Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

Ladret, Véronique; Lessard, Sabin

doi:10.1016/j.tpb.2007.04.001

Cited by 22 publications

(32 citation statements)

References 56 publications

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“…This result shows that the approximation for the probability of fixation of a newly introduced single mutant in the case of Wright's island model for demes of equal size N, and with the same game matrix W, given in Ladret and Lessard (2007) for DX3 demes, still holds for D ¼ 2 demes. …”

Section: Fixation Coefficient Under the Structured-coalescent Assumptmentioning

confidence: 75%

“…An approximation for the firstorder effect of selection on the probability of fixation of a single mutant is obtained, adapting a direct Markov chain method proposed by Rousset (2003) as ascertained in Lessard and Ladret (2007). When the population is panmictic (Lessard, 2005; see also Lessard, 2007) or when its structure is symmetric (Rousset and Billiard, 2000;Ladret and Lessard, 2007), the method allows to express this approximation as a function of expected coalescence times, under neutrality, for samples of individuals. In the case of unequal deme sizes and/or different migration rates, we have to resort to an extension of the direct Markov chain approach to perform the calculations.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Ladret

Lessard

2008

Journal of Theoretical Biology

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Section: Fixation Coefficient Under the Structured-coalescent Assumptmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Ladret

Lessard

2008

Journal of Theoretical Biology

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“…Another spatial structure is a population subdivided into two subpopulations with any migration rates (Ladret and Lessard, 2007), or an island model with a large number of islands and uniform or proportional dispersal (Rousset and Billiard, 2000;Ladret and Lessard, 2008;Lessard, 2011a,b). The stepping stone model (see, e.g., Rousset and Billiard, 2000;Rousset, 2006) is a spatial model with local dispersal.…”

Section: Introductionmentioning

confidence: 99%

Evolution of cooperation in a multidimensional phenotype space

Kroumi

Lessard

2015

Theoretical Population Biology

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“…[62]], which would allow to make use of coalescent theory [63] to obtain exact analytical expressions for the structure coefficients. However, such expected coalescence times can be difficult to obtain exactly [62,64]. Alternatively, for small graphs, the sigma rule and hence the structure coefficients can be explicitly calculated from the transition matrix of the evolutionary process [cf.…”

Section: Discussionmentioning

confidence: 99%

Evolutionary games of multiplayer cooperation on graphs

Peña

Arranz

et al. 2016

Preprint

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There has been much interest in studying evolutionary games in structured populations, often modelled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. Author SummaryCooperation can be defined as the act of providing fitness benefits to other individuals, often at a personal cost. When interactions occur mainly with neighbors, assortment of strategies can favor cooperation but local competition can undermine it. Previous research has shown that a single coefficient can capture this trade-off when cooperative interactions take place between two players. More complicated, but also more realistic models of cooperative interactions involving multiple players instead require several such coefficients, making it difficult to assess the effects of population structure. Here, we obtain analytical approximations for the coefficients of multiplayer games in graph-structured populations. Computer simulations show that, for particular instances of multiplayer games, these approximate coefficients predict the condition for cooperation to be promoted in random graphs well, but fail to do so in graphs with more structure, such as lattices. Our work extends and generalizes established results on the evolution of cooperation on graphs, but also highlights the importance of explicitly taking into account higher-order statistical associations in order to assess the evolutionary dynamics of cooperation in spatially structured populations.

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Fixation probability for a beneficial allele and a mutant strategy in a linear game under weak selection in a finite island model

Cited by 22 publications

References 56 publications

Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Evolution of cooperation in a multidimensional phenotype space

Evolutionary games of multiplayer cooperation on graphs

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