Phd Defence talk

In my defence...

by Steven Hamblin

Social foraging.

Game theory model that captures the logic of exploiting the labor of others.

Producer-Scrounger game.

a.k.a. kleptoparasitism.

Producer-Scrounger game.

Video of zebra finches in the lab?

Video of zebra finches in the lab?

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

Payoffs

Proportion scrounger

adapted from Giraldeau & Dubois, 2008

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

Payoffs

Proportion scrounger

adapted from Giraldeau & Dubois, 2008

Producer

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

Payoffs

Proportion scrounger

adapted from Giraldeau & Dubois, 2008

ProducerScrounger

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

Payoffs

Proportion scrounger

adapted from Giraldeau & Dubois, 2008

Equilibrium value of scrounging

ProducerScrounger

How do we model questions of such complexity?

Individual-based models

Genetic algorithmsselection

reproduction

termination

initialization

Cellular automata

Public Information: From Nosy Neighbors toCultural Evolution

Etienne Danchin,1 Luc-Alain Giraldeau,2 Thomas J. Valone,3 Richard H. Wagner4

Psychologists, economists, and advertising moguls have long known that humandecision-making is strongly influenced by the behavior of others. A rapidly accumu-lating body of evidence suggests that the same is true in animals. Individuals can useinformation arising from cues inadvertently produced by the behavior of otherindividuals with similar requirements. Many of these cues provide public informationabout the quality of alternatives. The use of public information is taxonomicallywidespread and can enhance fitness. Public information can lead to cultural evolu-tion, which we suggest may then affect biological evolution.

A nimals often face decisions such aswhere to forage, with whom to mate, orwhere to breed, each with different fit-

ness outcomes. To decide effectively, they needinformation about the various alternatives. Un-less conditions are constant, inheriting usefulinformation about the environment geneticallymay be impossible, and so the acquisition ofinformation becomes beneficial.

There are two ways to acquire information(Fig. 1): by using trial-and-error tactics to inter-act with the physical environment (personalinformation), or by monitoring others’ interac-tions with the environment (social information).Social information can be based on signals—traits specifically designed by selection to con-vey information. Alternatively, it can be basedon cues provided inadvertently by individualsengaged in efficient performance of their activ-ities (inadvertent social information, or ISI).The social cues of ISI may indicate the locationof resources when other individuals with simi-lar requirements for these resources are present[social attraction (1)] or their behavior is ob-served from a distance [i.e., local enhancement(2)]. ISI may also involve public information(PI) (3) about the quality of the resource whenit is revealed by the performance of other indi-viduals that share similar environmental re-quirements (4). Here we deal mostly with in-stances of PI use.

The reliability of ISI for bystanders re-sides in the fact that they are not intention-

ally produced; individuals providing themare selected to perform as well as possible,rather than to inform others. In particular,PI provides rich and reliable informationabout the quality of al-ternatives (3, 4). Thebenefits of using PI arethat it reduces the costsassociated with trial-and-error learning andprovides additional in-formation that can leadto more accurate esti-mates of environmentalparameters (5). The useof ISI can thus varyfrom situations wherethe bystander parasit-izes the information(involving a cost to theperformer), to com-mensalism (when thebystander’s use of ISIis neutral to the per-former), to mutualism(when both actors ben-efit from the use of ISIby the bystander).

The Diversity ofPublic InformationUseForaging as public in-formation. The idea thatanimals may observeothers to get informationabout resource qualityarose mostly in a forag-ing context (6). For in-stance, when Norwayrats (Rattus norvegicus)face unfamiliar food,they rely on ISI provid-ed by the breath of com-

panions to decide on the appropriate prey toeat (7). European starlings (Sturnus vulgaris;Fig. 2A) and red crossbills (Loxia curviros-tra) exploit hidden prey and must probe re-peatedly to estimate the current quality of aforaging patch. Both species observe theirflockmates’ probing success and use this asPI to decide when to leave a patch in searchof another (8–10). Scrub jays (Aphelocomacoerulescens; Fig. 2B) observe and remem-ber the food caches of conspecifics and pilferthem when given the opportunity (11). Thisuse of ISI could involve PI if the pilfereralso uses the information to estimate the

