Agent Based Models
Recommended reading:
Macal CM & North MJ (2010). Tutorial on agent-based modelling and
simulation. Journal of Simulation 4, 151-162.
Agent-based modelling and
simulation (ABMS)
• „relatively new approach to modelling systems composed of
autonomous, interacting agents“
• „a way to model the dynamics of complex systems and complex
adaptive systems“
• Important themes: self-organization, emergence of order,
collective effects of behaviors and interactions
• existence of modelling tools
Historical Roots
Game Theory
Complex Systems
Complex Adaptive
Systems
Artificial Life
(ALife)
Agent-based
modelling
Early Example 1:
J.
Phys.
I
France
(1992)
2
2221-2229
1992,
DECEMBER
PAGE
2221
aassification
Physics
Abstracts
02.50
02.70
A
o3AoG
cellular
Kai
Nagel(~)
and
Mathematisches
(~)
fir
(~) Institut
Germany
(Received
3
waves
with
analytical
Michael
We
introduce
increasing
results
can
vehicle
September 1992)
10
discrete
stochastic
a
of the
be
zu
accepted
1992,
simulations
traffic
I~6ln 41, Germany
I~6ln, Weyertal 86-90, W-sore
Universitit
I~6ln 41,
K61n, Zfilpicher Str. 77, W-sore
zu
Universitit
Physik,
Theoretische
freeway
for
Schreckenberg(~)
Institut,
September
Abstract.
Monte-Carlo
model
automaton
model
density,
obtained.
show
as
is
a
automaton
transition
observed
in
model
to
freeway
simulate
from
laminar
traffic
flow
real
freeway
traffic.
For
to
traffic.
start-stop-
special
cases
which
steps,
I)
Acceleration:
next
ahead
car
velocity
if the
Randomization:
3)
4)
motion:
Car
Through
reduces
speed
its
if
the
p,
by
site I
at
I [v
j
-
velocity
if the
and
vmax
advanced
vehicle
a
j
to
than
one
sees
[v
the
distance
v
-
to
the
at
site
+11.
vehicle
next
11.
of each
(if greater
vehicle
zero)
than
11.
v
-
vehicle
each
cars):
probability
[v
one
is lower
vehicle
a
I, the speed is
+
v
other
to
with
by
decreased
is
of
v
larger than
is
Slowing down (due
I + j (with j < v), it
2)
N°12
performed in parallel for all vehicles:
are
advanced
is
sites.
v
JOURNAL
2224
DE
PHYSIQUE
I
traffic
modelled
one
very general properties of single lane
are
on
(road)
space
probabilistic cellular
rules [9, 10]. Already this simple
the basis of integer valued
automaton
nontrivial
and realistic
behavior.
model shows
Step 3 is essential in simulating realistic traffic
flow since
otherwise
the dynamics is completely
deterministic.
natural
It takes into
account
4........,4,,.,,......4.............,.6.,,...01,1,2,,...3.,..,.,.,.,,.,
(road) to human
behavior
fluctuationsspace due
due to varying ....6.......,,6..,.,......6................O.1.0.2..3...,,.4...........
external
conditions.
Without
velocity
or
.........6.,...,...4...,,,,,,,.4...,....,,.1..00...3,..3.,...,.6,,,,...
randomness, every initial configuration of vehicles and corresponding
velocities
this
reaches
..,,.4.........,,,6,,,.....4........,,..3....000.........2...3.........
backwards (I.e. opposite the vehicle motion)
pattern which is shifted
very quickly a stationary
the
steps
AUTOMATON
CELLULAR
A
MODEL
to
four
FOR
FREEWAY
TRAFFIC
N°12
........4................6......6......6........OO.1.......4..........6
..4.........6.................4......6......2...00..2..........6.......
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2223
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.........................4.................,..............6...........6
.............................4.................................6.......
site
one
The
.6...............................6..................................4..
6.....6...............................6..............................:
.....4.....4.......,.......................6...........................
time.,.......6.....4..........:....................6......................
step.
per
.6............3....4.........,.....,.......,.......,.4.................
......6......,.,,3.....4.,,.......................,,.,...4,,....,......
simulations
Carlo
...........6......,.3......6................,..,..,...,......6..,......
Monte
~
~
for
below.
stated
reasons
Qd
positions
the
have
,......,,...,.,.6.,....4........4.....,..,........................4....
.....................4.....6........6.................................4
model
The
.........................6......4........4.............................
..............................6.....6........6.........................
...................................6.....4........6....................
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the
of
following
(usually only
been
carried
implemented
.+~
integer
an
l~
f~
been
has
and
cars
mainly
for
array
out
in
the
.,,,...,.4.,...........6.......4...........0.001.,........,3,...3......
