The Impact of Incomplete Taxon Sampling on Inference of Gene Flow by Bayesian and Summary Methods Using Genomic Sequence Data.

Interspecific gene flow is commonly inferred using genomic data under the multispecies coalescent model. Incomplete taxon sampling can impact inference of gene flow in multiple ways. First unsampled ghost lineages that are sources of introgression may mislead inference of gene flow in analysis of genomic data from sampled species. Second incomplete taxon sampling causes merges of branches on the species phylogeny and complicates the definition and estimation of the rate or magnitude of gene flow, measured by the expected proportion of immigrants in the recipient population (i.e., the introgression probability). We use mathematical analysis and computer simulation to examine the impact of incomplete taxon sampling on inference of gene flow and estimation of its rate using genomic data. We introduce a Bayesian testing approach to select models of gene flow for a species triplet (such as ghost introgression, inflow, and outflow), using the Savage-Dickey density ratio to calculate Bayes factors. We show that the approach has excellent sensitivity and specificity, whereas heuristic methods based on data summaries typically cannot distinguish among those scenarios. We find that genomic data allow reliable estimation of the proportion of immigrants (rather than the number of immigrants), even when the assumed demographic model is incorrect due to incomplete taxon sampling. When population size differs among species, assuming the same size may lead to seriously biased estimates of the rate of gene flow. The f-branch approach is effective in reducing the number of gene-flow events suggested by triplet analyses but often fails to identify the correct model of gene flow and tends to underestimate the rate of gene flow. Our results highlight the need for improving summary methods to accommodate different population sizes and to infer gene flow between sister lineages.