Stationary solutions for metapopulation Moran models with mutation and selection

Stationary solutions for metapopulation Moran models with mutation and selection

George W. A. Constable, Alan J. McKane
(Submitted on 19 Dec 2014)

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.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s