Interpreting the estimated timing of migration events between hybridizing species

The question of whether speciation can occur in the presence of gene flow has long been a contentious one. However, measuring the amount and timing of gene flow remains challenging. The computer program IMa2 allows researchers to estimate the timing of migration events for each locus during analyses, and these estimates have been used to infer the timing of introgression and mode of speciation. We use simulated data sets to examine the degree to which gene-flow timing estimates can be used for these purposes, and what demographic conditions and data sets may be most amenable to gene-flow timing estimation. We find that the 90% highest posterior density (HPD) interval of gene-flow timing is almost always substantially wider than the actual window of gene flow, and increasing the information content of the data set in terms of number of loci, number of sequences sampled or locus length (and thus number of variable sites) has little impact on the posterior distribution over the range of values we tested. Even when simulated gene flow only occurred over the most recent 0.01% of the species' history, the HPD interval usually encompasses the inferred divergence time. Our results indicate that gene-flow timing estimates made using the method currently implemented in IMa2 cannot reliably be used to make inferences about the timing of introgression between diverged species or to distinguish between speciation with gene flow and allopatric speciation followed by one or more episodes of gene flow.