Abstract
When populations become isolated, members of these populations can diverge genetically over time. This leads to genetic differences between these populations that increase over time if the isolation persists. This process can be counteracted by gene flow, i.e. when genes are exchanged between populations. In order to study the speciation processes when gene flow is present, isolation-with-migration methods have been developed. These methods typically assume that the ranked topology of the species history is already known. However, this is often not the case and the species tree is therefore of interest itself. For the inference of species trees, it is in turn often necessary to assume that there is no gene flow between co-existing species. This assumption, however, can lead to wrongly inferred speciation times and species tree topologies. We here introduce a new method that allows inference of the species tree while explicitly modelling the flow of genes between coexisting species. By using Markov chain Monte Carlo sampling, we co-infer the species tree alongside evolutionary parameters of interest. By using simulations, we show that our newly introduced approach is able to reliably infer the species trees and parameters of the isolation-with-migration model from genetic sequence data. We then use this approach to infer the species history of the mosquitoes from the Anopheles gambiae species complex. Accounting for gene flow when inferring the species history suggests a slightly different speciation order and gene flow than previously suggested.