Phd Seminar talk
description
Transcript of Phd Seminar talk
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A true story...
as told by Steven Hamblin
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IntroductionInformation use
Foraging in spaceConclusion
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Optimal foraging
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Social foraging
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Producer-scrounger game
producer
scrounger
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Evolutionarily stable strategy (ESS)
mechanism regulating the frequency of alternatives in the population.An initial population of pure producer, for instance, could be invaded byalleles for scrounger because the initially rare scroungers would do muchbetter than any of the individuals bearing producer alleles (Fig. 1A).Scrounger alleles could not go to fixation because a population made upof pure scroungers would be invaded by producers. So, neither producernor scrounger alone can be evolutionarily stable. The ESS in this case ismixed, allowing the frequency of scrounger alleles to increase until thefitness of scroungers drops to the fitness of producers.
2. The Behaviorally Stable Strategy
In most behavioral instances, however, animals reach game solutions byadjusting their use of strategies according to the conditions in which theyare playing the game. The mechanism of adjustment in this case is not
A
B
C
Pay
offs
Proportion scrounger
FIG. 1. The payoff functions of the producer–scrounger game. The three panels givedifferent possible effects of scroungers on the producers’ (thin line) and the scroungers’ payoffs(thick line). Panel A gives the classic producer–scrounger payoffs: producer and scroungerpayoffs are depressed by increased proportion of playing scrounger but scroungers are affectedmore strongly. Panel B shows a case where the producers are unaffected by scroungers,whereas in panel C, producer payoffs seem to benefit from increased frequencies of scrounger.
66 LUC‐ALAIN GIRALDEAU AND FREDERIQUE DUBOIS
Payo
ffs
Proportion scrounger
adapted from Giraldeau & Dubois, 2008
Scrounger
Producer
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ESS assumes !a genetic model.
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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.
343M O TTLEY & G IRAL D EA U : CONVERGING ON PS EQUILIBRIA
But individuals sample and learn.
Mottley & Giraldeau, 2000
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Information use
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Personal information
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Social informationSocial
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Foraging in space...
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Video of zebra finches in the lab?
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some words onmethodology
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Individual-based models
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Cellular automata
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Genetic algorithms
selection
reproduction
termination
initialization
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IntroductionInformation use
Foraging in spaceConclusion
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Personal information use:
Learning rules
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Learning rule: “A learning rule is defined as a rule which assigns for every possible behaviour the probability of displaying that behaviour at each trial of a game as a function of previous payoffs.” (Harley, 1981)
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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
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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
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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
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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
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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
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Relative payoff sum
Linear operator
Perfect memory
Hamblin & Giraldeau, 2009
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selection
reproduction
termination
initialization
+
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Time
Popu
latio
n The RPS rule dominates LOP and PM.
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01
23
45
Group size
Para
met
er v
alue
s
●
●
● ●
●
●
10 40 90 160 360 1000
Producer residual
Scrounger residual
Memory factor
Why are the producer residuals so high?
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Social learning
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Social learning heuristic:A “rule of thumb” in which individuals!observe their neighbours and adopt the!strategy which led to the highest payoff!in their neighbourhood.
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possible updating rules, including stochastic rules that allow for a more realistic
(but no longer replicable) updating, and which may have an effect on the results
(e.g. Moyano and Sánchez 2009), but we do not deal with these here.
1.500.75
2.00
1.50
2.00 2.00
1.50 2.25
1.50
S S S S
S
S
S
SSSSS
S
S
S
S
SS
P
S
P
S S
S S
1.500.75
2.75
1.50
2.75 2.75
1.50
1.50
S S S S
S
S
S
SSSSS
S
S
S
S
SS
P
S
P
S
S
2.75
P
P
Figure 5.2: Updating a cell. As before, red is scrounger and blue is producer. Cellscalculate their payoffs against each of their neighbours, in this case using GE (1) andan� of 0.75. Here, we look at the cell in the centre of the grid section pictured. On theleft hand side, the scrounger in the bottom-right of the focal cell’s neighbourhoodhas a higher payoff than the focal cell, so the focal cell will become a scrounger inthe next time step (though this is not depicted, so will the other two producers). Onthe right hand side, the addition of one more producer in the neighbourhood drivesthe focal cell’s fitness high enough that it will no longer change to scrounger in thenext time step.
