Detection and Polarization of Introgression in a Five-Taxon Phylogeny.

When multiple speciation events occur rapidly in succession, discordant genealogies due to incomplete lineage sorting (ILS) can complicate the detection of introgression. A variety of methods, including the [Formula: see text]-statistic (a.k.a. the "ABBA-BABA test"), have been proposed to infer introgression in the presence of ILS for a four-taxon clade. However, no integrated method exists to detect introgression using allelic patterns for more complex phylogenies. Here we explore the issues associated with previous systems of applying [Formula: see text]-statistics to a larger tree topology, and propose new [Formula: see text] tests as an integrated framework to infer both the taxa involved in and the direction of introgression for a symmetric five-taxon phylogeny. Using theory and simulations, we show that the [Formula: see text] statistics correctly identify the introgression donor and recipient lineages, even at low rates of introgression. [Formula: see text] is also shown to have extremely low false-positive rates. The [Formula: see text] tests are computationally inexpensive to calculate and can easily be applied to phylogenomic data sets, both genome-wide and in windows of the genome. In addition, we explore both the principles and problems of introgression detection in even more complex phylogenies.