.............4..............6......4.......0.00.2.............4....4...
4................4...............6.....2...I.Ol.,,2.,..........,.,3....
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........6................6..............0,I.0.2.,2,..,.3.......,.......
.............6................6.........0..00...I,.2,.....3....,......,
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.6.....4.......6............,.6.........0.000...........3......4.......
a
......4....6........6..............4....1.001..............3.......4...
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....6..........4.....6......,6......,,..0000..I...,.......,....,..6....
.........4.........6..,.,,4.,.,...4.....0000.,.2,..........,...........
.............6..........4.....6.......0.O001.....2.....................
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a
.6................,.,.4.........2...0.1.000...3..,...3.................
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....6.......6.......6.......,...,.00.0.O.I.1....3.............4......6.
.........4.......6.......6........0i,I.O.,0,I,.....3..............4....
.............4........6..,..,.2...I.O.00.,1..2.,......4...,...........6
......,..........6.........4....2..0i.0i...2...3..........6............
6,.,.,.,,.,...,.......4...,,,..2..0i,00.2....3.,..3,...........4.......
.....4....................6......00.000...3.,...3....4.....,.......6...
with
the
choice
of vmax
FORTRAN, using
velocities.
For
=
logical
the
'realistic
5 for
array
case'
interesting regime of
relatively low
about one fifth), an
density of occupied sites
implementation using
IF-statements
about five times faster than an implementation using only boolean
variables
has been
and
Fig.
(low) density
complete velocity-update
just
(necessary
Empty
represented for
fordensity
multispin
coding
As the expected gain of
operations
32 cars
at once).
low traffic
by
occupied by
dot,
represented by
integer
velocity.
densities,
multispin coding would therefore give only a factor of about six, we postponed the work on a
bitwise
implementation.
Fig.2.
figure I,
picture
higher density
Note the
usually
possible
reality. Thus,
conditions,
high
traffic density microsecp~
densities (=
occupancies)
fixed
site
averaged
period
motion
traffic jam. about
workstation
site-updates
The speed on an IBM-RS/6000 320H
0.2
was
per
of
I.
after
=
Simulated
traffic
5
at
made
we
sites
a
of o.03
a
is
and
which
we
the
....................................................6.....6.........4..
.........................................................6.....4.......
.........................................................4....4...
...........................................................3....
.....................................................................3.
further
one
low
which
vmax
see
not
are
a
undisturbed
car
cars
before
per
the
Each
site.
new
the
are
line
shows
motion.
car
sites
number
observations:
the
traffic
in
the
lane
are
of its
At
motion.
in
on
in
a
I
order
to
mimick
over
a
real
time
we
T:
Same
measured
of
the
as
but
at
a
of
o.I
cars
per
site.
backward
Early Example 2:
Schooling of fish
Advantage of schooling and flocking
Richard Dawkins: (The Selfish Gene)
A simple strategy for a predator animal is to chase the closest prey animal in its
vicinity. This is reasonable because it expends the least amount of effort for the
predator.
Also: fish in school may be harder to find
If you have buddies all around you, you are pretty save!
But how? Bird Flocking and Boids
(bird+android = boid)
Craig Reynolds (1986): a few local rules sufficient to produce
flocking. Nice and simple example of emergent property.
Each individual follows these (informal) rules:
1. fly towards the centre of mass of neighbors
2. keep small distance away from other objects (including other
boids).
3. match velocity with near boids.
1. cohesion
2. separation
3. alignment
BOIDS in action
http://www.youtube.com/watch?v=kJiKKNCQorQ
Modern Application Areas
• economics (stock markets, supply chains, comsumer purchasing
behavior, „agent-based computational economics“, ...)
• biology/medicine (tissue growth, modelling the immune system,
spread of epidemics, ...)
• social sciences (traffic simulations, crowd behavior, tourism, fall
of ancient civilizations, modeling engagement of forces on the
battle field, ...)
• ecology (interactions between individuals of different species,
predator-prey dynamics, ...)
• physics (self-assembly of nano-materials, ...)
Continuum of models
• simple and elegant
• complex, large-scale
•„academic“, idealized
• great detail
• only essential details
• models validated against
• aimed at developing
insights into a process or
behavior
data
• results intended to inform
policies and decision making
Figure 1 Articles published yearly
Niazi & Hussain
(2010).
Agent-based
computing
multi-agent
systems
In addition,
since
the popularity
of from
a domain
is known
totobeagent-based
based on
Models: a visual survey
its
number of citations, we need to observe this phenomena closely. It can be
observed in the graph using data from the Web of Science in Figure 2. Thus,
starting from a very small number of citations, Agent-based computing has risen
to almost 1630 citations alone during the year 2009.
