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

Lee DeVille, Meghan Galiardi

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1197-1222
Number of pages26
JournalJournal of Mathematical Biology
Volume74
Issue number5
DOIs
StatePublished - Apr 1 2017

Keywords

  • Iterated Prisoner’s dilemma
  • Metastability
  • Stochastic processes
  • WKB asymptotics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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