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

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  • Vogl, Claus
  • Clemente, Florian

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.

Suggested Citation

  • Vogl, Claus & Clemente, Florian, 2012. "The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates," Theoretical Population Biology, Elsevier, vol. 81(3), pages 197-209.
    • Handle: RePEc:eee:thpobi:v:81:y:2012:i:3:p:197-209
    DOI: 10.1016/j.tpb.2012.01.001
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    References listed on IDEAS

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    1. RoyChoudhury, Arindam & Wakeley, John, 2010. "Sufficiency of the number of segregating sites in the limit under finite-sites mutation," Theoretical Population Biology, Elsevier, vol. 78(2), pages 118-122.
    2. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
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    Cited by:

    1. Jüri Lember & Chris Watkins, 2022. "An Evolutionary Model that Satisfies Detailed Balance," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 1-37, March.
    2. Mikula, Lynette Caitlin & Vogl, Claus, 2024. "The expected sample allele frequencies from populations of changing size via orthogonal polynomials," Theoretical Population Biology, Elsevier, vol. 157(C), pages 55-85.
    3. Xinkai Wu & Mengze Xu & Jian-Rong Yang & Jian Lu, 2024. "Genome-wide impact of codon usage bias on translation optimization in Drosophila melanogaster," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    4. Vogl, Claus, 2014. "Estimating the scaled mutation rate and mutation bias with site frequency data," Theoretical Population Biology, Elsevier, vol. 98(C), pages 19-27.
    5. Vogl, Claus & Bergman, Juraj, 2015. "Inference of directional selection and mutation parameters assuming equilibrium," Theoretical Population Biology, Elsevier, vol. 106(C), pages 71-82.
    6. Vogl, Claus & Mikula, Lynette Caitlin, 2021. "A nearly-neutral biallelic Moran model with biased mutation and linear and quadratic selection," Theoretical Population Biology, Elsevier, vol. 139(C), pages 1-17.
    7. Malaguti, Giulia & Singh, Param Priya & Isambert, Hervé, 2014. "On the retention of gene duplicates prone to dominant deleterious mutations," Theoretical Population Biology, Elsevier, vol. 93(C), pages 38-51.
    8. Vogl, Claus & Mikula, Lynette C. & Burden, Conrad J., 2020. "Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation–drift model," Theoretical Population Biology, Elsevier, vol. 134(C), pages 106-118.
    9. Schrempf, Dominik & Hobolth, Asger, 2017. "An alternative derivation of the stationary distribution of the multivariate neutral Wright–Fisher model for low mutation rates with a view to mutation rate estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 114(C), pages 88-94.

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