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Sufficiency of the number of segregating sites in the limit under finite-sites mutation

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  • RoyChoudhury, Arindam
  • Wakeley, John

Abstract

We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter (θ) in the limit as the number of sites tends to infinity and there is free recombination between sites. We assume that the mutation parameter at each site tends to zero such than the total mutation parameter (θ) is constant in the limit. Our results show that Watterson’s estimator is the maximum likelihood estimator in this case, but that it estimates a composite parameter which is different for different mutation models. Some of our results hold when recombination is limited, because Watterson’s estimator is an unbiased, method-of-moments estimator regardless of the recombination rate. The quantity it estimates depends on the details of how mutations occur at each site.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:78:y:2010:i:2:p:118-122
    DOI: 10.1016/j.tpb.2010.05.003
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    1. Carlos D. Bustamante & Rasmus Nielsen & Stanley A. Sawyer & Kenneth M. Olsen & Michael D. Purugganan & Daniel L. Hartl, 2002. "The cost of inbreeding in Arabidopsis," Nature, Nature, vol. 416(6880), pages 531-534, April.
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    Cited by:

    1. 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.
    2. Vogl, Claus & Bergman, Juraj, 2015. "Inference of directional selection and mutation parameters assuming equilibrium," Theoretical Population Biology, Elsevier, vol. 106(C), pages 71-82.
    3. 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.
    4. Burden, Conrad J. & Tang, Yurong, 2017. "Rate matrix estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 113(C), pages 23-33.
    5. 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.
    6. Ferretti, Luca & Ramos-Onsins, Sebástian E., 2015. "A generalized Watterson estimator for next-generation sequencing: From trios to autopolyploids," Theoretical Population Biology, Elsevier, vol. 100(C), pages 79-87.

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