Evolutionary Game Dynamics in a Finite Continental Island Population Model and Emergence of Cooperation

Abstract

We consider the continental island model for a finite haploid population with a total number of \({\textit{n}}\) demes consisting of one continent and \(n-1\) islands. We assume viability differences in the population captured by a linear game within each deme as a result of pairwise interactions. Assuming weak selection, conservative migration and the limit case of the structured coalescent assumptions, we derive the first-order approximation for the fixation probability of a single mutant, initially introduced in the continent, with respect to the intensity of selection. This result is applied to the case of the iterated Prisoner’s Dilemma, when the resident strategy is always defect and the mutant cooperative strategy is tit-for-tat. In this context, we investigate the condition under which selection favors the emergence of cooperation and we derive an extension of the “one-third law” of evolution. When the continent and the islands are of the same size, we compare the continental island model to its Wright’s island model counterpart. When the islands have the same size, but this size differs from the size of the continent, we investigate how the asymmetry in the deme sizes can better promote the evolution of tit-for-tat compared to its equal deme sizes model counterpart.