Hierarchically Interacting Fleming-Viot Processes With Selection and Mutation: Multiple Space Time Scale Analysis and Quasi-Equilibria

Abstract

Genetic models incorporating resampling and migration are now fairly well-understood. Problems arise in the analysis, if both selection and mutation are incorporated. This paper addresses some aspects of this problem, in particular the analysis of the long-time behaviour before the equilibrium is reached (quasi-equilibrium, which is the time range of interest in most applications).