Modeling in Behavioral Ecology
Dr. Mike Heithaus
MS361
Office Hours: Give me a ring!
heithaus@fiu.edu
(305) 919-5234
Course Structure
• Initial meetings
• Start developing your own model
• Suggested books
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Haefner (2005) Modeling biological systems: principles and applications
Grimm and Railsback (2005) Individual-based modeling and ecology
Mangel and Clark (2000) Dynamic state variable models in ecology
Dugatkin and Reeve (1998) Game theory and animal behavior
Hilborn and Mangel (1997) The ecological detective: confronting models with data
What is a model?
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A description of a system
– System – any collection of interrelated objects
– Object – some unit upon which observations can be made
– “. . . systems are anything humans wish to discuss and models are one tool that
facilitates that discussion.” (Haefner 2005)
– Metaphorical descriptions of nature (Hilborn and Mangel 1997)
Why model?
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Three uses of models in science
– Understanding a system
• Use knowledge of inputs and outputs to infer system characteristics
– Prediction about some future state
• Use knowledge of the parts of a system and their stimuli to account for
responses
– Control or manipulation of a system (Decisions)
• Design a system to obtain a desired output
Why model?: Island biogeography
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Understanding:
– Develop quantitative hypotheses about how the number of species on an island
should change with rates of immigration and extinction
Prediction
– Predict how long an island to recover after disturbance or how many species will be
supported by an island
Decision/Control
– Aid in the design of island-like reserves to maximize the number of species
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Why model: an ecologists perspective
The utility of models often comes from the predictions that it generates that can be
tested
Types of models
Conceptual or Verbal (Qualitative)
– Descriptions in language
Diagrammatic (Qualitative)
– Graphical representations of objects and relationships
Physical
– a real mock-up
Formal (Quantitative)
– Mathematical model
Types of mathematical models I
Scientific
– Describes how nature might work and then proceeds to a set of predictions relating
dependent and independent variables
Statistical
– Describes relationships among variables without any explanation for why an
interaction occurs
Types of mathematical models II
Mechanistic models
– Explicit representation of mechanistic processes; also called a process-oriented
model
Descriptive models
– No representation of mechanistic processes
Types of mathematical models III
Static
– Responses to input variables do not change over time
Dynamic
– Responses may change over time
Types of mathematical models IV
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Continuous
– Time may take any value
Discrete
– Time is only expressed as an integer
Types of mathematical models V
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Spatially homogeneous
– No spatial structure to model
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Spatially heterogeneous
– Objects have a position in space
– May be:
• Discrete if space is represented in blocks or cells that are homogeneous
• Continuous if every point in space is different
Types of mathematical models VI
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Stochastic
– Allows random fluctuations
Deterministic
– All parameters are constant
Constraints on models
Trade-offs are inherent in modeling: you can’t simultaneously maximize all three of
the major properties of models
– Realism
– Accuracy of outputs
– Generality
How you solve the tradeoffs depends on the goal of your model
Model tradeoffs
Prediction: don’t need much generality, good accuracy and realism
– Does this depend on the type of prediction?
Understanding: need generality and some reality, but accuracy less important
Control: need reality, but virtually no generality
Misuse of models
• Models are sometimes given greater weight than is appropriate
– Not all models are equal
• Models don’t “prove” anything
– A particular problem with the interpretation of ecosystem models like ECOSIM
these days
• No model is “correct” – there can be a “best” model or several models may be equally
likely
– The presence of competing models is critical, otherwise a poor one may continue to
be used
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What is behavioral ecology?
The study of the adaptive nature of behavior in relation to ecological conditions
Why do animals do what they do?
Concerned with ultimate questions – why and how? Not what?
Key Concepts in Behavioral Ecology
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Optimality
– Organisms are optimized by natural selection
1. fitness is a function of design (e.g. behavior)
2. selection tends to maximize fitness
3. like begets like (heritable genetic variation)
– Therefore, given enough time and raw material, selection will lead to optimal
design (behavior)
Optimality
– Optimization model
• Hypothesis about how things work
• Provides quantitative predictions that can be tested by observations or
experiments
– Optimization modeling steps
1. Specify constraints in a system
a. Possible phenotypes (options) – allowable
outcomes: STRATEGY SET
b. State equations: morphology and physiology –
constraints on
behavior
2. Hypothesize an optimization criteria (what is being maximized or minimized)
fitness (the ultimate optimization)
surrogate of fitness (e.g. net energy intake, lifetime energy intake)
measure “indifference” – how much will be given up for something else –
UTILITY FUNCTION (mean vs variance; food vs distance from
cover)
3. Assumption about heredity
a. Behavior passed on from one generation to the next (genetics of behavior
are largely unstudied)
Optimality
– Optimality models
• Optimality modeling does not test whether nature optimizes, just the constraints
and assumptions of the model
• Optimality is a modeling technique, not what animals try to do.
