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The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates
Authors:Vogl Claus  Clemente Florian
Institution:
  • a Institute of Animal Breeding and Genetics, Veterinärmedizinische Universität Wien, Veterinärplatz 1, A-1210 Vienna, Austria
  • b Institut of Population Genetics, Veterinärmedizinische Universität Wien, Veterinärplatz 1, A-1210 Vienna, Austria
  • 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
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