1U.P.M.C. CNRS-UMR7625, Bat A–7e etage–Case 237,7 quai Saint Bernard, 75252 Paris Cedex 05, France.E-mail: edanchin@snv.jussieu.fr 2Group de Rechercheen Ecologie Comportementale et Animale, Departe-ment des Sciences Biologiques, Universite du Quebeca Montreal, Case Postale 8888, Succursale Centre-Ville, Montreal, Quebec H3C 3P8, Canada. E-mail:giraldeau.luc-alain@uqam.ca 3Department of Biology,St. Louis University, St. Louis, MO 63103, USA. E-mail:valone@slu.edu 4Konrad Lorenz Institute, AustrianAcademy of Sciences, Savoyenstrasse 1a, A-1160 Vi-enna, Austria. E-mail: r.wagner@klivv.oeaw.ac.at

Fig. 1. The various forms of nongenetically acquired information(apart from parental effects). Information is anything that reducesuncertainty. Personal information is acquired individually by interact-ing with the physical environment. The interaction can generate bothprivate information (inaccessible to others) and nonprivate informa-tion that produces social information (red arrow). A behavior canconvey information by design; it is then a signal that is produced byselection. In many cases, however, social information is producedinadvertently; it is then a cue, and we refer to it as inadvertent socialinformation (ISI). Topics covered in this review are in blue. ISI com-prises cues that indicate the spatial location of resources (based onthe location of the information producers) and cues produced by theperformance of others, which is public information (PI). PI may play amajor role in cultural transmission and evolution. The arrow from thecues box to the signals box indicates that signals directed to one partymay inadvertently be used by a third party. The use of that informa-tion by others may create the selective pressures that transform ISIinto signals (34 ). Thus, PI may be viewed in some contexts as theplatform from which signals evolve.

REVIEW

www.sciencemag.org SCIENCE VOL 305 23 JULY 2004 487

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Danchin et al., 2004

Public Information: From Nosy Neighbors toCultural Evolution

Etienne Danchin,1 Luc-Alain Giraldeau,2 Thomas J. Valone,3 Richard H. Wagner4

Psychologists, economists, and advertising moguls have long known that humandecision-making is strongly influenced by the behavior of others. A rapidly accumu-lating body of evidence suggests that the same is true in animals. Individuals can useinformation arising from cues inadvertently produced by the behavior of otherindividuals with similar requirements. Many of these cues provide public informationabout the quality of alternatives. The use of public information is taxonomicallywidespread and can enhance fitness. Public information can lead to cultural evolu-tion, which we suggest may then affect biological evolution.

A nimals often face decisions such aswhere to forage, with whom to mate, orwhere to breed, each with different fit-

ness outcomes. To decide effectively, they needinformation about the various alternatives. Un-less conditions are constant, inheriting usefulinformation about the environment geneticallymay be impossible, and so the acquisition ofinformation becomes beneficial.

There are two ways to acquire information(Fig. 1): by using trial-and-error tactics to inter-act with the physical environment (personalinformation), or by monitoring others’ interac-tions with the environment (social information).Social information can be based on signals—traits specifically designed by selection to con-vey information. Alternatively, it can be basedon cues provided inadvertently by individualsengaged in efficient performance of their activ-ities (inadvertent social information, or ISI).The social cues of ISI may indicate the locationof resources when other individuals with simi-lar requirements for these resources are present[social attraction (1)] or their behavior is ob-served from a distance [i.e., local enhancement(2)]. ISI may also involve public information(PI) (3) about the quality of the resource whenit is revealed by the performance of other indi-viduals that share similar environmental re-quirements (4). Here we deal mostly with in-stances of PI use.

The reliability of ISI for bystanders re-sides in the fact that they are not intention-

ally produced; individuals providing themare selected to perform as well as possible,rather than to inform others. In particular,PI provides rich and reliable informationabout the quality of al-ternatives (3, 4). Thebenefits of using PI arethat it reduces the costsassociated with trial-and-error learning andprovides additional in-formation that can leadto more accurate esti-mates of environmentalparameters (5). The useof ISI can thus varyfrom situations wherethe bystander parasit-izes the information(involving a cost to theperformer), to com-mensalism (when thebystander’s use of ISIis neutral to the per-former), to mutualism(when both actors ben-efit from the use of ISIby the bystander).

