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

Liu Xiran (), Ahsan Zarif (), Martheswaran Tarun K. () and Rosenberg Noah A. ()
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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

Statistical Applications in Genetics and Molecular Biology, 2023, vol. 22, issue 1, 24

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.

Keywords: allele-sharing; genetic dissimilarity; population genetics (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/sagmb-2023-0004

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