seminar talk, 2008
DESCRIPTION
A seminar talk I gave in 2008 to the University of Toronto graduate students seminar.TRANSCRIPT
![Page 1: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/1.jpg)
Learning to Forage:Rules, rules, everywhere a rule.
!
Steven Hamblin - Dept. of Biology, UQÀM
![Page 2: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/2.jpg)
The road ahead...
![Page 3: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/3.jpg)
Some background:
Components of the problem: learning, foraging, optima.
Producer-Scrounger game.
Learning rules.
The road ahead...
![Page 4: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/4.jpg)
Our approach:
Simulations and genetic algorithms.
Results.
Next steps.
The road ahead...
![Page 5: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/5.jpg)
Learning
![Page 6: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/6.jpg)
Learning
![Page 7: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/7.jpg)
Learning
![Page 8: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/8.jpg)
![Page 9: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/9.jpg)
![Page 10: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/10.jpg)
![Page 11: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/11.jpg)
![Page 12: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/12.jpg)
![Page 13: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/13.jpg)
![Page 14: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/14.jpg)
ESS: A strategy which, if adopted a population, cannot be invaded by a rare mutant strategy.
![Page 15: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/15.jpg)
Social foraging
Equilibrium
behaviour
Learning
![Page 16: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/16.jpg)
Evolution of Learning Rules
![Page 17: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/17.jpg)
Producer
Producer-Scrounger Game
![Page 18: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/18.jpg)
Producers
Scrounger
Producer-Scrounger Game
![Page 19: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/19.jpg)
Producer-Scrounger Game
![Page 20: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/20.jpg)
544 A N I M A L B E H A V I O U R , 2 9 , 2
Where the two pay-of f curves intersect , bo th types fare equal ly well: to one side o f the inter-
section p roducers do better, to the other, scroungers do better. We can call this the ESS po in t in accordance with the principle o f evo-
lu t ionar i ly stable strategies ( M a y n a r d Smith
1974; Dawkins 1976). The ESS po in t represents the stable mixture o f producers and scroungers
in selective terms to which groups which conta in the two types should converge (Fig. lb) .
However , the s i tuat ion is unl ikely to be as
s t ra ight forward as that . Because bo th frequency-
dependent and dens i ty-dependent factors are
l ikely to opera te with changes in g roup size, pay- offs to p roducers and scroungers are more accu-
ra te ly represented as pay-off surfaces (Fig. lc). The same principles app ly to the surfaces as to the curves in Fig. l a , except now the intersect ion
between the surfaces for p roducers and scroungers produces a line ra ther than a single
point . The line o f intersect ion can be m a p p e d as
an ESS line on to the two-dimensional surface between the p roducer / sc rounger axes (Fig. l d),
and groups should now ' t r ack ' the line ra ther than converge to a single point . A new and im-
p o r t an t impl ica t ion arising f rom the idea o f an
ESS line is t ha t the ra t io o f p roducers to scroungers at equi l ibr ium is l ikely to depend on
group size. Depend ing on the shape of the two intersecting surfaces, the ESS l ine in the hori-
zonta l p lane can describe a wide var ie ty o f curves all o f which, except for s t raight lines
th rough the origin, show a group size effect. The
at
No. scroungers No. producers
Here producers do better
Pay-off to / S C F O U n Q @ r s
S:- ducers
5 4 3 2 1 0 1 2 3 4 5 6
Here scroungers
b)
So group composit ion should adjust
I
i
ESS
,Fig. 1
PaY-~ f t / /
, o rod cer - ,
E S S - l i n e
I No. producers
0 1 J 3 4 5 6 ~._
d) ~ ~ = 2 "",~.. g j y H e r e scroungers ~ do bet ter
#
6 / Here producers i
Fig. I. (a) Pay-off to individual producers and scroungers as a function of the producer :scrounger ratio in the group (here arbitrarily set at six individuals). The intersection of the two curves is a point representing equal pay-offs to producers and scroungers; when strategies are conditional it is the point at which it would not pay any individual to change strategy. (b) The ESS corresponding to the pay- offs shown in (a). (c) The pay-off to individual producers and scroungers as a function of the number of scroungers at a site yields two surfaces. The intersection of the sur- faces is a line giving the ESS for each group size. (d) The projection of these ESS's onto the horizontal plane, giving the ESS line as a function of the number of pro- ducers and the number of scroungers.
General note: For simplicity the ESS line has been drawn as if non-integer numbers of producers and scroungers were possible. Restriction to integers gives a line to the right of that shown, usually as close as possible. The integer ESS for a given flock size gives a ratio of scroungers to producers such that if any one changed strategy be would do worse.
precise shapes of the surfaces may vary depend- ing on the na ture o f the p roducer / sc rounger
re la t ionship. In gua rde r / ' sneak ' re la t ionships dur ing mat ing, for example, the pay-of f to
guarders (producers) might decrease mono-
Barnard & Sibley, 1981.
![Page 21: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/21.jpg)
50% producer. 50% scrounger.100% 0%
0% 100%producer.
producer.
scrounger.
scrounger.