Figure 2 Citations per year
Analysis
using
NWB
Niazi
& Hussain
(2010)
ARTIF INT” and “P NATL ACAD SCI USA”.
Table 3 Core Journals based on frequency
Frequency
Title
Abbreviated Title
295
Ecological Modelling
ECOL MODEL
231
Nature
NATURE
216
Science
SCIENCE
167
Journal of Theoretical
J THEOR BIOL
Biology
145
Ecology
ECOLOGY
123
The American Naturalist
AM NAT
121
Trends in Ecology &
TRENDS ECOL EVOL
Evolution
121
Lecture Notes in Artificial
LECT NOTES ARTIF INT
Intelligence
121
Proceedings of the National
Academy of Sciences
Analysis of Categories
Niazi & Hussain (2010)
P NATL ACAD SCI USA
n,
),
u2.2. Structure of an agent-based model
nt
ll
A typical agent-based model has three elements:
x
s;
1. A set of agents, their attributes and behaviours.
y
2. A set of agent relationships and methods of interaction:
An underlying topology of connectedness defines how
s.
and with whom agents interact.
ht
3. The agents’ environment: Agents interact with their
as
environment in addition to other agents.
d
y
A model developer must identify, model, and program these
g
elements to create an agent-based model. The structure of a
y
typical agent-based model is shown in Figure 1. Each of the
g
components in Figure 1 is discussed in this section. A
d
Macal & North (2010)
computational engine for simulating agent behaviours and
nt
Structure of an agent-based
model
term ABMS in this article to refer to both
simulation, in which a dynamic and time-
Figure 1
time-stepped, activity-based, or discrete-event
structures.
The structure of a typical agent-based model, as in Sugarscape (Epstein and Axtell, 1996).
Macal & North (2010)
What is an „agent“?
• different definitions in the literature
• single most important defining
characteristic is „capability to act
autonomously“
• for some authors: simple set of fixed ifthen-rules is sufficient
• other authors require adaptation: ability to
change rules governing behavior; ability to
learn
Essential Agent Characteristics
• self-contained, modular, and uniquely
identifiable individual
• autonomous and self-directed
• has state that varies over time
• is social, i.e., has dynamic interactions with
other agents that influence its behavior
Other Useful Agent
Characteristics
• adaptive: adapt behavior based on
previous experiences (learning and
memory); learning can also occur in a
population through (evolutionary) selection
• goal-directed: try to achieve goals or
maximize objectives
• heterogeneous: not like indistinguishable
atoms but with different properties, goals,
experiences, etc.
Typical Agent Structure
154 Journal of Simulation Vol. 4, No. 3
2.4. Interacting
Macal & North (2010)
Figure 2
A typical agent.
Agent-based mo
relationships an
agent behaviour
interactions are
to who, and t
interactions. Bo
agent-based mod
One of the te
modelling is tha
agent. Agent-ba
is no central a
available inform
viour in an effo
interact with oth
with all the oth
systems. Agents
agents, termed t
Creating Agent Models
Option 1: begin with normative model, e.g., agent
attemps to maximize profits
Option 2: begin with behavioral model. Could be
based on behavioral theory or empirical data
Links to ethology, psychology, neuroscience,
artificial intelligence, machine learning, ...
Agent Interactions
• local information: agent‘s decision based on the
information that is locally available to it (and
changing)
• interaction typically with (changing) neighbors
• many different topologies
interact with their environment and with other
The environment may simply be used to provide
ation on the spatial location of an agent relative to
that do not currently exist. Several agent-based model
applications are summarized in this section, but the
is only a small sampling. Several of the papers cove
Interaction Topologies
Figure 3
Macal & North (2010)
Topologies for agent relationships and social interaction.
Questions for Agent Design
1. What specific problem should be solved by the model? What specific questions should the
model answer? What value-added would agent-based modelling bring to the problem that
other modelling approaches cannot bring?
2. What should the agents be in the model? Who are the decision makers in the system? What
are the entities that have behaviours? What data on agents are simply descriptive (static
attributes)? What agent attributes would be calculated endogenously by the model and
updated in the agents (dynamic attributes)?
3. What is the agents’ environment? How do the agents interact with the environment? Is an
agent’s mobility through space an important consideration?
4. What agent behaviours are of interest? What decisions do the agents make? What
behaviours are being acted upon? What actions are being taken by the agents?
5. How do the agents interact with each other? With the environment? How expansive or
focused are agent interactions?
