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

TL;DR

This paper analyzes the Moran process with mutation in finite populations, focusing on bifurcations, invariant distributions, and switching times, especially when multiple stable strategies exist.

Contribution

It provides a comprehensive bifurcation analysis and asymptotic results for switching times in Moran dynamics with mutation, highlighting finite-size effects.

Findings

Bifurcation structure of the deterministic limit identified

Asymptotic formulas for invariant distribution derived

Metastable switching times characterized for large populations

Abstract

We consider the Moran process with two populations competing under an iterated Prisoners' 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.