![Page 22: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/22.jpg)
![Page 23: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/23.jpg)
![Page 24: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/24.jpg)
![Page 25: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/25.jpg)
Do they learn?
![Page 26: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/26.jpg)
Do they learn?
Yes:
![Page 27: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/27.jpg)
Do they learn?
Yes:
Mottley & Giraldeau, 2000.
![Page 28: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/28.jpg)
Do they learn?
Yes:
Mottley & Giraldeau, 2000.
Katsnelson et al. , 2008
![Page 29: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/29.jpg)
Do they learn?
Yes:
Mottley & Giraldeau, 2000.
Katsnelson et al. , 2008
ISBE, 2008.
![Page 30: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/30.jpg)
![Page 31: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/31.jpg)
![Page 32: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/32.jpg)
![Page 33: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/33.jpg)
![Page 34: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/34.jpg)
Individual-based model (a.k.a. agent-based model).
Rules tested in isolation; stability test was questionable.
![Page 35: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/35.jpg)
Rules
![Page 36: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/36.jpg)
RulesRelative payoff sum
![Page 37: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/37.jpg)
RulesRelative payoff sum
Perfect Memory
![Page 38: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/38.jpg)
RulesRelative payoff sum
Perfect Memory
Linear Operator
![Page 39: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/39.jpg)
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 40: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/40.jpg)
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 41: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/41.jpg)
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 42: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/42.jpg)
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 43: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/43.jpg)
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 44: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/44.jpg)
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 45: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/45.jpg)
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 46: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/46.jpg)
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 47: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/47.jpg)
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 48: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/48.jpg)
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 49: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/49.jpg)
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 50: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/50.jpg)
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 51: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/51.jpg)
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?
![Page 52: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/52.jpg)
Relative Payoff Sum?
Perfect Memory?
Linear Operator?
![Page 53: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/53.jpg)
Agent Start
At a patch with food?
Feed
Produce or scrounge?
Produce Scrounge
Move randomly
No
Yes
Any conspecifics
feeding?No
Move to closest
Closest still feeding?
There yet?Still food in
patch?Yes
No
Feed
YesNo
No
Yes
![Page 54: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/54.jpg)
Agent Start
At a patch with food?
Feed
Produce or scrounge?
Produce Scrounge
Move randomly
No
Yes
Any conspecifics
feeding?No
Move to closest
Closest still feeding?
There yet?Still food in
patch?Yes
No
Feed
YesNo
No
Yes
Simulation notes...Foraging grid is a variable-sized square grid with movement in the 4 cardinal directions.
Number of patches and number of agents kept to 20% and 10% of grid size.
Thus: 40x40 grid would have 320 patches and 160 agents
![Page 55: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/55.jpg)
Genetic Algorithms
Algorithms that simulate evolution to solve optimization problems.
![Page 56: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/56.jpg)
Initial population
Measure fitness
Select for
reproduction
Mutation
Exit> n generations
![Page 57: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/57.jpg)
One final wrinkle.
Environmental vs. frequency-dependent variance in payoff.
![Page 58: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/58.jpg)
![Page 59: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/59.jpg)
![Page 60: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/60.jpg)
![Page 61: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/61.jpg)
![Page 62: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/62.jpg)
![Page 63: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/63.jpg)
Environmental variation.
Manipulating patch density.
N changes, with greater N meaning greater variation.
![Page 64: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/64.jpg)
Foraging / Learning rule simulation.
![Page 65: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/65.jpg)
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
![Page 66: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/66.jpg)
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Sources of variation
![Page 67: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/67.jpg)
Problem Solution
Rules tested in isolation. Simulation population randomly generated, using all rule types.
Parameter values arbitrarily chosen; few values tested.
Genetic algorithm to optimize across the whole parameter space.
Will rules converge on an ESS? Are they ES Learning rules?
Genetic algorithm to simulate population dynamics.
![Page 68: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/68.jpg)
Results to date
![Page 69: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/69.jpg)
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
0 500
![Page 70: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/70.jpg)
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
0 500
![Page 71: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/71.jpg)
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
0 500
![Page 72: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/72.jpg)
01
23
45
Group size
Para
met
er v
alue
s
●
●
● ●
●
●
10 40 90 160 360 1000
![Page 73: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/73.jpg)
01
23
45
Group size
Para
met
er v
alue
s
●
●
● ●
●
●
10 40 90 160 360 1000
Producer residual
![Page 74: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/74.jpg)
01
23
45
Group size
Para
met
er v
alue
s
●
●
● ●
●
●
10 40 90 160 360 1000
Scrounger residual
Producer residual
![Page 75: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/75.jpg)
01
23
45
Group size
Para
met
er v
alue
s
●
●
● ●
●
●
10 40 90 160 360 1000
Scrounger residual
Producer residual
Memory factor
![Page 76: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/76.jpg)
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 77: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/77.jpg)
●
●
●●
● ●
0.0
0.2
0.4
0.6
0.8
1.0
Group size
Prop
ortio
n of
spe
cial
ists
.