112
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Producer
ScroungerFormer producer
Former scrounger
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Producer
ScroungerFormer producer
Former scrounger
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020
40
60
80
100
1-5
6-10
11-15
16-20
Figure 5.7: A chaotic outcome. Shown is the first twenty steps of a run that did notachieve an fixed outcome after 10000 time steps, with the population proportion ofscrounger and producer over the twenty steps graphed below. Red is a scrounger,blue is a producer, green is a scrounger that was a producer in the previous timestep, and yellow is a producer that was a scrounger in the previous time step; thegraph lines include cells that switched, such that the red scrounger line is the totalof the red and green cells in that step, just as the blue producer line includes the blueand yellow cells.
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Coevolving information: !Predator-prey dynamics
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Predator search efficiency
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Dispersed prey favours producers...
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... while clumped prey induces increased scrounging.
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Thus: will prey evolve to manipulate !predator information use?
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selection
reproduction
termination
initialization
selection
reproduction
termination
initialization
+ +
Prey: !clumpiness
Predators:!NI!SI!
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●
●
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●
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●0.
00.
20.
40.
60.
8Fr
eque
ncy
of sc
roun
ger A
●
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●
●
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1 5 10 15 20 25 30 35 40 45 50
300
500
700
Prey clump size
Prey
surv
ival
B
~60-65%
Roughly !constant
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No social !information
Social !information
010
2030
4050 A
0.0
0.2
0.4
0.6
0.8
1.0
010
2030
4050
Prey
clu
mp
size
B
0.0
0.2
0.4
0.6
0.8
1.0
Freq
uenc
y of
scro
unge
r
0 100 200 300 400 500
010
2030
4050
Generation
C0.
00.
20.
40.
60.
81.
0solid line: prey clump size!dashed line: predator scrounging
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Prey clump in a way that induces maximum!social information use among predators.
●
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●
●
●
●
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250
300
350
400
450
Prey
surv
ival
100 200 300 400 500 100 200 300 400 500 100 200 300 400 500
No social information Social information Public information
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IntroductionInformation use
Foraging in spaceConclusion
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Where is as important as what.
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Foraging with personality.
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Boldness
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Bold
Shy
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Bold
Shy
~ producer
~ scrounger
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Can we get such a dimorphism to evolve?
selection
reproduction
termination
initialization
+
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No ... not within a population.
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Genome by Patch Richness and Density, Population Size 50
Boldness
Scrounging
0.2
0.4
0.6
0.8
0.2 0.4 0.6 0.8
: Patch Richness { 5 } : Patch Richness { 10 }
0.2 0.4 0.6 0.8
: Patch Richness { 20 } : Patch Richness { 30 }
: Patch Richness { 40 } : Patch Richness { 50 } : Patch Richness { 60 }
0.2
0.4
0.6
0.8
: Patch Richness { 70 }
0.2
0.4
0.6
0.8
: Patch Richness { 80 }
0.2 0.4 0.6 0.8
: Patch Richness { 90 } : Patch Richness { 100 } Patch Density5102030405060
Patch density ▸ Boldness Patch richness ▸ Scrounging
Shy scroungers
Bold producers
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Genome by Patch Richness and Density, Population Size 50
Boldness
Scrounging
0.2
0.4
0.6
0.8
0.2 0.4 0.6 0.8
: Patch Richness { 5 } : Patch Richness { 10 }
0.2 0.4 0.6 0.8
: Patch Richness { 20 } : Patch Richness { 30 }
: Patch Richness { 40 } : Patch Richness { 50 } : Patch Richness { 60 }
0.2
0.4
0.6
0.8
: Patch Richness { 70 }
0.2
0.4
0.6
0.8
: Patch Richness { 80 }
0.2 0.4 0.6 0.8
: Patch Richness { 90 } : Patch Richness { 100 } Patch Density5102030405060
Patch density ▸ Space Patch richness ▸ Information
Shy scroungers
Bold producers
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Conclusion
IntroductionInformation use
Foraging in space
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selection
reproduction
termination
initialization
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Down the road...