6. Where might the data come from, especially on agent behaviours, for such a model?
7. How might you validate the model, especially the agent behaviours?
Macal & North (2010)
Examples
Model (GSAM)
• 6.5 billion distinct
agents, 300 million
cyber-people in US
• movement and
day-to-day
interactions
• epidemic „war
games“, quick
feedback for
decision makers
Modelling to contain pandemics
Agent-based computational models can capture irrational behaviour, complex social networks
and global scale — all essential in confronting H1N1, says Joshua M. Epstein.
A
s the world braces for an autumn wave appropriately; the capacity to do so is improvof swine flu (H1N1), the relatively new ing through survey research, cognitive science,
technique of agent-based computational and quantitative historical study.
modelling is playing a central part in mapping
Robert Axtell and I published a full agentthe disease’s possible spread, and designing based epidemic model1 in 1996. Agents with
policies for its mitigation.
diverse digital immune systems roamed a landClassical epidemic modelling, which began scape, spreading disease. The model tracked
in the 1920s, was built on differential equa- dynamic epidemic networks, simple mechations. These models assume that the popula- nisms of immune learning, and behavioural
tion is perfectly mixed, with people moving
from the susceptible pool,
to the infected one, to the
recovered (or dead) one.
Within these pools, everyone is identical, and no one
adapts their behaviour. A triumph of parsimony, this approach
revealed the threshold nature of epidemics and explained ‘herd immunity’, where
the immunity of a subpopulation can stifle
outbreaks, protecting the entire herd.
But such models are ill-suited to capturing complex social networks and the direct
Simulation of a pandemic beginning in Tokyo.
contacts between individuals, who adapt their
behaviours — perhaps irrationally — based on changes resulting from disease progression, all
disease prevalence.
of which fed back to affect epidemic dynamics.
Agent-based models (ABMs) embrace this However, the model was small (a few thousand
complexity. ABMs are artificial societies: every agents) and behaviourally primitive.
single person (or ‘agent’) is represented as a disNow, the cutting edge in performance is the
tinct software individual. The computer model Global-Scale Agent Model (GSAM)2, developed
tracks each agent, ‘her’ contacts and her health by Jon Parker at the Brookings Institution’s
status as she moves about virtual space — travel- Center on Social and Economic Dynamics in
ling to and from work, for instance. The models Washington DC, which I direct. This includes
can be run thousands of times to build a robust 6.5 billion distinct agents, with movement
statistical portrait comparable to epidemic data. and day-to-day local interactions modelled as
ABMs can record exact chains of transmission available data allow. The epidemic plays out
from one individual to another. Perhaps most on a planetary map, colour-coded for the disimportantly, agents can be
ease state of people in different
made to behave something like
“Agents can be made regions — black for susceptireal people: prone to error, bias,
to behave something ble, red for infected, and blue
for dead or recovered. The
fear and other foibles.
like real people: prone map pictured shows the state of
Such behaviours can have a
huge effect on disease progresaffairs 4.5 months into a simuto error, bias, fear.”
sion. What if significant numlated pandemic beginning in
bers of Americans refuse H1N1 vaccine out of Tokyo, based on a plausible H1N1 variant.
fear? Surveys and historical experience indicate
For the United States, the GSAM contains 300
that this is entirely possible, as is substantial million cyber-people and every hospital and
absenteeism among health-care workers. Fear staffed bed in the country. The National Center
itself can be contagious. In 1994, hundreds of for the Study of Preparedness and Catastrophic
thousands of people fled the Indian city of Surat Event Response at Johns Hopkins University in
to escape pneumonic plague, although by World Baltimore is using the model to optimize emerHealth Organization criteria no cases were con- gency surge capacity in a pandemic, supported
firmed. The principal challenge for agent mod- by the Department of Homeland Security.
elling is to represent such behavioural factors
Models, however, are not crystal balls
and the simulation shown here is not a prediction. It is a ‘base case’ which by design is
highly unrealistic, ignoring pharmaceuticals,
quarantines, school closures and behavioural
adaptations. It is nonetheless essential because,
base case in hand, we can rerun the model to
investigate the questions that health agencies
face. What is the best way to allocate limited
supplies of vaccine or antiviral drugs? How
effective are school or work closures?
Agent-based models helped to
shape avian flu (H5N1) policy,
through the efforts of the National
Institutes of Health’s Models of
Infectious Disease Agent Study
(MIDAS) — a research network
to which the Brookings
Institution belongs. The
GSAM was recently
presented to officials
from the Centers for
Disease Control and
Prevention in Atlanta,
Georgia, and other agencies, and will be integral to MIDAS consulting on H1N1 and other
emerging infectious diseases. In the wake of
the 11 September terrorist attacks and anthrax
attacks in 2001, ABMs played a similar part in
designing containment strategies for smallpox.