– An animal doesn’t consciously think they are trying to maximize energy
intake, they respond to proximate cues (e.g. gut fullness) but the end result
is optimization
• If test of model does not fit predictions of the model, refine the hypothesis and
repeat the process – note: this is not circular, it is attempting to zero in on how
systems work
Optimality
– Fitness function
• Relationship between the magnitude of expression of a behavior or trait and the
fitness associated with it
• A way to generate predictions about what behaviors should be used
• Determining an optimum doesn’t tell us how a population will evolve towards
the optimum or the costs of suboptimal behavior – need to know the shape of
the fitness function
Optimality
– Dynamic optimization models (state-variable models)
• Tell us the optimal policy at a given state and time
– For example: what habitat should a bird use based on its energy reserves if
habitats vary in risk and food
• There must be an end time T
• Based on a terminal fitness function – the expected fitness of an animal in a
given state at time T and a dynamic programming equation (DPE) that
incorporates state-dependent survival probabilities and transitions in state
variables
• Uses backwards iteration (start with terminal function then calculate possible
ways to get there from T-1 and so on)
• Assumes that optimal decisions are made in each cell
• Can look at cost of inappropriate decisions
• Once optimal decisions have been determined, can use forward simulations to
determine likely outcomes
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Game theory
Optimal policy depends on behavior of others
Optimization in a frequency dependent cast
• e.g. interactions between predators and prey or between prey
Analyzes the outcomes of behavioral decisions when these outcomes depend on the
behavior of other players
Predicts the individual’s behavior based the best estimates of
• the other contestant’s response
The rewards or costs of various outcomes
ESS and game theory
– Evolutionarily Stable Strategy (ESS)
• Nash equilibrium in which no “invading” strategy or mutation can invade the
populations and do better than other individuals in the population
• Nash Equilibrium = no individual can do better by unilaterally switching tactics
• May involve mixed strategies within individuals
– Evolutionarily stable state (ESSt)
• Fixed frequencies of pure strategies in the population (e.g. 60% of individuals
sneak, 40 % of individuals guard)
ESS and game theory
– There may be more than one ESS for a population and the one attained may depend
on history.
• There may even be a better ESS but the population can’t get there from here
(complex adaptive landscape) so an ESS can be a local optimum but not a
global optimum
– When solving for an ESS need to set up starting conditions, alternate strategies
– Compare fitness of specified strategies : note, you only find the ESS against
specified strategies!
Key concepts in behavioral ecology
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Principle of Allocation
– Probably the most important concept in behavioral ecology
– An organism only has so much of a currency (e.g. time, energy)
• How are these allocated among behaviors?
– Underlies the idea of tradeoffs
– All problems in behavioral ecology come down to allocation and tradeoffs
The place of models in behavioral ecology
Generate testable hypotheses
Makes assumptions obvious
Forces identification of important components of a system
Serve as starting point for iterative work
Some major types of models in Behavioral Ecology
Optimality models
Game theoretical models
Dynamic state variable models
Genetic algorithms
– Technique to solve optimization problems
– Mimic natural selection
– Do not represent actual genetics!
– Used at the population level
– Include density and frequency dependence
Building a model
• Identify a problem
• Identify important factors and interactions
– A graphical model can be a good first step
• Determine mathematical relationships between factors
– Build the model
• Solve or implement model
• Confront model with data
• Modify model based on empirical evidence and complete iterations
– Depending on the question, this may serve to decrease generality and increase
realism
Building a dynamic state variable model
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Identify a problem
Choose basic time period (t and T)
Specify Decision
Identify Constraints (e.g. mortality rate)
– be sure not to make decisions a constraint
Add dynamics (e.g. probability of finding food)
Choose Optimization Criteria
Specify Terminal Fitness Function
Develop Dynamic Programming Equation
Code (sometimes Excel works!)
Run Forward Iterations