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).
Donald Dawson. Andreas Greven. "Hierarchically Interacting Fleming-Viot Processes With Selection and Mutation: Multiple Space Time Scale Analysis and Quasi-Equilibria." Electron. J. Probab. 4 1 - 81, 1999. https://doi.org/10.1214/EJP.v4-41