On the heterozygosity of an admixed population
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Mathematical Biology
On the heterozygosity of an admixed population Simina M. Boca1
· Lucy Huang2 · Noah A. Rosenberg3
Received: 11 October 2019 / Revised: 4 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we consider admixed populations through their expected heterozygosity, a measure of genetic diversity. A population is termed admixed if its members possess recent ancestry from two or more separate sources. As a result of the fusion of source populations with different genetic variants, admixed populations can exhibit high levels of genetic diversity, reflecting contributions of their multiple ancestral groups. For a model of an admixed population derived from K source populations, we obtain a relationship between its heterozygosity and its proportions of admixture from the various source populations. We show that the heterozygosity of the admixed population is at least as great as that of the least heterozygous source population, and that it potentially exceeds the heterozygosities of all of the source populations. The admixture proportions that maximize the heterozygosity possible for an admixed population formed from a specified set of source populations are also obtained under specific conditions. We examine the special case of K = 2 source populations in detail, characterizing the maximal admixture in terms of the heterozygosities of the two source populations and the value of FST between them. In this case, the heterozygosity of the admixed population exceeds the maximal heterozygosity of the source groups if the divergence between them, measured by FST , is large enough, namely above a certain bound that is a function of the heterozygosities of the source groups. We present applications to simulated data as well as to data from human admixture scenarios, providing results useful for interpreting the properties of genetic variability in admixed populations. Keywords Admixture · Allele frequencies · Heterozygosity · Population genetics
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Simina M. Boca [email protected]
1
Department of Oncology, Department of Biostatistics, Bioinformatics and Biomathematics, Innovation Center for Biomedical Informatics, Georgetown University Medical Center, Washington, DC 20007, USA
2
Bioinformatics Graduate Program, University of Michigan, Ann Arbor, MI 48109, USA
3
Department of Biology, Stanford University, Stanford, CA 94305, USA
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S. M. Boca et al.
Mathematics Subject Classification 15A63 · 92D10
1 Introduction Admixed populations are populations that possess ancestry from multiple source groups. They result from the fusion of populations that have long been separated, in processes such as long-distance migration and hybrid-zone formation at population boundaries. Several features of ancestry and allele frequencies are characteristic of admixed populations (Chakraborty 1986; Long 1991; Verdu and Rosenberg 2011; Gravel 2012). In an admixed population, the values of allele frequencies are typically intermediate between those of the various sources. U
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