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Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation–drift model

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  • Vogl, Claus
  • Mikula, Lynette C.
  • Burden, Conrad J.

Abstract

The stationary sampling distribution of a neutral decoupled Moran or Wright–Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this distribution as a starting point we derive results for maximum likelihood estimates of scaled mutation rates from site frequency data under three model assumptions: a twelve-parameter general rate matrix, a nine-parameter reversible rate matrix, and a six-parameter strand-symmetric rate matrix. The site frequency spectrum is assumed to be sampled from a fixed size population in equilibrium, and to consist of allele frequency data at a large number of unlinked sites evolving with a common mutation rate matrix without selective bias. We correct an error in a previous treatment of the same problem (Burden and Tang, 2017) affecting the estimators for the general and strand-symmetric rate matrices. The method is applied to a biological dataset consisting of a site frequency spectrum extracted from short autosomal introns in a sample of Drosophila melanogaster individuals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:134:y:2020:i:c:p:106-118
    DOI: 10.1016/j.tpb.2020.06.001
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    References listed on IDEAS

    as
    1. Burden, Conrad J. & Tang, Yurong, 2017. "Rate matrix estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 113(C), pages 23-33.
    2. Burden, Conrad J. & Tang, Yurong, 2016. "An approximate stationary solution for multi-allele neutral diffusion with low mutation rates," Theoretical Population Biology, Elsevier, vol. 112(C), pages 22-32.
    3. 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.
    4. Vogl, Claus & Bergman, Juraj, 2015. "Inference of directional selection and mutation parameters assuming equilibrium," Theoretical Population Biology, Elsevier, vol. 106(C), pages 71-82.
    5. Matthew Stephens & Peter Donnelly, 2000. "Inference in molecular population genetics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 605-635.
    6. 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.
    7. 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.
    8. 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.
    9. 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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