Leveraging shared ancestral variation to detect local introgression

Introgression is a common evolutionary phenomenon that results in shared genetic material across non-sister taxa. Existing statistical methods such as Patterson's D statistic can detect introgression by measuring an excess of shared derived alleles between populations. The D statistic is effective to detect genome-wide patterns of introgression but can give spurious inferences of introgression when applied to local regions. We propose a new statistic, D+, that leverages both shared ancestral and derived alleles to infer local introgressed regions. Incorporating both shared derived and ancestral alleles increases the number of informative sites per region, improving our ability to identify local introgression. We use a coalescent framework to derive the expected value of this statistic as a function of different demographic parameters under an instantaneous admixture model and use coalescent simulations to compute the power and precision of D+. While the power of D and D+ is comparable, D+ has better precision than D. We apply D+ to empirical data from the 1000 Genome Project and Heliconius butterflies to infer local targets of introgression in humans and in butterflies.