●
●
●
●
● ●
10 40 90 160 360 1000
mean=0.981
mean=0.008
![Page 78: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/78.jpg)
●
●
●
●
●
●
●
●
●
●
2 4 6 8 10
0.24
50.
250
0.25
50.
260
Periods of environmental variability
Mea
n pr
opor
tion
of sc
roun
ging
.
![Page 79: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/79.jpg)
●
●
●
●
●
●
●
●
●
●
2 4 6 8 10
0.52
0.54
0.56
0.58
Periods of environmental variability
Mea
n pr
opor
tion
of sp
ecia
lists.
![Page 80: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/80.jpg)
What does that mean?
![Page 81: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/81.jpg)
![Page 82: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/82.jpg)
Under the assumptions of this model, the Relative Payoff Sum rule is optimal.
![Page 83: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/83.jpg)
Under the assumptions of this model, the Relative Payoff Sum rule is optimal.
Differences in residuals gives a prediction for empirical tests.
![Page 84: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/84.jpg)
Under the assumptions of this model, the Relative Payoff Sum rule is optimal.
Differences in residuals gives a prediction for empirical tests.
Small, but consistent effect of environmental variability.
![Page 85: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/85.jpg)
Under the assumptions of this model, the Relative Payoff Sum rule is optimal.
Differences in residuals gives a prediction for empirical tests.
Small, but consistent effect of environmental variability.
Learning is selected against.
![Page 86: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/86.jpg)
Next steps?
![Page 87: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/87.jpg)
Questions?
Thanks to:
The Giraldeau Lab.
Guy Beauchamp.
Maria Modanu and Steve Walker, for the invitation.
![Page 88: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/88.jpg)
Evolution of learning rule form.
![Page 89: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/89.jpg)
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 90: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/90.jpg)
![Page 91: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/91.jpg)
![Page 92: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/92.jpg)
![Page 93: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/93.jpg)
Initial population
Measure fitness
Select for
reproduction
Mutation
Exit> n generations
![Page 94: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/94.jpg)
![Page 95: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/95.jpg)
![Page 96: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/96.jpg)
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
![Page 97: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/97.jpg)
Foraging / Learning rule simulation.
Genetic algorithm to optimize parameters and simulate population dynamics.
Genetic programming to optimize rule structure.
![Page 98: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/98.jpg)
![Page 99: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/99.jpg)
![Page 100: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/100.jpg)
![Page 101: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/101.jpg)
![Page 102: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/102.jpg)
![Page 103: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/103.jpg)
![Page 104: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/104.jpg)
![Page 105: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/105.jpg)
![Page 106: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/106.jpg)
![Page 107: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/107.jpg)
Learning
![Page 108: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/108.jpg)
Learning
![Page 109: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/109.jpg)
Learning
![Page 110: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/110.jpg)
Learning
![Page 111: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/111.jpg)
Learning
![Page 112: Seminar talk, 2008](https://reader036.vdocuments.mx/reader036/viewer/2022062319/55629ec6d8b42a68128b59e9/html5/thumbnails/112.jpg)
housed in flocks of six in common cages (59!32 and46 cm high) made of galvanized wire mesh and kept on a12:12 h light:dark cycle at 27"C (#2"). They were fed adlibitum on a mixture of white and red millet seeds andoffered ad libitum water. Each bird was marked with aunique combination of two coloured leg bands. Inaddition, the tail and neck feathers of each individualwere coloured with acrylic paint to allow individualidentification from a distance.
ApparatusThe purpose of the experimental apparatus was to
constrain subjects to act as either producers or scroungersin order to manipulate the frequency of each tactic
within a flock. The apparatus consisted of an indoor cage(273!102 cm and 104 cm high) with a producer and ascrounger compartment divided by a series of 22 patches,of which every second one contained seeds (Fig. 2a). Anopaque barrier placed length-wise from ceiling to floorprevented birds from moving between the producer andscrounger compartments (Fig. 2a).
Each patch consisted of a seed container and a stringthat prevented the seeds from falling out. Pulling thestring caused the seeds to fall into a 2!2 cm collectingdish located directly below the seed container. Oncein the collecting dish the seeds were available to theindividual that pulled the string from the producercompartment and all individuals within the scrounger
BarrierScrounger side
Producer side
Seed container
Division
Collecting dish
String
Perch
Scrounger sideProducer side
(b)
(a)
Figure 2. Top view of the experimental apparatus (a) and foraging patch (b). Individuals could search for seed-containing patches by pullingthe string associated with each patch. Strings were available only in the producer compartment. Birds in the scrounger compartment searchedfor individuals feeding from produced patches. When the top portion of an opaque barrier was in place, the birds in one compartment couldnot move into the other compartment. A close-up view of the patch (b) shows that producers had to sit on a perch directly in front of a patchto pull the string associated with that patch, and if seeds were present, they were released into the collecting dish. From the perch, a producercould reach the collecting dish by stretching its neck through a small hole in the division placed between compartments. The arrow indicatesthe direction in which the string had to be pulled to release the seeds.
343MOTTLEY & GIRALDEAU: CONVERGING ON PS EQUILIBRIA