Bayesian inference of introgression between sister lineages using genomic data

Inference of interspecific gene flow using genomic data is important to reliable reconstruction of species phylogenies and to our understanding of the speciation process. Gene flow is harder to detect if it involves sister lineages than nonsisters; for example, most heuristic methods based on data summaries are unable to infer gene flow between sisters. Likelihood-based methods can identify introgression between sisters but the test exhibits several nonstandard features, including boundary problems, indeterminate parameters, and multiple routes from the alternative to the null hypotheses. In the Bayesian test, those irregularities pose challenges to the use of the Savage-Dickey (S-D) density ratio to calculate the Bayes factor. Here we develop a theory for applying the S-D approach under nonstandard conditions. We show that the Bayesian test of introgression between sister lineages has low false-positive rates and high power. We discuss issues surrounding the estimation of the rate of gene flow between sister lineages, especially at very low or very high rates, and suggest that evidence for gene flow between sisters be assessed via a Bayesian test. We find that the species split time has a major impact on the information content in the data, with more information at deeper divergence. We use a genomic dataset from Sceloporus lizards to illustrate the test of gene flow between sister lineages.