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Landscapes project
landscape had a mean of exactly six neighbours, though therewas variation about this value within individual landscapeinstances. The CGD virtual landscapes all resembled pixe-lated versions of the Dirichlet landscape. However, both thevisual and mathematical approximation improved as theresolution of the underlying raster was increased, asdemonstrated by both the mean and standard deviation ofthe number of neighbours (Table 1). Cells in the aggregatemap had approximately six neighbours, and were a range ofshapes because the sequential building rules meant thatgrowing cells were often geometrically constrained byneighbours. Of the geometries tested in this study, the meannumber of neighbours of a cell was six, or its approximation,with the exception of the rasters. There was variation in thedistribution of cell sizes within the irregular virtual land-scapes (Table 1).We measured and compared all possible unique cell-to-cell
step lengths (measured between centre-of-mass centroids) infive landscapes: the three regular landscapes, and singleinstances of the Dirichlet and the CGD4 landscapes (Figure 3).In the von Neumann and hexagonal landscapes, only one steplength was ever possible, with lengths 1 km and 1.074 km,respectively. In the Moore landscape, two steps were equallyprobable, with lengths 1 km and 1.41 km producing a meanstep of 1.21 km per landscape. Step lengths in the Dirichletlandscape were gamma distributed (Figure 3) with a mean of1.095 km, which is close to that found in the hexagonallandscape; the step lengths of each cell in the CDG4landscape were similarly distributed with a mean of 1.18km, though the distribution was less smooth as a result of thefinite distribution of cell shapes and hence step lengths(Figure 3).
Moving across Model LandscapesAccessibility. We used three methods to investigate move-
ment (of individuals or information) across our virtuallandscapes; these were accessibility, random movement, anddirected random movement. Accessibility (sensu [43]) meas-ured the shortest possible sequence of cell-to-cell stepsbetween two points in the virtual landscape. We implementedthis as the maximum geographical distance accessible from acommon origin in a fixed number of steps (Figure 2). Therewere striking differences between the accessibility of theregular virtual landscapes and those with an irregularstructure (Figure 2). The mean minimum steps required toaccess a fixed distance (effectively the inverse of Figure 2)varied considerably between the regular models (to travel 100km took a mean of 125.9, 90.7, and 102.6 steps for the vonNeumann, Moore, and hexagonal virtual landscapes, respec-tively) and were large compared to the mean minimum stepsrequired in the irregular landscapes (approximately 73 stepsin all five irregular landscapes).There was considerable directional bias shown in the
accessibility of the three regular virtual landscapes. Themaximum distance accessible in a fixed number of steps inthe von Neumann, Moore, and hexagonal landscapes pro-duced a distinctive shape dependent on their neighbourhoodrules: a diamond, a square, and a hexagon, respectively. Incontrast, accessibility in the irregular virtual landscapes wasalways circular. The angular variation in maximum distanceaccessible is demonstrated numerically by the standarddeviation of the minimum number of steps required to travel
Figure 1. Example Instances of Eight Virtual Landcapes
Example virtual landscape geometries (7 km 3 7 km section). (A) vonNeumann and (B) Moore neighbourhoods in a raster grid; (C) hexagonal;(D) Dirichlet tessellation; CGD tessellation with a mean of (E) four, (F)nine, and (G) 16 raster cells per km2; (H) land cover aggregate map. Theneighbourhood (grey) of a focal cell (black) is highlighted in each virtuallandscape.doi:10.1371/journal.pcbi.0030200.g001
PLoS Computational Biology | www.ploscompbiol.org October 2007 | Volume 3 | Issue 10 | e2001981
Geometry of Virtual Landscapes
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Genetic programming.
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Learning in butterflies
Emilie Snell-Rood!University of Minnesota
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Thanks to this guy, and his lab...
... and these groups ...
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... and a big thank you !to Brandy, for
!
(among many other things) !!
visual support
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Incompatibility
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Patch discovery
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Scroungers converge