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We consider the Moran process with two populations competing under aniterated Prisoners' Dilemma in the presence of mutation, and concentrate on thecase where there are multiple Evolutionarily Stable Strategies. We perform acomplete bifurcation analysis of the deterministic system which arises in theinfinite population size. We also study the Master equation and obtainasymptotics for the invariant distribution and metastable switching times forthe stochastic process in the case of large but finite population. We also showthat the stochastic system has asymmetries in the form of a skew for parametervalues where the deterministic limit is symmetric.

Finite-size effects and switching times for Moran dynamics with mutation