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. Existing allele frequency or phylogeny-based methods are excellent for inferring the existence of admixture or its proportions, but have less power for estimating admixture times. Recently introduced approaches for estimating these times use spatial information from admixed chromosomes, such as the local ancestry or the decay of admixture linkage disequilibrium (ALD). 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. 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 show how this new statistic behaves on a range of admixture histories. As an example, we also apply our method to the Colombian and Mexican samples from the 1000 Genomes project.