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The story so far... Steven Hamblin

GRECA talk

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The talk I gave to the GRECA at UQAM in 2008. My first talk of the PhD.

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Page 1: GRECA talk

The story so far...Steven Hamblin

Page 2: GRECA talk

The Hero of our story...

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Act I

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Producer

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Producers

Scrounger

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Other forms of scrounging.

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50% producer. 50% scrounger.100% 0%

0% 100%producer.

producer.

scrounger.

scrounger.

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Rules

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Rules• Relative payoff sum

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Rules• Relative payoff sum

• Perfect Memory

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Rules• Relative payoff sum

• Perfect Memory

• Linear Operator

Page 23: GRECA talk

Relative Payoff Sum

where 0 < x < 1 is a memory factor,

ri > 0 is the residual value associated with alternative i,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Page 24: GRECA talk

Relative Payoff Sum

where 0 < x < 1 is a memory factor,

ri > 0 is the residual value associated with alternative i,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Page 25: GRECA talk

Relative Payoff Sum

where 0 < x < 1 is a memory factor,

ri > 0 is the residual value associated with alternative i,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Page 26: GRECA talk

Relative Payoff Sum

where 0 < x < 1 is a memory factor,

ri > 0 is the residual value associated with alternative i,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Page 27: GRECA talk

Relative Payoff Sum

where 0 < x < 1 is a memory factor,

ri > 0 is the residual value associated with alternative i,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Page 28: GRECA talk

Perfect Memory

Si(t) = � + Ri(t)/(⇥ + Ni(t))

where Ri(t) is the cumulative payo�s from alternative i to time t,

Ni(t) is the number of time periods from the beginning in which the option

was selected,

� and ⇥ are parameters.

Page 29: GRECA talk

Perfect Memory

Si(t) = � + Ri(t)/(⇥ + Ni(t))

where Ri(t) is the cumulative payo�s from alternative i to time t,

Ni(t) is the number of time periods from the beginning in which the option

was selected,

� and ⇥ are parameters.

Page 30: GRECA talk

Perfect Memory

Si(t) = � + Ri(t)/(⇥ + Ni(t))

where Ri(t) is the cumulative payo�s from alternative i to time t,

Ni(t) is the number of time periods from the beginning in which the option

was selected,

� and ⇥ are parameters.

Page 31: GRECA talk

Perfect Memory

Si(t) = � + Ri(t)/(⇥ + Ni(t))

where Ri(t) is the cumulative payo�s from alternative i to time t,

Ni(t) is the number of time periods from the beginning in which the option

was selected,

� and ⇥ are parameters.

Page 32: GRECA talk

Linear Operator

Si(t) = xSi(t� 1) + (1� x)Pi(t)

where 0 < x < 1 is a memory factor,

Pi(t) is the payo� to alternative i at time t, and

Si(t) is the value that the animal places on the behavioural alternative i at

time t.

Page 33: GRECA talk

Relative Payoff Sum?

Perfect Memory?

Linear Operator?

Page 34: GRECA talk

Bird Start

At a patch with food?

Feed

Produce or scrounge?

Produce Scrounge

Move randomly

Yes

Any conspecifics

feeding?No

Move to closest

Closest still feeding?

There yet?

No

Yes

No

NO

Yes

Page 35: GRECA talk

Bird Start

At a patch with food?

Feed

Produce or scrounge?

Produce Scrounge

Move randomly

Yes

Any conspecifics

feeding?No

Move to closest

Closest still feeding?

There yet?

No

Yes

No

NO

Yes

• 5 or 10 birds.

• Foraging grid is a regular 10x10 grid, with movement in the 4 cardinal directions.

• 20 patches on the grid, with 10 or 20 food items in each.

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Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Si(t) = � + Ri(t)/(⇥ + Ni(t))

Si(t) = xSi(t� 1) + (1� x)Pi(t)

Relative Payoff Sum?

Perfect Memory?

Linear Operator?

Page 38: GRECA talk

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Si(t) = � + Ri(t)/(⇥ + Ni(t))

Si(t) = xSi(t� 1) + (1� x)Pi(t)

Relative Payoff Sum?

Perfect Memory?

Linear Operator?

Page 39: GRECA talk

Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)

Si(t) = � + Ri(t)/(⇥ + Ni(t))

Si(t) = xSi(t� 1) + (1� x)Pi(t)

Relative Payoff Sum?

Perfect Memory?

Linear Operator?

Multiple stable rules with multiple parameters?

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Genetic Algorithms

• Algorithms that simulate evolution to solve optimization problems.

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Initial population

Measure fitness

Select for

reproduction

Mutation

Exit> n generations

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Foraging / Learning rule simulation.

Genetic algorithm to optimize parameters and simulate population dynamics.

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Results to date

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rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules

02

46

810

Relative Payoff Sum Perfect Memory Linear Operator

0 100

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rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules

0200

400

600

800

Relative Payoff Sum Perfect Memory Linear Operator

0 100

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rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules rules

050

100

150

200

250

300

350

Relative Payoff Sum Perfect Memory Linear Operator

0 100

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Si(t) = xSi(t� 1) + (1� x)ri + Pi(t)Relative Payoff Sum

rp >> rs for large population sizes.

-1 0 1 2 3 4 5 6 7 8

1

2

3

4

5

Producer residual

Scrounger residual

Time without payo! to behaviour

Value assignedto behaviour

Page 48: GRECA talk

What does that mean?

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• Under the assumptions of this model, the Relative Payoff Sum rule is optimal.

• Whether RPS is favored depends on payoff variance:

• low variance = more attractive power.

• Differences in residuals gives a prediction for empirical tests.

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Next steps?

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Other games...

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Foraging / Learning rule simulation.

Genetic algorithm to optimize parameters and simulate population dynamics.

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Foraging / Learning rule simulation.

Genetic algorithm to optimize parameters and simulate population dynamics.

Genetic programming to optimize rule structure.

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Act II

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+

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Foraging / Learning rule simulation.

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Foraging / Learning rule simulation.

Swappable grids (Moore / VN / Hex / Dirichlet)

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Foraging / Learning rule simulation.

Genetic algorithm to optimize parameters and simulate population dynamics.

Swappable grids (Moore / VN / Hex / Dirichlet)

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Results to date

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Act III

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+

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Node Relationship

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Node Relationship

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Node Relationship

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One field, a few names...

• Graph theory....

• Social network analysis....

• Network theory...

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Graph measures...

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Graph measures...

• Degree

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Graph measures...

• Degree

• Centrality

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Graph measures...

• Degree

• Centrality

• Clustering

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Graph measures...

• Degree

• Centrality

• Clustering

• Path length

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Graph measures...

• Degree

• Centrality

• Clustering

• Path length

• Etc...

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Six degrees...

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• Small world network:

• High clustering, low path length.

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# of connections to other foragers

Birds

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# of connections to other foragers

Birds

Most birds have few connections

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# of connections to other foragers

Birds

Most birds have few connections

A few birds have many connections

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=

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=

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Foraging / Learning rule simulation.

Small world network analysis

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The end of the story.