These policy exercises highlight another
important feature of agent models. Because
they are rule-based, user-friendly and highly
visual, they are natural tools for participatory
modelling by teams — clinicians, public-health
experts and modellers. The GSAM executes
an entire US run in around ten minutes, fast
enough for epidemic ‘war games’, giving decision-makers quick feedback on how interventions may play out. This speed may even permit
the real-time streaming of surveillance data for
disease tracking, akin to hurricane tracking. As
H1N1 progresses, and new health challenges
emerge, such agent-based modelling efforts
will become increasingly important.
■
J. PARKER
• Global-Scale Agent
OPINION
NATURE|Vol 460|6 August 2009
Joshua M. Epstein is director of the Center on
Social and Economic Dynamics at the Brookings
Institution, 1775 Massachusetts Avenue,
Washington DC 20036, USA.
e-mail: [email protected]
1. Epstein, J. M. & Axtell, R. L. Growing Artificial Societies:
Social Science from the Bottom Up Ch. V. (MIT Press, 1996).
2. Parker, J. A. ACM Trans Model. Comput. S. (in the press).
See Opinion, page 685, and Editorial, page 667.
Further reading accompanies this article online.
Ÿ)''0DXZd`ccXeGlYc`j_\ijC`d`k\[%8cci`^_kji\j\im\[
687 Opinion Epstein Flu models MH CNS.indd 687
J.M. Epstein, Nature (2009)
687
30/7/09 14:46:10
„Base case“ of swine flu (H1N1) epidemic
black: susceptible
red: infected
blue: dead or recovered.
http://www.youtube.com/watch?v=3Q6BJPqgNZI
handle a far wider range of
nonlinear behavior than
conventional equilibrium
models“
• first promising efforts:
•models for bubbles and
crashes
•growth and decline of
companies
•credit sector
• how leverage
(investment of
borrowed funds) affects
fluctuations in stock
prices
• ...
Vol 460|6 August 2009
OPINION
The economy needs agent-based modelling
The leaders of the world are flying the economy by the seat of their pants, say J. Doyne Farmer and
Duncan Foley. There is, however, a better way to help guide financial policies.
I
n today’s high-tech age, one naturally
pull society out of a recession; that, as
assumes that US President Barack
rising prices had historically stimulated
Obama’s economic team and its intersupply, producers would respond to
the rising prices seen under inflation
national counterparts are using sophisby increasing production and hiring
ticated quantitative computer models
more workers. But when US policyto guide us out of the current economic
crisis. They are not.
makers increased the money supply in
The best models they have are of two
an attempt to stimulate employment, it
types, both with fatal flaws. Type one is
didn’t work — they ended up with both
econometric: empirical statistical models
high inflation and high unemployment,
that are fitted to past data. These suca miserable state called ‘stagflation’.
Robert Lucas and others argued in
cessfully forecast a few quarters ahead
as long as things stay more or less the
1976 that Keynesian models had failed
same, but fail in the face of great change.
because they neglected the power of
Type two goes by the name of ‘dynamic
human learning and adaptation. Firms
stochastic general equilibrium’. These
and workers learned that inflation is
just inflation, and is not the same as a
models assume a perfect world, and by
their very nature rule out crises of the
real rise in prices relative to wages.
type we are experiencing now.
As a result, economic policy-makers
Realistic behaviour
are basing their decisions on common
The cure for macroeconomic theory,
sense, and on anecdotal analogies to
however, may have been worse than the
previous crises such as Japan’s ‘lost
disease. During the last quarter of the
decade’ or the Great Depression (see Agent-based models could help to evaluate policies designed to
twentieth century, ‘rational expectations’
Nature 457, 957; 2009). The leaders of foster economic recovery.
emerged as the dominant paradigm
the world are flying the economy by the
in economics. This approach assumes
seat of their pants.
current optimism about the future, and behav- that humans have perfect access to informaThis is hard for most non-economists to ioural rules deduced from psychology experi- tion and adapt instantly and rationally to new
believe. Aren’t people on Wall Street using ments. The computer keeps track of the many situations, maximizing their long-run personal
fancy mathematical models? Yes, but for a agent interactions, to see what happens over advantage. Of course real people often act on
completely different purpose: modelling the time. Agent-based simulations can handle a far the basis of overconfidence, fear and peer prespotential profit and risk of individual trades. wider range of nonlinear behaviour than con- sure — topics that behavioural economics is
There is no attempt to assemble the pieces ventional equilibrium models. Policy-makers now addressing.
