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The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele

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  • Jenkins, Paul A.
  • Song, Yun S.

Abstract

The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to be polymorphic. This distribution is widely used in population genetic inferences, including statistical tests of neutrality in which a skew in the observed frequency spectrum across independent sites is taken as a signature of departure from neutral evolution. Theoretical aspects of the frequency spectrum have been well studied and several interesting results are available, but they are usually under the assumption that a site has undergone at most one mutation event in the history of the sample. Here, we extend previous theoretical results by allowing for at most two mutation events per site, under a general finite allele model in which the mutation rate is independent of current allelic state but the transition matrix is otherwise completely arbitrary. Our results apply to both nested and nonnested mutations. Only the former has been addressed previously, whereas here we show it is the latter that is more likely to be observed except for very small sample sizes. Further, for any mutation transition matrix, we obtain the joint sample frequency spectrum of the two mutant alleles at a triallelic site, and derive a closed-form formula for the expected age of the younger of the two mutations given their frequencies in the population. Several large-scale resequencing projects for various species are presently under way and the resulting data will include some triallelic polymorphisms. The theoretical results described in this paper should prove useful in population genomic analyses of such data.

Suggested Citation

  • Jenkins, Paul A. & Song, Yun S., 2011. "The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele," Theoretical Population Biology, Elsevier, vol. 80(2), pages 158-173.
  • Handle: RePEc:eee:thpobi:v:80:y:2011:i:2:p:158-173
    DOI: 10.1016/j.tpb.2011.04.001
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    References listed on IDEAS

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    1. Hobolth, Asger & Wiuf, Carsten, 2009. "The genealogy, site frequency spectrum and ages of two nested mutant alleles," Theoretical Population Biology, Elsevier, vol. 75(4), pages 260-265.
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    Cited by:

    1. Hayman, Elizabeth & Ignatieva, Anastasia & Hein, Jotun, 2023. "Recoverability of ancestral recombination graph topologies," Theoretical Population Biology, Elsevier, vol. 154(C), pages 27-39.
    2. Klassmann, A. & Ferretti, L., 2018. "The third moments of the site frequency spectrum," Theoretical Population Biology, Elsevier, vol. 120(C), pages 16-28.
    3. Ralph, Peter L., 2019. "An empirical approach to demographic inference with genomic data," Theoretical Population Biology, Elsevier, vol. 127(C), pages 91-101.
    4. Ferretti, Luca & Klassmann, Alexander & Raineri, Emanuele & Ramos-Onsins, Sebastián E. & Wiehe, Thomas & Achaz, Guillaume, 2018. "The neutral frequency spectrum of linked sites," Theoretical Population Biology, Elsevier, vol. 123(C), pages 70-79.
    5. Reppell, M. & Zöllner, S., 2018. "An efficient algorithm for generating the internal branches of a Kingman coalescent," Theoretical Population Biology, Elsevier, vol. 122(C), pages 57-66.

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