The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates

Claus Vogl and Florian Clemente

Theoretical Population Biology, 2012, vol. 81, issue 3, 197-209

Abstract: We analyze a decoupled Moran model with haploid population size N, a biallelic locus under mutation and drift with scaled forward and backward mutation rates θ1=μ1N and θ0=μ0N, and directional selection with scaled strength γ=sN. With small scaled mutation rates θ0 and θ1, which is appropriate for single nucleotide polymorphism data in highly recombining regions, we derive a simple approximate equilibrium distribution for polymorphic alleles with a constant of proportionality. We also put forth an even simpler model, where all mutations originate from monomorphic states. Using this model we derive the sojourn times, conditional on the ancestral and fixed allele, and under equilibrium the distributions of fixed and polymorphic alleles and fixation rates. Furthermore, we also derive the distribution of small samples in the diffusion limit and provide convenient recurrence relations for calculating this distribution. This enables us to give formulas analogous to the Ewens–Watterson estimator of θ for biased mutation rates and selection. We apply this theory to a polymorphism dataset of fourfold degenerate sites in Drosophila melanogaster.

Keywords: Moran model; Mutation bias; Genic selection; Small mutation rates; Small samples; Drosophila melanogaster (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:81:y:2012:i:3:p:197-209

DOI: 10.1016/j.tpb.2012.01.001

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