  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.