and understand the behaviour of the whole can thus simulate an artificial economy under
But there is a still larger problem. Even if
economic system.
different policy scenarios and quantitatively rational expectations are a reasonable model of
There is a better way: agent-based models. explore their consequences.
human behaviour, the mathematical machinery
An agent-based model is a computerized simuWhy is this type of modelling not well- is cumbersome and requires drastic simplificalation of a number of decision-makers (agents) developed in economics? Because of his- tions to get tractable results. The equilibrium
torical choices made to address the models that were developed, such as those used
and institutions, which interact
through prescribed rules. The agents
complexity of the economy and the by the US Federal Reserve, by necessity stripped
can be as diverse as needed — from
importance of human reasoning and away most of the structure of a real economy.
consumers to policy-makers and Wall
adaptability.
There are no banks or derivatives, much less
Street professionals — and the instituThe notion that financial econo- sub-prime mortgages or credit default swaps
mies are complex systems can be — these introduce too much nonlinearity and
tional structure can include everything
traced at least as far back as Adam complexity for equilibrium methods to handle.
from banks to the government. Such
models do not rely on the assumption
Smith in the late 1700s. More recently When it comes to setting policy, the predictions
that the economy will move towards
John Maynard Keynes and his fol- of these models aren’t even wrong, they are sima predetermined equilibrium state, as other lowers attempted to describe and quantify ply non-existent (see Nature 455, 1181; 2008).
models do. Instead, at any given time, each this complexity based on historical patterns.
Agent-based models potentially present
agent acts according to its current situation, the Keynesian economics enjoyed a heyday in the a way to model the financial economy as a
state of the world around it and the rules gov- decades after the Second World War, but was complex system, as Keynes attempted to do,
erning its behaviour. An individual consumer, forced out of the mainstream after failing a cru- while taking human adaptation and learning
for example, might decide whether to save or cial test during the mid-seventies. The Keyne- into account, as Lucas advocated. Such modspend based on the rate of inflation, his or her sian predictions suggested that inflation could els allow for the creation of a kind of virtual
Ÿ)''0DXZd`ccXeGlYc`j_\ijC`d`k\[%8cci`^_kji\j\im\[
685-686 Opinion Farmer modelling MH CNS.indd 685
Farmer&Foley, Nature (2009)
P. NOBLE/REUTERS
• „agent-based models can
685
30/7/09 15:40:48
Finding the right level of
abstraction
• good model should
Medawar zone
1
UFZ Umweltforschungszentrum Leipzig-Halle, Department Ökologische Systemanalyse, PF 500 136,
04301 Leipzig, Germany. 2Department of Applied Biology, Estación Biológica de Doñana, Spanish Council for
Scientific Research CSIC, Ave. Maria Luisa s/n, E-41013
Seville, Spain. 3Zentrum für Marine Tropenökologie,
Fahrenheitstrasse 6, 28359 Bremen, Germany. 4Institut für Biochemie und Biologie, Universität Potsdam,
Maulbeerallee 2, 14469 Potsdam, Germany. 5Netherlands Institute of Ecology, Centre for Limnology,
Rijksstraatweg 6, 3631 AC Nieuwersluis, Netherlands.
6
Lang, Railsback and Associates and Department of
Mathematics, Humboldt State University, 250 California Avenue, Arcata, CA 95521, USA. 7Botany Section,
Department of Ecology, Royal Veterinary and Agricultural University Rolighedsvej 21, DK-1958 Frederiksberg,
Denmark. 8U.S. Geological Survey/Florida Integrated
Science Centers and Department of Biology, University of Miami, Post Office Box 249118, Coral Gables,
FL 33124, USA.
*To whom correspondence should be addressed.
E-mail: [email protected]
Bottom-up models have been developed
for many types of ACSs (4), but the identification of general principles underlying the
organization of ACSs has been hampered by
the lack of an explicit strategy for coping
with the two main challenges of bottom-up
modeling: complexity and uncertainty (5, 6).
Consequently, model structure often is chosen
ad hoc, and the focus is often on how to
represent agents without sufficient emphasis
on analyzing and validating the applicability of
models to real problems (5, 7).
A strategy called pattern-oriented modeling
(POM) attempts to make bottom-up modeling
more rigorous and comprehensive (6, 8–10). In
POM, we explicitly follow the basic research
program of science: the explanation of observed patterns (11). Patterns are defining characteristics of a system and often, therefore,
indicators of essential underlying processes
and structures. Patterns contain information on
the internal organization of a system, but in a
Bcoded[ form. The purpose of POM is to
Bdecode[ this information (10).