The Diversity ofPublic InformationUseForaging as public in-formation. The idea thatanimals may observeothers to get informationabout resource qualityarose mostly in a forag-ing context (6). For in-stance, when Norwayrats (Rattus norvegicus)face unfamiliar food,they rely on ISI provid-ed by the breath of com-

panions to decide on the appropriate prey toeat (7). European starlings (Sturnus vulgaris;Fig. 2A) and red crossbills (Loxia curviros-tra) exploit hidden prey and must probe re-peatedly to estimate the current quality of aforaging patch. Both species observe theirflockmates’ probing success and use this asPI to decide when to leave a patch in searchof another (8–10). Scrub jays (Aphelocomacoerulescens; Fig. 2B) observe and remem-ber the food caches of conspecifics and pilferthem when given the opportunity (11). Thisuse of ISI could involve PI if the pilfereralso uses the information to estimate the

1U.P.M.C. CNRS-UMR7625, Bat A–7e etage–Case 237,7 quai Saint Bernard, 75252 Paris Cedex 05, France.E-mail: edanchin@snv.jussieu.fr 2Group de Rechercheen Ecologie Comportementale et Animale, Departe-ment des Sciences Biologiques, Universite du Quebeca Montreal, Case Postale 8888, Succursale Centre-Ville, Montreal, Quebec H3C 3P8, Canada. E-mail:giraldeau.luc-alain@uqam.ca 3Department of Biology,St. Louis University, St. Louis, MO 63103, USA. E-mail:valone@slu.edu 4Konrad Lorenz Institute, AustrianAcademy of Sciences, Savoyenstrasse 1a, A-1160 Vi-enna, Austria. E-mail: r.wagner@klivv.oeaw.ac.at

Fig. 1. The various forms of nongenetically acquired information(apart from parental effects). Information is anything that reducesuncertainty. Personal information is acquired individually by interact-ing with the physical environment. The interaction can generate bothprivate information (inaccessible to others) and nonprivate informa-tion that produces social information (red arrow). A behavior canconvey information by design; it is then a signal that is produced byselection. In many cases, however, social information is producedinadvertently; it is then a cue, and we refer to it as inadvertent socialinformation (ISI). Topics covered in this review are in blue. ISI com-prises cues that indicate the spatial location of resources (based onthe location of the information producers) and cues produced by theperformance of others, which is public information (PI). PI may play amajor role in cultural transmission and evolution. The arrow from thecues box to the signals box indicates that signals directed to one partymay inadvertently be used by a third party. The use of that informa-tion by others may create the selective pressures that transform ISIinto signals (34 ). Thus, PI may be viewed in some contexts as theplatform from which signals evolve.

REVIEW

www.sciencemag.org SCIENCE VOL 305 23 JULY 2004 487

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Personal information:

Social information:

Learning rules.

Predator-prey coevolution.Social learning.

Chapter 2

Chapter 3

Chapter 5

Predator-prey coevolution.

Predator search efficiency

Dispersed prey favours producers...

... while clumped prey induces increased scrounging.

Thus: will prey evolve to manipulate predator information use?

Prey: clumpiness

Predators:NISIPI

selection

reproduction

termination

initialization

+ +selection

reproduction

termination

initialization

●

●

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●

●

●0.

00.

20.

40.

60.

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eque

ncy

of sc

roun

ger A

●

●●

●

●

●●

●●●

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

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

C

0.0

0.2

0.4

0.6

0.8

1.0

No social information

Social information

Public information

●

●

●

●

●

●

●

●

●

●

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

Prey clump in a way that induces maximumsocial information use among predators.

Video of zebra finches in the lab?

Video of zebra finches in the lab?

Spatial relationships

Spatial environmentLandscape geometry.

Cellular automata PS game. Chapter 5

Chapter 6

Landscape geometry.

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

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

+

Individuals play a PS game on one of the grid types.ESS values and flock geometry (convex hull) are then calculated for each run.

Manipulated: patch density, population size.Also: movement costs and food benefits (not shown).

