Stationary solutions for metapopulation Moran models with mutation and selection

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.

16 pages, 8 figures

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Cited by in corpus (3)

• Exploiting fast-variables to understand population dynamics and evolution
• High fraction of silent recombination in a finite population two-locus neutral birth-death-mutation model
• Reduction of a metapopulation genetic model to an effective one island model