The motivation for POM is that, for complex systems, a single pattern observed at a
specific scale and hierarchical level is not
sufficient to reduce uncertainty in model structure and parameters. This has long been known
in science. For example, Chargaff_s rule of
DNA base pairing was not sufficient to decode the structure of DNA—until combined
with patterns from x-ray diffraction of DNA
and from the tautomeric properties of the purine and pyrimidine bases (12). Thus, in POM,
multiple patterns observed in real systems at
different hierarchical levels and scales are used
systematically to optimize model complexity
and to reduce uncertainty.
POM was formulated in ecology, a science
with a long tradition of bottom-up modeling.
www.sciencemag.org
SCIENCE VOL 310
Ecology, in the past 30 years, has produced as
many individual-based models as all other disciplines together have produced agent-based
models (13), and has focused more on bottomup models that address real systems and problems (14).
We describe here how observed patterns
can be used to optimize model structure, test
and contrast theories for agent behavior, and
reduce parameter uncertainty. Finally, we
discuss POM as a unifying framework for the
science of agent-based complex systems in
general.
Patterns for Model Structure:
The Medawar Zone
Finding the optimal level of resolution in a
bottom-up model’s structure is a fundamental
problem. If a model is too simple, it neglects
essential mechanisms of the real system,
limiting its potential to provide understanding
and testable predictions regarding the problem
it addresses. If a model is too complex, its
analysis will be cumbersome and likely to get
bogged down in detail. We need a way to find
an optimal zone of model complexity, the
‘‘Medawar zone’’ (Fig. 1).
Modeling has to start with specific questions (15). From these questions, we first
formulate a conceptual model that helps us
decide which elements and processes of the
real system to include or ignore. With complex
systems, however, the question addressed by
the model is not sufficient to locate the
Medawar zone because ACSs include too
many degrees of freedom. Moreover, the conceptual model may too much reflect our perspective as external observers, with our specific
interests, beliefs, and scales of perception.
A key idea of POM is to use multiple
patterns observed in real systems to guide
design of model structure. Using observed
patterns for model design directly ties the
model’s structure to the internal organization
of the real system. We do so by asking: What
observed patterns seem to characterize the
system and its dynamics, and what variables
and processes must be in the model so that
these patterns could, in principle, emerge? For
example, if there are patterns in age structure,
sex ratio, and spatial distribution, then age,
sex, and space should be represented in the
11 NOVEMBER 2005
987
Data
Fig. 1. Payoff of bottom-up models versus their
complexity. A model’s payoff is determined not
only by how useful it is for the problem it was
developed for, but also by its structural realism;
, 2012
Problem
Agent-based complex systems are dynamic networks of many interacting agents; examples
include ecosystems, financial markets, and cities. The search for general principles
underlying the internal organization of such systems often uses bottom-up simulation
models such as cellular automata and agent-based models. No general framework for
designing, testing, and analyzing bottom-up models has yet been established, but recent
advances in ecological modeling have come together in a general strategy we call patternoriented modeling. This strategy provides a unifying framework for decoding the internal
organization of agent-based complex systems and may lead toward unifying algorithmic
theories of the relation between adaptive behavior and system complexity.
hat makes James Bond an agent?
He has a clear goal, he is autonomous in his decisions about
achieving the goal, and he adapts these decisions to his rapidly changing situation. We
are surrounded by such autonomous, adaptive
agents: cells of the immune system, plants, citizens, stock market investors, businesses, etc.
The agent-based complex systems (1) (ACSs)
around us are made up of myriad interacting
agents. One of the most important challenges
confronting modern science is to understand
and predict such systems. Bottom-up simulation modeling is one tool for doing so: We
compile relevant information about entities at
a lower level of the system (in Bagent-based
models,[ these are individual agents), formulate theories about their behavior, implement
these theories in a computer simulation, and
observe the emergence of system-level properties related to particular questions (2, 3).
Model complexity
Multiple
Patterns
Volker Grimm,1* Eloy Revilla,2 Uta Berger,3 Florian Jeltsch,4 Wolf M. Mooij,5 Steven F. Railsback,6
Hans-Hermann Thulke,1 Jacob Weiner,7 Thorsten Wiegand,1 Donald L. DeAngelis8
W
Payoff
gain understanding
tions.
logical epidemiolded the stepwise
model describing
ed foxes in central
erns included the
revalence, disease
and temporal osocal and regional
reproduced these
y applying a prend then fitting it to
ttern after another
e model structure
of this model is
ch between model
data set of hunted
ects of rabies epiof rabies control),
and their interac-
Pattern-Oriented Modeling of Agent-Based
Complex Systems: Lessons from Ecology
Farmer&Foley, Science (2005)
Downloaded from www.sciencemag.org on June 26, 2012
neither be too simple
nor too complex
REVIEW
Using Patterns at multiple Scales
REVIEW
none of the simulations reproduced all
the observed market
patterns, the assumption that all investors
use 25-year memories
failed to reproduce
the most basic pattern: price volatility.
