greca talk
DESCRIPTION
The talk I gave to the GRECA at UQAM in 2008. My first talk of the PhD.TRANSCRIPT
The story so far...Steven Hamblin
The Hero of our story...
Act I
Producer
Producers
Scrounger
Other forms of scrounging.
50% producer. 50% scrounger.100% 0%
0% 100%producer.
producer.
scrounger.
scrounger.
Rules
Rules• Relative payoff sum
Rules• Relative payoff sum
• Perfect Memory
Rules• Relative payoff sum
• Perfect Memory
• Linear Operator
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)
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)
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)
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)
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)
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.
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.
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.
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.
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.
Relative Payoff Sum?
Perfect Memory?
Linear Operator?
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
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.
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?
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?
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?
Genetic Algorithms
• Algorithms that simulate evolution to solve optimization problems.
Initial population
Measure fitness
Select for
reproduction
Mutation
Exit> n generations
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Results to date
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
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
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
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
What does that mean?
• 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.
Next steps?
Other games...
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Genetic programming to optimize rule structure.
Act II
+
Foraging / Learning rule simulation.
Foraging / Learning rule simulation.
Swappable grids (Moore / VN / Hex / Dirichlet)
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Swappable grids (Moore / VN / Hex / Dirichlet)
Results to date
Act III
+
Node Relationship
Node Relationship
Node Relationship
One field, a few names...
• Graph theory....
• Social network analysis....
• Network theory...
Graph measures...
Graph measures...
• Degree
Graph measures...
• Degree
• Centrality
Graph measures...
• Degree
• Centrality
• Clustering
Graph measures...
• Degree
• Centrality
• Clustering
• Path length
Graph measures...
• Degree
• Centrality
• Clustering
• Path length
• Etc...
Six degrees...
• Small world network:
• High clustering, low path length.
# of connections to other foragers
Birds
# of connections to other foragers
Birds
Most birds have few connections
# of connections to other foragers
Birds
Most birds have few connections
A few birds have many connections
=
=
Foraging / Learning rule simulation.
Small world network analysis
The end of the story.