)
– Movement is determined by “collapsing”
preferences into a local probability space
surrounding a model rat
Two views of the Pen
The Trails Map
ABM Model
Synchrony
Synchrony by Chance
Synchrony Distributions
Male Quality & Synchrony
0.78
Male Quality
0.73
N=5
N=6
N=7
N=8
N=9
N = 10
8
9
0.68
0.63
0.58
2
3
4
5
6
Synchrony Level
7
10
Matings & Synchrony
21
N=5
N=6
17
N=7
N=8
15
N=9
N = 10
Matings
19
13
11
9
7
5
2
3
4
5
6
Synchrony Level
7
8
9
10
Male Quality & Cycle Length
0.675
0.670
Male Quality
0.665
0.660
0.655
0.650
0.645
0.640
0.635
0.630
4
5
6
Cycle Length
7
Matings & Cycle Length
19
Maings
18
17
16
15
4
5
6
Cycle Length
7
Conclusions
• Ovarian cycles may have evolved to
facilitate female mate choice
• Synchrony has fitness costs
• Cycle variability may have fitness
benefits in promiscuous mating
systems
The Development of Locomotion
•
How do animals do what they do?
How do we answer this question?
•
Start simple and work to the complex
•
If we want to understand how something works
in space and time, it is often a good idea to
build it or something like it.
•
We cannot just build animals at different stages
of development, but we can build models of
them, which may help us understand them
better (i.e., simulation, robotic)
•
Rat Pups
•
Born with very limited sensorimotor
capabilities
– Blind and deaf till days 13 to 15
– Legs cannot lift the body off the ground till after
day 10
•
However, they can
aggregate in huddles
and thermoregulate
Locomotor Development
Eyes and ears
open
First projections
from brainstem
CPG begin to
function (birth)
Motor Neurons
Excitable
Corticospinal
Coupled activity
Tract
walking
crawling
In vitro and In vivo studies
Fetal
-7
-6
-5
-4
-3
Immature
-2
-1
0
1
2
3
4
5
Transitory
6
7
8
9
10
Stages of Developement (Days)
11
12
13
Adult
14
15
16
17
18
19
Behavior in a Temperature Controlled
Arena: A Simple Paradigm
Metrics
•
Basic metric: tip of nose
base of tail location
•
Derived metrics
–
Activity
–
Object Contact
–
Speed
–
Aggregation
–
Conditional Probabilities
7 and 10 Day Old Individual
Locomotion: Examples
20
0.25
15
Day 7
10
0.2
0.15
0.1
0.05
5
0
0
0
5
10
15
20
25
30
20
0.45
0.4
0.35
15
Day 10
0.3
0.25
0.2
10
0.15
5
0.05
0
0.1
0
0
5
10
15
20
25
30
7 and 10 Day Old Individual & Group
Locomotion
Individual
Group
An Agent-Based Model
Column
Row
P
P W
E
E
E
E E
Whole-Body Locomotion Kinematics
0 0 0
0 0 0
.5 0 .5
3
2
1,5
4,7,11 9
6,10
8
1: R, 2: L, 3: L, 4: R, 5: L, 6: R, 7: R, 8: L, 9: L, 10: R
Whole-Body Locomotion Kinematics
é0 0 0 ù
ê
ú
ê.5 0 .5ú
êë0 0 0 úû
3
9 8
5
10,11 7
6
2
4 1
1: R, 2: L, 3: L, 4: R, 5: L, 6: R, 7: R, 8: L, 9: L, 10: R
Genetic Algorithms
•
Arrange the parameters of the into a
“chromosome”
r
w
f
f
fl
l
bl
b
…
•
Create a population of models
•
Perform mutation and crossover on pairs of
models
•
Run a number of simulations and choose the
parameters that best fit the data
Locomotion Kinematic Results
Day 7
Individual
Group
Day 10
é.090 .017 .090ù
ê
ú
ê.091 0 .091ú
êë.276 .070 .276úû
é.068 .054 .068ù
ê
ú
0 .314ú
ê.314
êë.056 .068 .056úû
é.090 .017 .090ù
ê
ú
ê.091 0 .091ú
êë.276 .070 .276úû
é.003 .401 .003ù
ê
ú
ê.181 0 .181ú
êë.114 .003 .114úû
7 and 10 Day Subgroup Formation
Day 7
Day 10
7 and 10 Day Old Individual
Locomotion: Examples
20
0.25
15
Day 7
10
0.2
0.15
0.1
0.05
5
0
0
0
5
10
15
20
25
30
20
0.45
0.4
0.35
15
Day 10
0.3
0.25
0.2
10
0.15
5
0.05
0
0.1
0
0
5
10
15
20
25
30
Model Examples
0.3
0.16
0.25
0.14
0.12
0.2
0.1
0.15
0.1
0.05
0.08
Day 7
0.06
0.04
0.02
0
0
0.35
0.35
0.3
0.3
0.25
0.25
0.2
0.15
0.1
0.05
0
Day 10
0.2
0.15
0.1
0.05
0