This pattern-oriented
analysis indicates
that individual variation in investment
decision-making is
crucial to stock market dynamics.
Testing and contrasting alternative
theories or decision
models has several
benefits. We are
forced to be explicit
about how decision
models are formuFig. 2. Pattern-oriented model design. Observed patterns that characterize old-growth beech forests [(A); images: front, M. lated and tested; we
Flade; right, C. Rademacher; top, S. Winter] include a horizontal mosaic of developmental stages [(B); x scale: 400 m; modified can demonstrate how
from (42)], the vertical patterns of tree size that define the developmental stages [(C), showing the late decaying stage; important the spex scale: È60 m; modified from (43)], and distributions of fallen large trees [(D), a map of fallen wood; ellipses indicate crown cific formulation of
projections of standing trees; x scale: È60 m; modified from (43)]. To allow these patterns to emerge from it, the model
includes a grid-based horizontal structure [(E), showing grid cells in three developmental stages; x scale: 570 m], a grid-based a decision—or any
vertical structure [(F), showing each grid cell’s percentage cover for four height classes; total area shown: 1 ha)], and other low-level—
individual representation of large trees [(G), showing one cell’s trees in the largest two height classes; cell area: 204 m2); (E) model is; we can exto (G) modified from (18)].
plore null models;
and we can continually refine models by applying additional
together they were able to falsify all but one
closest in front. These two ‘‘priority’’ theories
patterns.
theory of habitat selection.
failed to reproduce realistic polarization values
In a model exploring what determines the
(Fig. 3), eliminating them as valid theory.
Farmer&Foley, This
Science
(2005)
Patterns for Parameters:
access of nomadic herdsmen to pasture lands
example shows
that looking at one
Comparing different theories of
agent behavior
EVIEW
ncemag.org on June 26, 2012
Polarization
Nearest neighbor
distance
model output. To reA
B 1.5
uce this uncertainty,
wo data sets were
1.0
sed to identify five
atterns. Quantitave criteria for the
0.5
greement between
bserved and sim0.0
lated patterns were
0 1 2 3 4 5 6 7 8 9 10 11
eveloped. The in60
irect modeling analsis started with 557
50
andom parameter
40
ets covering the plauible ranges of all pa30
ameters. The five
20
bserved patterns
were used as filters:
10
Only 10 of the 557
0 1 2 3 4 5 6 7 8 9 10 11
arameter sets reModel version
roduced all of them.
This parameter fil- Fig. 3. Strong inference by contrasting alternative theories of the agents’ behavior. Boids (27) is a conceptual model that
demonstrates how schools or flocks can emerge from simple rules for behavior [(A); a version of boids by H. Hildenbrandt (44)]. (B)
ering reduced the In a similar model of fish schools (28, 45), 11 alternative theories of fish behavior were contrasted by looking at two school-level
model’s global sen- patterns: polarization (p) and nearest neighbor distance (NND); p is 0- if all fish swim in the same direction and p approaches 90itivity by a factor if all fish swim in random directions. Values of p observed in real fish schools are 10- to 20-; observed NND is often G1 fish body
length. In model versions 1 to 9, the influence of neighbor fish is averaged; in model version 10 and 11 (shaded), fish select a single
f 4 (fig. S1).
Indirect parame- neighbor fish and orient their swimming to this neighbor only.
erization is routine
n physical process models (i.e., in chemistry,
ydrology, and climate modeling), but rare
o far in models of ACSs. An encouraging
Farmer&Foley, Science (2005)
xception is the agent-based model of an
„Bottom-up models are virtual laboratories where
controlled experiments distinguish noise from signal in the
system’s organization. In particular, experiments
contrasting hypotheses for the behavior of interacting
agents will lead to an accumulation of theory for how the
dynamics of systems from molecules to ecosystems and
economies emerge from bottom-level processes. This
approach may change our whole notion of scientific
theory, which until now has been based on the theories of
physics. Theories of complex systems may never be
reducible to simple analytical equations, but are more
likely to be sets of conceptually simple mechanisms (e.g.,
Darwinian natural selection) that produce different
dynamics and outcomes in different contexts. POM thus
may lead us to an algorithmic, rather than analytical,
approach to theory.“
Farmer&Foley, Science (2005)