Individual Based Models

1
Individual Based Models
2
Outline

• Emergent Behaviour
• 4 simple rules for living in my world
• Conways Game of Life
• Natural examples of emergent behaviour
• Individual Based Models
• From State Variables to IBMs
• IBM use and characteristics
• Unification of State Variable and IBM models
• Parting Words on model use in Population Ecology

3
Emergent Behaviour
Order From Chaos
The chaos is actions of individual agents
without feedback to central control (individual
rules still exist and are shared by agents) The
order is system level structure and the
appearance of coordinated behaviours
The phenomena is of potential significance in
fields dealing with organization of systems
genetics development, evolution, ecology,
sociology
4
Conways Game of Life (1970s)

• For a space that is 'populated'
• Each cell with one or no neighborsdies, as if by
  loneliness.
• Each cell with four or more neighbors dies, as if
  by overpopulation.
• Each cell with two or three neighbors survives.
• For a space that is 'empty' or 'unpopulated'
• Each cell with three neighbors becomes populated.

5
Game of Life Stable Cell Patterns
http//www.bitstorm.org/gameoflife/
Emergent Behaviour Patterns from simple rules
6
Concepts of chaos, fractals, complexity, and
emergent behaviour

• developed through the computer revolution
• 1970s and 1980s
• Computer systems were rapidly changing
• FROM Single facility with many users
• central control
• TO Many units, one per user, in a network
• distributed control
• Researchers, using computers, see similarities in
  their own field of investigation
• traffic patterns, predator-prey systems, etc.

7
In 1980s California the developing ideas spill
over into cinema TRON

• central vs. individual control
• social analogies are beyond this course

8
Why care about abstract computer models?
They are important in the same way that the
development of Newtons Leibnizs calculus was
important to the exponential, logistic, and
Lotka-Volterra models in ecology.

• Quantitative tools are required to develop our
  concepts into predictive quantitative models
• rate concepts ? calculus
• time steps ? difference equations
• Understanding model/tool assumptions and
  properties is needed for their application
• limits to population growth ? add K
• all N individuals assumed identical

9

• Are there observations in the natural world that
• cannot be represented by classical population
  ecology perspectives like rate based models?
  (new conceptual models)
• suggest the need for new mathematics/analysis
  (new modeling tools)

• Old observations, but a new perspective
• Look for examples of complex structure or
  behaviour
• many independent individuals
• lack of centralized coordination/control

10
Natural Emergent Behaviour Population Relevance
Reproduction
Myxamoebae come together as migrating slug
Dictyostelium sp. photos by David Geiser
Formssorocarp
Slime mold sorocarps
11
Natural Emergent Behaviour Population Relevance
Space
Honeycomb
Fish territories
Hexagons in Nature
What are the rules here?
12
Natural Emergent Behaviour Population Relevance
Reproduction/Dispersal/Foraging
Tetramorium tsushimae carrying dandelion seed
Coordination in Ant Colonies
Lasius japonicus nest in wood
http//ant.edb.miyakyo-u.ac.jp/INTRODUCTION/Gakken
79E/title.html
13
These Concepts Form The Basis of Individual
Based Models (IBMs) a.k.a. Agent Based Models
(ABMs)

• Individual agents following their own rules
• May be more than one type of agent
• An agent is defined by its rules (by what it
  does)
• Usually spatially explicit
• 2 or 3 dimensional, depending on the process
• Programmed, not entered into existing program
• Many subroutines exist to ease development
• Performance is an issue ? C (Java slower)

14
From State Variable Models to IBMs
spatially explicit compartments
one speciescompartment state variable N eg.
logistic
two speciescompartments state variables N,
P eg. Lotka-Volterra
individualagents
one speciescompartments eg. SIR
Also spatially explicit IBMs(how would you
illustrate this?)
15
How Often Are IBMs Used?

• IBMs have become more popular as tools have
  become more available
• The New Hope For Ecological Insights
• build it and they will come (emerge)
• a bit optimistic

From Grimm, V. 1999 Ecological Modelling 115
(1999) 129148
16
Characteristics of IBMs? (From a review of 50
papers)

• Often (gt 60)
• specific for 1 species
• pragmatic

• Seldom (lt 40)
• compared to classical model results
• looking for patterns
• dynamic resources
• dynamic ind. variation
• Probed with extreme values (strong cues)
• validated with data

17
Often Extremely Large Number Of Parameters
May be realistic, relevant, but can be hard to
estimate.
18
Perspective A Unification of Approaches
19
Unification Through Common Evaluation

• Remember the indicators applied to classic models
• return time - after disturbance
• persistence - in the face of disturbances
• variability of time series - pattern and magnitude

Unification Through Integrated Methodology

• Choosing the appropriate level of aggregation
• top-down - general model refined
• use aggregate behavior to evaluate refinements
• bottom-up - detailed model trimmed
• remove details with little influence

20
Some Thoughts on Modelingin Population Ecology

• True or False Models?
• a meaningless question - all models are false
• Models are either useful or not useful
• relative to its designed purpose
• Level of detail should be appropriate to question
• states, compartments, spatial, individuals,
  resources, etc.
• limited by data and resources to collect it?
• Model failures are often data failures
• cannot model/manage effectively without
  information