Grid type

Mea

n f

lock

are

a

50

100

150

: Patch density { 5 } : Population size { 5 }

Dirichlet Hexagonal Moore von Neumann

: Patch density { 10 } : Population size { 5 }

: Patch density { 15 } : Population size { 5 }

Dirichlet Hexagonal Moore von Neumann

: Patch density { 20 } : Population size { 5 }

: Patch density { 25 } : Population size { 5 }

: Patch density { 5 } : Population size { 10 }

: Patch density { 10 } : Population size { 10 }

: Patch density { 15 } : Population size { 10 }

: Patch density { 20 } : Population size { 10 }

50

100

150

: Patch density { 25 } : Population size { 10 }

50

100

150

Dirichlet Hexagonal Moore von Neumann

: Patch density { 5 } : Population size { 20 }

: Patch density { 10 } : Population size { 20 }

Dirichlet Hexagonal Moore von Neumann

: Patch density { 15 } : Population size { 20 }

: Patch density { 20 } : Population size { 20 }

Dirichlet Hexagonal Moore von Neumann

: Patch density { 25 } : Population size { 20 }

Range of ESS values between grids.

Range # of Combinations

< 0.05 8

0.05 - 0.10 33

0.10 - 0.15 11

0.15 - 0.23 8

Landscape has significant effects on equilibrium behaviour and flock geometry.

Conclusions:

+

Both space and information.Personality and the PS game. Chapter 4

Cellular automata PS game. Chapter 5

Social learning in a spatial PS game.

Social learning heuristic:

A “rule of thumb” in which individualsobserve their neighbours and adopt thestrategy which led to the highest payoffin their neighbourhood.

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

Producer

ScroungerFormer producer

Former scrounger

Producer

ScroungerFormer producer

Former scrounger

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.

122

Simple use of social information and spatial structure leads to complex, emergent behaviour.

Individuals are flexible while the population achieves equilibrium.

Conclusions:

Conclusions...

Mixing the elegant simplicity of the PS game with information use and spatial effects adds value to our study of social foraging.

Simulation techniques like IBMs, GAs, and CAs can be invaluable tools to do so.

The evolution of mechanisms (“evo-mecho”) underlying flexible use of information and response to spatial variation is a rich field of study.

The spatial environment (conspecifics and landscape geometry) has an under-appreciated effect on behaviour and should be studied more broadly.

... for which I give thanks ...

Learning rules.

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)

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)

Relative Payoff Sum

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)

Relative Payoff SumLinear Operator

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)

Relative Payoff SumLinear OperatorPerfect Memory

selection

reproduction

termination

initialization

+

Which rule allows individuals to best usepersonal information in a PS game?

Conclusions:

One rule (RPS) out-performed the others.

Producing was predicted to be difficult to extinguish.

Personality and PS games.

Boldness

Bold

Shy

~ producer

~ scroungerfix me: not happy withthis placement

Can we get such a dimorphism to evolve?

selection

reproduction

termination

initialization

+

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

Patch richness ▸ Information Patch density ▸ Space

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

Conclusions:

Both space and information use affect this system.

This is a record of my contribution.

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

Payoffs

Proportion scrounger

ProducerScrounger

A population composed entirely of producers has higher average fitness (more prey consumed).

Progress in the producer-scrounger game:information use and spatial models.

A thesis submitted in partial fulfillmentof the requirements for the degree of

Doctor of Philosophy in Biology

Kleptoparasitism

From so simple a beginning...

Kleptoparasitism

Social information

Kleptoparasitism

Social information

Learni

ng

Kleptoparasitism

Social information

Le

arning

Animal personality

Kleptoparasitism

Social information

Le

arning Animal personality

ChaptersChapter 2

Chapter 4

Chapter 5

Grid type

ESS

val

ue

0.2

0.4

0.6

0.8

: Patch density: { 5 } : Population size: { 5 }

Dirichlet Hexagonal Moore von Neumann

: Patch density: { 25 } : Population size: { 5 }

Dirichlet Hexagonal Moore von Neumann

: Patch density: { 5 } : Population size: { 20 }

0.2

0.4

0.6

0.8

: Patch density: { 25 } : Population size: { 20 }

Landscape has significant effects on equilibrium behaviour and flock geometry.

Conclusions:

Patch density is an important spatial variable.

Alpha (α)

Mea

n pr

opor

tion

of s

crou

ngin

g

0

20

40

60

80

100

GE(1) GE 2 GE(3)0.51

0.56

0.61

0.66

0.71

0.81

0.86

0.96

GE(4)0.51

0.56

0.61

0.66

0.71

0.76

0.81

0.86

0.91

0.96

GE(5)

0.51

0.56

0.61

0.71

0.76

0.81

0.86

0.91

0.96

0

20

40

60

80

100

GE(6

Text

Text