Inferring the direction of introgression using genomic sequence data

Genomic data are informative about the history of species divergence and interspecific gene flow, including the direction, timing, and strength of gene flow. However, gene flow in opposite directions generates similar patterns in multilocus sequence data, such as reduced sequence divergence between the hybridizing species. As a result, inference of the direction of gene flow is challenging. Here we investigate the information about the direction of gene flow present in genomic sequence data using likelihood-based methods under the multispecies-coalescent-with-introgression (MSci) model. We analyze the case of two species, and use simulation to examine cases with three or four species. We find that it is easier to infer gene flow from a small population to a large one than in the opposite direction, and easier to infer inflow (gene flow from outgroup species to an ingroup species) than outflow (gene flow from an ingroup species to an outgroup species). It is also easier to infer gene flow if there is a longer time of separate evolution between the initial divergence and subsequent introgression. When introgression is assumed to occur in the wrong direction, the time of introgression tends to be correctly estimated and the Bayesian test of gene flow is often significant, while estimates of introgression probability can be even greater than the true probability. We analyze genomic sequences from Heliconius butterflies to demonstrate that typical genomic datasets are informative about the direction of interspecific gene flow, as well as its timing and strength.