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The expected sample allele frequencies from populations of changing size via orthogonal polynomials

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  • Mikula, Lynette Caitlin
  • Vogl, Claus

Abstract

In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for stepwise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:157:y:2024:i:c:p:55-85
    DOI: 10.1016/j.tpb.2024.03.005
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    References listed on IDEAS

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    1. 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.
    2. Burden, Conrad J. & Tang, Yurong, 2017. "Rate matrix estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 113(C), pages 23-33.
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    4. 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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    12. 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.
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