Evolutionary Games in Deme Structured, Finite Populations

We describe a fairly general model for the evolutionary dynamics in a sub-divided (or deme structured) population with migration and mutation. The number and size of demes are finite and fixed. The fitness of each individual is determined by pairwise interactions with other members of the same deme. The dynamics within demes can be modeled according to a broad range of evolutionary processes. With a probability proportional to fitness, individuals migrate to another deme. Mutations occur randomly. In the limit of few migrations and even rarer mutations we derive a simple analytic condition for selection to favor one strategic type over another. In particular, we show that the Pareto efficient type is favored when competition within demes is sufficiently weak. We then apply the general results to the prisoner's dilemma game and discuss selected dynamics and the conditions for cooperation to prevail.