On the effects of selection and mutation on species tree inference

A common question that arises when inferring species-level phylogenies from genome-scale data is whether selection acting on certain parts of the genome could create a bias in the inferred phylogeny. While most methods for species tree inference currently assume the multispecies coalescent (MSC), all methods that we are aware of utilize only the neutral coalescent process. If selection is in fact present, failure to adequately model it could introduce substantial bias. We work toward rigorously addressing this question using mathematical theory by deriving a version of the coalescent including selection and mutation as a limiting approximation of the Wright-Fisher model with selection and mutation, and showing that it can be used to closely approximate the distribution of coalescent times in the presence of selection and mutation. We confirm the adequacy of the approximation with a simulation study, and discuss its implications for species tree inference. Our results show that in a general class containing many cases of interest, selection has only a small impact on the coalescent process, and ignoring selection when it is present does not have a substantial negative impact on inference of the species tree topology.