  Most current methods for inferring species-level phylogenies under the
coalescent model assume that no gene flow occurs following speciation. While
some studies have examined the impact of gene flow on estimation accuracy for
certain methods, limited analytical work has been undertaken to directly assess
the potential effect of gene flow across a species phylogeny. In this paper, we
consider a three-taxon isolation-with-migration model that allows gene flow
between sister taxa for a brief period following speciation, as well as
variation in the effective population sizes across the tree. We derive the
probabilities of each of the three gene tree topologies under this model, and
show that for certain choices of the gene flow and effective population size
parameters, anomalous gene trees (i.e., gene trees that are discordant with the
species tree but that have higher probability than the gene tree concordant
with the species tree) exist. We characterize the region of parameter space
producing anomalous trees, and show that the probability of the gene tree that
is concordant with the species tree can be arbitrarily small. We then show that
the SVDQuartets method is theoretically valid under the model of gene flow
between sister taxa. We study its performance on simulated data and compare it
to two other commonly-used methods for species tree inference, ASTRAL and
MP-EST. The simulations show that ASTRAL and MP-EST can be statistically
inconsistent when gene flow is present, while SVDQuartets performs well, though
large sample sizes may be required for certain parameter choices.
