The Timing and Direction of Introgression Under the Multispecies Network Coalescent.

Introgression is a pervasive biological process, and many statistical methods have been developed to infer its presence from genomic data. However, many of the consequences and genomic signatures of introgression remain unexplored from a methodological standpoint. Here, we develop a model for the timing and direction of introgression based on the multispecies network coalescent, and from it suggest new approaches for testing introgression hypotheses. We suggest two new statistics, D 1 and D 2, which can be used in conjunction with other information to test hypotheses relating to the timing and direction of introgression, respectively. D 1 may find use in evaluating cases of homoploid hybrid speciation (HHS), while D 2 provides a four-taxon test for polarizing introgression. Although analytical expectations for our statistics require a number of assumptions to be met, we show how simulations can be used to test hypotheses about introgression when these assumptions are violated. We apply the D 1 statistic to genomic data from the wild yeast Saccharomyces paradoxus-a proposed example of HHS-demonstrating its use as a test of this model. These methods provide new and powerful ways to address questions relating to the timing and direction of introgression.