Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation.
We consider evolutionary game dynamics in a finite population subdivided into two demes with both unequal deme sizes and different migration rates. Assuming viability differences in the population according to a linear game within each deme as a result of pairwise interactions, we specify conditions for weak selection favoring a mutant strategy to go to fixation, under the structured-coalescent assumptions, and their connections with evolutionary stability concepts. In the framework of the Iterated Prisoner's Dilemma with strategy 'tit-for-tat' as mutant strategy and 'always defect' as resident strategy, we deduce a condition under which the emergence of cooperation is favored by selection, when the game matrix is the same in both demes. We show how this condition extends the one-third law for a panmictic population and when an asymmetry in the spatial structure of a two-deme population facilitates the emergence of the cooperative tit-for-tat strategy in comparison with both its symmetric and panmictic population structure counterparts. We find that the condition is less stringent in the asymmetric scenario versus the symmetric scenario if both the fraction of the population in the deme where the mutant was initially introduced, and the expected proportion of migrant offspring in this deme among all migrant offspring after population regulation, are smaller than, or equal to, 12, provided they are not too small. On the other hand, the condition is less stringent than the one-third law, which holds in the panmictic case, if the latter proportion remains not too close to 1.
Ladret
Véronique
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Centre de recherche du CHU Sainte-Justine, 3175 Côte-Ste-Catherine, Montréal, Québec, Canada H3T1C5.
Lessard
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D000818:Animals; D005075:Biological Evolution; D003299:Cooperative Behavior; D004641:Emigration and Immigration; D005716:Game Theory; D009154:Mutation; D012641:Selection, Genetic