Stationary distribution of a 2-island 2-allele Wright–Fisher diffusion model with slow mutation and migration rates

Conrad J. Burden and Robert C. Griffiths

Theoretical Population Biology, 2018, vol. 124, issue C, 70-80

Abstract: The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright–Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for approximating the forward Kolmogorov equation, the stationary distribution is obtained to leading order as a set of line densities on the edges of the sample space, corresponding to states for which one island is bi-allelic and the other island is non-segregating, and a set of point masses at the corners of the sample space, corresponding to states for which both islands are simultaneously non-segregating. Analytic results for the corner probabilities and line densities are verified independently using the backward generator and for the corner probabilities using the coalescent.

Keywords: Migration; Diffusion process; Subdivided population (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:124:y:2018:i:c:p:70-80

DOI: 10.1016/j.tpb.2018.09.004

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