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Modeling in Behavioral Ecology

Sander van Doorn

sander.vandoorn@iee.unibe.ch

Does it also work in theory?

“Very impressive, my dearcolleague, but does it also work

in theory?”

…know what science is all about

[Sinervo & Lively, Nature 380, (1996)]

Rock–Scissors–Paper

Frequencies of

phenotypes at time t&

fitness values

Frequencies of

phenotypes at time t+1

Model

Different kinds of models

! Different purposes

! Predict

! Control

! Understand

! Different strategies

! process-oriented or mechanistic

! descriptive or phenomenological

! Different evaluation criteria

! Realistic

! Precise

! General

! Different techniques

! Computer simulation

! Analytical techniques

systeminput output

2

Different kinds of models

! Different purposes

! Predict! Control

! Understand

! Different strategies

! process-oriented or mechanistic

! descriptive or phenomenological

! Different evaluation criteria

! Realistic

! Precise! General

! Different techniques

! Computer simulation! Analytical techniques

systeminput output

Example:

A model to predict the

weather

?

Different kinds of models

! Different purposes

! Predict

! Control! Understand

! Different strategies

! process-oriented or mechanistic

! descriptive or phenomenological

! Different evaluation criteria

! Realistic

! Precise! General

! Different techniques

! Computer simulation

! Analytical techniques

systeminput output

Example:

A model to discover

new elementary

particles

?

Different kinds of models

! Different purposes! Predict

! Control

! Understand

! Different strategies

! process-oriented or mechanistic! descriptive or phenomenological

! Different evaluation criteria

! Realistic! Precise

! General

! Different techniques

! Computer simulation

! Analytical techniques

systeminput output

?

Models in

behavioural ecology

Models of adaptive behaviour

! Optimality models

! Game Theory

! Adaptive Dynamics

! Genetic models

Optimality models:Is behavior adaptive?

! Different species of air-breathing divers show differences in theirdiving behavior

! If breathing efficiency has effect on fitness, and if diving behaviorhas a genetic component, one would expect evolution to optimizethe efficiency of the diving behavior

! Q: Can we posit adaptation as the explanation for the observeddifferences between species, and the strategies of individualspecies?

oxygen intake

per divea

b time spent per dive

a / b = breathing efficiency

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• On average, tufted ducks show optimal behavior

• But, there is a lot of variation between individuals

• Selection on another aspect of behavior may cause an individual to

deviate from what (we think) is optimal.

• Does evolution always optimize, and, if it optimizes something, what is it

exactly?

Frequency-dependent selection

[Parker, Anim. Ecol. 39, (1970)]

Conflict outcome

A

B

1/2

A BA’s genetically coded

behavioral strategyB’s genetically coded

behavioral strategy

Conflict

resolution

B’s decision h hd d

A’s decision “hawk” (h) “dove” (d)

1/21/2 1/2

payoff

V

V

V V

V

0 0

00 V

-C

-C

Strategies and Payoff

V/20dove

V(V-C)/2hawk

dovehawk

my b

ehavio

ur

opponent!s behaviour

Suppose everybody plays Hawk with probability p, then everyone can

expect to obtain payoff

P= p2V !C2

+ p 1! p"#$

%&'V + 1! p"

#$%&'2V2

=V2

! p2C2

P=V2

! p2C2

V

2

V !C

2

4

Evolutionarily Stable Strategy (ESS)

V

C

Evolutionarily Stable Strategies

! A strategy is an ESS if it cannot be replaced by an alternativestrategy

! If there are alternative best replies to an ESS,

then the ESS should be able to replace the alternative best replies

[Maynard-Smith & Parker]

! Note: the ESS criterion applies to a population in which the

ESS has become established, and considers its stability

against invasion by mutants with alternative strategies

! Will evolution actually lead to the establishment of the ESS?

In other words, is an ESS always attainable?

Adaptive DynamicsNo!

Adaptive Dynamics[in a single slide]

! Evolution as a sequence of mutation and trait-substitution events

! The pairwise invasability plot

Evolution of differences in aggression in a model of repeated conflicts

Evolution to a

point that is not

an ESS,

followed bydiversification

Where!s the genetics?

! So far: phenotypic models

! Is it okay to ignore the underlying

genetics?

When do we need to worry about genes?

Two examples

! Calculating relatedness in kin-selectionmodels

Hamilton!s rule: r b > c

! Indirect selection

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Why do females prefer to mate with

males that exhibit costly display traits?

Mean female preference

Mean

male display

Mean female preference

What natural selectionon males favors

Mean

male display

Mean female preference

What sexual selectionon males favors

Mean

male display

Mean female preference

Equilibrium thatmaximizes malelifetime fitness

Mean

male display

Mean female preference

The mean femalepreference ...

Mean

male display

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Mean female preference

Mean

male display

... determines theequilibrium for the

mean display

Mean female preference

Mean

male display

But what determinesthe mean preference???

Indirect benefits of female choice – Fishers runaway process

Certain remarkable consequences do, however, follow if somesexual preferences of this kind, determined, for example, by aplumage character, are developed in a species in which the

preferences of one sex, in particular the female, have a greatinfluence on the number of offspring left by individual males

The importance of this situation lies in the fact that the furtherdevelopment of the plumage character will still proceed, by

reason of the advantage gained in sexual selection, even after ithas passed the point in development at which its advantage in

Natural Selection has ceased

Moreover, as long as there is a net advantage infavour of further plumage development, there willalso be a net advantage in favour of giving to it a

more decided preference

The two characteristics affected by such aprocess … must thus advance together, and so

long as the process is unchecked by severecounterselection, will advance with ever-

increasing speed.

Fisher (1930), in The Genetical Theory of Natural Selection

sexy-son mechanism

runawayMean female preference

Mean

male display

Fisher’s runaway process

Mean female preference

Mean

male display

Fisher’s runaway process

Mean female preference

Mean

male display

Fisher’s runaway process

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Mean female preference

Mean

male display

Fisher’s runaway process

After onegeneration

Mean female preference

Mean

male display

Fisher’s runaway process

No linkagedisequilibrium

Mean female preference

Mean

male display

Fisher’s runaway process

Weak linkage

disequilibrium

Mean female preference

Mean

male display

Fisher’s runaway process

Very strong linkage

disequilibrium

Mean female preference

Mean

male display

Fisher’s runaway process

RUNAWAY!

PP

tt

Tt

TT

pp Pp

Allele frequencies

survival

mate choice

sexual reproduction

Models in behavioral ecology

genetic

game theory

optimality models

phenotypic

adaptive dynamics

static analysis

can weignore

genetics?

how do wedeal with

dynamics?

Is selectionfrequency-

dependent?

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Take home messages

! Models are great tools to help us sharpen ourintuition of how evolution works

! Models should be as simple as possible but nosimpler. Simplifying assumptions are okay, aslong as they don!t generate artifacts.

! In most cases don!t expect quantitativepredictions

! Instead, think critically about whether a modelhas really captured the essence of thebiological problem that you are interested in

Interested in more?

! Mail me atsander.vandoorn@iee.unibe.ch

! Current opportunities for

student projects! Cooperation

! Sexual selection

! Speciation

! Animal personalities