Substack cometh, and lo it is good. (Pricing)

Details on the back of the envelope

panam-09-backYears ago when I was noticing specific population genomic estimates I asked a friend about the confidence intervals, and how much to trust the values therein. One thing he mentioned offhand is that linkage disequilibrium based estimates of time since admixture often seem to give a relatively low figure in terms of generations. When it comes to non-human organisms in the field one doesn’t know always the demographic history, but with humans we have better records, and I too have noticed that the dates seem extremely skewed toward the recent. Part of this is accounted for by the dodge that these estimates are often sensitive only to the last pulse of admixture. But even then….

A new preprint discusses in detail why this occurs, The Effects of Migration and Assortative Mating on Admixture Linkage Disequilibrium:

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 non-random 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 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.

The intuition isn’t that difficult. Assortative mating in this case often means that within population there are going to be correlations of segments of genomic ancestry which are the patterns you are tracking to infer backward the initial admixture. The dynamic of the mating, random or not, is going to effect the shape of decay over time. If you see more dense local ancestry tracts in individuals because of positive assortative mating, you may confuse it in your model for very recent admixture.

This sort of thing crops up in all sorts of models. Assortative mating within a population may lead to higher heritable transmission of a trait across generations than you might expected. Many of the model based clustering algorithms which generate the bar plots now ubiquitous in admixture analyses assume Hardy-Weinberg Equilibrium in one’s populations.

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