As a chromosome is sliced into pieces by recombination after entering an admixed population, ancestral tracks of chromosomes are shortened with the pasting of generations. The length distribution of ancestral tracks reflects information of recombination and thus can be used to infer the histories of admixed populations. Previous studies have shown that inference based on ancestral tracks is powerful in recovering the histories of admixed populations. However, population histories are always complex, and previous studies only deduced the length distribution of ancestral tracks under very simple admixture models. The deduction of length distribution of ancestral tracks under a more general model will greatly elevate the power in inferring population histories. Here we first deduced the length distribution of ancestral tracks under a general model in an admixed population, and proposed general principles in parameter estimation and model selection with the length distribution. Next, we focused on studying the length distribution of ancestral tracks and its applications under three typical admixture models, which were all special cases of our general model. Extensive simulations showed that the length distribution of ancestral tracks was well predicted by our theoretical models. We further developed a new method based on the length distribution of ancestral tracks and good performance was observed when it was applied in inferring population histories under the three typical models. Notably, our method was insensitive to demographic history, sample size and threshold to discard short tracks. Finally, we applied our method in African Americans and Mexicans from the HapMap dataset, and several South Asian populations from the Human Genome Diversity Project dataset. The results showed that the histories of African Americans and Mexicans matched the historical records well, and the population admixture history of South Asians was very complex and could be traced back to around 100 generations ago.

Length Distribution of Ancestral Tracks under a General Admixture Model and Its Applications in Population History Inference