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When is the allele-sharing dissimilarity between two populations exceeded by the allele-sharing dissimilarity of a population with itself?

Author

Listed:
  • Liu Xiran

    (Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA)

  • Ahsan Zarif

    (Department of Biology, Stanford University, Stanford, CA 94305, USA)

  • Martheswaran Tarun K.

    (Department of Biology, Stanford University, Stanford, CA 94305, USA)

  • Rosenberg Noah A.

    (Department of Biology, Stanford University, Stanford, CA 94305, USA)

Abstract

Allele-sharing statistics for a genetic locus measure the dissimilarity between two populations as a mean of the dissimilarity between random pairs of individuals, one from each population. Owing to within-population variation in genotype, allele-sharing dissimilarities can have the property that they have a nonzero value when computed between a population and itself. We consider the mathematical properties of allele-sharing dissimilarities in a pair of populations, treating the allele frequencies in the two populations parametrically. Examining two formulations of allele-sharing dissimilarity, we obtain the distributions of within-population and between-population dissimilarities for pairs of individuals. We then mathematically explore the scenarios in which, for certain allele-frequency distributions, the within-population dissimilarity – the mean dissimilarity between randomly chosen members of a population – can exceed the dissimilarity between two populations. Such scenarios assist in explaining observations in population-genetic data that members of a population can be empirically more genetically dissimilar from each other on average than they are from members of another population. For a population pair, however, the mathematical analysis finds that at least one of the two populations always possesses smaller within-population dissimilarity than the value of the between-population dissimilarity. We illustrate the mathematical results with an application to human population-genetic data.

Suggested Citation

  • Liu Xiran & Ahsan Zarif & Martheswaran Tarun K. & Rosenberg Noah A., 2023. "When is the allele-sharing dissimilarity between two populations exceeded by the allele-sharing dissimilarity of a population with itself?," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 22(1), pages 1-24, January.
    • Handle: RePEc:bpj:sagmbi:v:22:y:2023:i:1:p:24:n:1
    DOI: 10.1515/sagmb-2023-0004
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    References listed on IDEAS

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    1. Noah A Rosenberg & Saurabh Mahajan & Sohini Ramachandran & Chengfeng Zhao & Jonathan K Pritchard & Marcus W Feldman, 2005. "Clines, Clusters, and the Effect of Study Design on the Inference of Human Population Structure," PLOS Genetics, Public Library of Science, vol. 1(6), pages 1-12, December.
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