Abstract
The detection of introgression from genomic data is transforming our view of species and the origins of adaptive variation. Among the most widely used approaches to detect introgression is the so-called ABBA-BABA test or D-statistic, which identifies excess allele sharing between nonsister taxa. Part of the appeal of D is its simplicity, but this also limits its informativeness, particularly about the timing and direction of introgression. Here we present a simple extension, D frequency spectrum or DFS, in which D is partitioned according to the frequencies of derived alleles. We use simulations over a large parameter space to show how DFS carries information about various factors. In particular, recent introgression reliably leads to a peak in DFS among low-frequency derived alleles, whereas violation of model assumptions can lead to a lack of signal at low frequencies. We also reanalyze published empirical data from six different animal and plant taxa, and interpret the results in the light of our simulations, showing how DFS provides novel insights. We currently see DFS as a descriptive tool that will augment both simple and sophisticated tests for introgression, but in the future it may be usefully incorporated into probabilistic inference frameworks.