title: Finite-size effects and switching times for Moran process with mutation.
abstract: We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.
authors.affiliation: Department of Mathematics, University of Illinois, 1409 W Green St, Urbana, IL, 61801, USA.
authors.forename: Lee
authors.initials: L
authors.lastname: DeVille
authors.affiliation: Department of Mathematics, University of Illinois, 1409 W Green St, Urbana, IL, 61801, USA. galiard2@illinois.edu.
authors.forename: Meghan
authors.initials: M
authors.lastname: Galiardi
mesh_terms: D005075:Biological Evolution; D005716:Game Theory; D008954:Models, Biological; D009154:Mutation; D011156:Population Density; D013269:Stochastic Processes
keywords: Iterated Prisoner’s dilemma; Metastability; Stochastic processes; WKB asymptotics