Estimating the timing of multiple admixture events using 3-locus linkage disequilibrium

Estimating admixture histories is crucial for understanding the genetic diversity we see in present-day populations. Allele frequency or phylogeny-based methods are excellent for inferring the existence of admixture or its proportions. However, to estimate admixture times, spatial information from admixed chromosomes of local ancestry or the decay of admixture linkage disequilibrium (ALD) is used. One popular method, implemented in the programs ALDER and ROLLOFF, uses two-locus ALD to infer the time of a single admixture event, but is only able to estimate the time of the most recent admixture event based on this summary statistic. To address this limitation, we derive analytical expressions for the expected ALD in a three-locus system and provide a new statistical method based on these results that is able to resolve more complicated admixture histories. Using simulations, we evaluate the performance of this method on a range of different admixture histories. As an example, we apply the method to the Colombian and Mexican samples from the 1000 Genomes project. The implementation of our method is available at https://github.com/Genomics-HSE/LaNeta.Author summary: We establish a theoretical framework to model 3-locus admixture linkage disequilibrium of an admixed population taking into account the effects of genetic drift, migration and recombination. The theory is used to develop a method for estimating the times of multiple admixtures events. We demonstrate the accuracy of the method on simulated data and we apply it to previously published data from Mexican and Colombian populations to explore the complex history of American populations in the post-Colombian period.