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Rate matrix estimation from site frequency data

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  • Burden, Conrad J.
  • Tang, Yurong

Abstract

A procedure is described for estimating evolutionary rate matrices from observed site frequency data. The procedure assumes (1) that the data are obtained from a constant size population evolving according to a stationary Wright–Fisher or decoupled Moran model; (2) that the data consist of a multiple alignment of a moderate number of sequenced genomes drawn randomly from the population; and (3) that within the genome a large number of independent, neutral sites evolving with a common mutation rate matrix can be identified. No restrictions are imposed on the scaled rate matrix other than that the off-diagonal elements are positive, their sum is ≪1, and that the rows of the matrix sum to zero. In particular the rate matrix is not assumed to be reversible. The key to the method is an approximate stationary solution to the diffusion limit, forward Kolmogorov equation for neutral evolution in the limit of low mutation rates.

Suggested Citation

  • Burden, Conrad J. & Tang, Yurong, 2017. "Rate matrix estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 113(C), pages 23-33.
    • Handle: RePEc:eee:thpobi:v:113:y:2017:i:c:p:23-33
    DOI: 10.1016/j.tpb.2016.10.001
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    References listed on IDEAS

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    1. Burden, Conrad J. & Simon, Helmut, 2016. "Genetic drift in populations governed by a Galton–Watson branching process," Theoretical Population Biology, Elsevier, vol. 109(C), pages 63-74.
    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. 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.
    5. 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.
    6. 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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    Cited by:

    1. 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.
    2. 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.
    3. 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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