The Effects of Migration and Assortative Mating on Admixture Linkage Disequilibrium

Abstract

Statistical models in medical and population genetics typically assume that individuals assort randomly in a population. While this simplifies model complexity, it contradicts an increasing body of evidence of nonrandom mating in human populations. Specifically, it has been shown that assortative mating is significantly affected by genomic ancestry. In this work, we examine the effects of ancestry-assortative mating on the linkage disequilibrium between local ancestry tracks of individuals in an admixed population. To accomplish this, we develop an extension to the Wright-Fisher model that allows for ancestry-based assortative mating. We show that ancestry-assortment perturbs the distribution of local ancestry linkage disequilibrium (LAD) and the variance of ancestry in a population as a function of the number of generations since admixture. This assortment effect can induce errors in demographic inference of admixed populations when methods assume random mating. We derive closed form formulae for LAD under an assortative-mating model with and without migration. We observe that LAD depends on the correlation of global ancestry of couples in each generation, the migration rate of each of the ancestral populations, the initial proportions of ancestral populations, and the number of generations since admixture. We also present the first direct evidence of ancestry-assortment in African Americans and examine LAD in simulated and real admixed population data of African Americans. We find that demographic inference under the assumption of random mating significantly underestimates the number of generations since admixture, and that accounting for assortative mating using the patterns of LAD results in estimates that more closely agrees with the historical narrative.

Keywords: admixture; assortative mating; demography; migration; population genetics.

Figure 1

The distribution of local ancestry linkage disequilibrium (LAD) for different values of t with no migration (and $P=0.6$). The thick lines correspond to the expected LAD based on Lemma 3.1, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 2

The distribution of local ancestry linkage disequilibrium (LAD) for different values of P with no migration and $t=10.$ The thick lines correspond to the expected LAD based on Lemma 3.1, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 3

Demonstrating the effect of a random mating assumption when truly $P=0.8,t=10.$ All curves correspond to scenarios with no migrations. The thick lines correspond to the expected local ancestry linkage disequilibrium (LAD) based on Lemma 3.1, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 4

Demonstrating the effect of a random mating assumption when truly $P=0.6,t=15.$ All curves correspond to scenarios with no migrations. The thick lines correspond to the expected local ancestry linkage disequilibrium (LAD) based on Lemma 3.1, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 5

The distribution of local ancestry linkage disequilibrium (LAD) for different values of $m_1,m_2,$ with equal migration rates from both populations. The thick lines correspond to the expected LAD based on Equation 2, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 6

The distribution of local ancestry linkage disequilibrium (LAD) for different values of $m_1,m_2,$ with no migration from population 1. The thick lines correspond to the expected LAD based on Equation 2, and the thin lines correspond to simulation runs of a single locus in the genome.

Figure 7

The expected local ancestry linkage disequilibrium (LAD) decay under two conditions, one with assortative mating and another with random mating. In the presence of migration, the two curves almost overlap, and distinguishing between the two cases will be challenging in practice, particularly if LAD is measured only up to a few dozen centimorgans.

Figure 8

Each of the plots shows the best fit of the parameters to the mean local ancestry linkage disequilibrium (LAD) in the Study of African Americans, Asthma, Genes and Environments (SAGE) data set. (A) The parameters were searched over the entire grid, resulting in the best fit with estimated number of generations 13, migration rates $m_1=0.01,m_2=0.05,$ and correlation $P=\mathrm{0.46.}$ (B) The best fit under the assumption of no migration. The number of generations was estimated to be eight, and $P=\mathrm{0.6.}$ (C) The best fit under the assumption of random mating with migration. The number of generations is estimated as 16. (D) The best fit under the assumption of random mating and no migration – the number of generations is estimated as 3.