On the heterozygosity of an admixed population

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 [Formula: see text] source populations in detail, characterizing the maximal admixture in terms of the heterozygosities of the two source populations and the value of [Formula: see text] 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 [Formula: see text], 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.