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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

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  • Schrempf, Dominik
  • Hobolth, Asger

Abstract

Recently, Burden and Tang (2016) provided an analytical expression for the stationary distribution of the multivariate neutral Wright–Fisher model with low mutation rates. In this paper we present a simple, alternative derivation that illustrates the approximation. Our proof is based on the discrete multivariate boundary mutation model which has three key ingredients. First, the decoupled Moran model is used to describe genetic drift. Second, low mutation rates are assumed by limiting mutations to monomorphic states. Third, the mutation rate matrix is separated into a time-reversible part and a flux part, as suggested by Burden and Tang (2016). An application of our result to data from several great apes reveals that the assumption of stationarity may be inadequate or that other evolutionary forces like selection or biased gene conversion are acting. Furthermore we find that the model with a reversible mutation rate matrix provides a reasonably good fit to the data compared to the one with a non-reversible mutation rate matrix.

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  • 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.
    • Handle: RePEc:eee:thpobi:v:114:y:2017:i:c:p:88-94
    DOI: 10.1016/j.tpb.2016.12.001
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    References listed on IDEAS

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    1. 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.
    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. 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.
    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.
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    1. Burden, Conrad J. & Griffiths, Robert C., 2018. "Stationary distribution of a 2-island 2-allele Wright–Fisher diffusion model with slow mutation and migration rates," Theoretical Population Biology, Elsevier, vol. 124(C), pages 70-80.
    2. 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.

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