The Generalised Isolation-With-Migration Model: a Maximum-Likelihood Implementation for Multilocus Data Sets

Statistical inference about the speciation process has often been based on the isolation-with-migration (IM) model, especially when the research aim is to learn about the presence or absence of gene flow during divergence. The generalised IM model introduced in this paper extends both the standard two-population IM model and the isolation-with-initial-migration (IIM) model, and encompasses both these models as special cases. It can be described as a two-population IM model in which migration rates and population sizes are allowed to change at some point in the past. By developing a maximum-likelihood implementation of this GIM model, we enable inference on both historical and contemporary rates of gene flow between two closely related species. Our method relies on the spectral decomposition of the coalescent generator matrix and is applicable to data sets consisting of the numbers of nucleotide differences between one pair of DNA sequences at each of a large number of independent loci.