On the heterozygosity of an admixed population

Abstract

A population is termedadmixedif 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 variation, reflecting contributions of their multiple ancestral groups. For a model of an admixed population derived fromKsource groups, we obtain a relationship between its level of genetic variation, as measured by 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 ofallof 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 ofK= 2 source populations in detail, characterizing the maximal admixture in terms of the heterozygosities of the two source populations and the value ofFSTbetween them. In this case, the heterozygosity of the admixed population exceeds the maximal heterozygosity of the source groups if the divergence between them, measured byFST, 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.