Efficient Maximum-Likelihood Inference For The Isolation-With-Initial-Migration Model With Potentially Asymmetric Gene Flow

The isolation-with-migration (IM) model is commonly used to make inferences about gene flow during speciation, using polymorphism data. However, Becquet and Przeworski (2009) report that the parameter estimates obtained by fitting the IM model are very sensitive to the model's assumptions (including the assumption of constant gene flow until the present). This paper is concerned with the isolation-with-initial-migration (IIM) model of Wilkinson-Herbots (2012), which drops precisely this assumption. In the IIM model, one ancestral population divides into two descendant subpopulations, between which there is an initial period of gene flow and a subsequent period of isolation. We derive a very fast method of fitting an extended version of the IIM model, which also allows for asymmetric gene flow and unequal population sizes. This is a maximum-likelihood method, applicable to data on the number of segregating sites between pairs of DNA sequences from a large number of independent loci. In addition to obtaining parameter estimates, our method can also be used to distinguish between alternative models representing different evolutionary scenarios, by means of likelihood ratio tests. We illustrate the procedure on pairs of Drosophila sequences from approximately 30,000 loci. The computing time needed to fit the most complex version of the model to this data set is only a couple of minutes. The R code to fit the IIM model can be found in the supplementary files of this paper.