Inference of multiple-wave population admixture by modeling decay of linkage disequilibrium with multiple exponential functions

Admixture-introduced linkage disequilibrium (LD) has recently been introduced into the inference of the histories of complex admixtures. However, the influence of ancestral source populations on the LD pattern in admixed populations is not properly taken into consideration by currently available methods, which affects the estimation of several gene flow parameters from empirical data. We first illustrated the dynamic changes of LD in admixed populations and mathematically formulated the LD under a generalized admixture model with finite population size. We next developed a new method, MALDmef, by fitting LD with multiple exponential functions for inferring and dating multiple-wave admixtures. MALDmef takes into account the effects of source populations which substantially affect modeling LD in admixed population, which renders it capable of efficiently detecting and dating multiple-wave admixture events. The performance of MALDmef was evaluated by simulation and it was shown to be more accurate than MALDER, a state-of-the-art method that was recently developed for similar purposes, under various admixture models. We further applied MALDmef to analyzing genome-wide data from the Human Genome Diversity Project (HGDP) and the HapMap Project. Interestingly, we were able to identify more than one admixture events in several populations, which have yet to be reported. For example, two major admixture events were identified in the Xinjiang Uyghur, occurring around 27-30 generations ago and 182-195 generations ago, respectively. In an African population (MKK), three recent major admixtures occurring 13-16, 50-67, and 107-139 generations ago were detected. Our method is a considerable improvement over other current methods and further facilitates the inference of the histories of complex population admixtures.