Stationary solutions for metapopulation Moran models with mutation and selection

TL;DR

This paper develops a reduced model for a metapopulation Moran process with mutation and selection, capturing the effects of migration and island structure, and validates it through simulations.

Contribution

It introduces an effective one-variable description of the metapopulation Moran model that incorporates network structure and island sizes, enhancing analytical tractability.

Findings

Predictions match stochastic simulations across parameters

Effective parameters depend on network and island sizes

Fast-variable elimination accurately describes slow dynamics

Abstract

We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion approximation and timescale separation arguments, an effective one-variable description of the model is developed. The effective description bears similarities to the well-mixed Moran model with effective parameters which depend on the network structure and island sizes, and is amenable to analysis. Predictions from the reduced theory match the results from stochastic simulations across a range of parameters. The nature of the fast-variable elimination technique we adopt is further studied by applying it to a linear system, where it provides a precise description of the slow-dynamics in the limit of large timescale separation.