Linking micro and macroevolution in the presence of migration

The process of speciation is of key importance in evolutionary biology because it shapes macroevolutionary patterns. This process starts at the microevolutionary level, for instance, when two subpopulations evolve towards different phenotypic optima. The speed at which these optima are reached is controlled by the degree of stabilising selection, which pushes a mean trait towards an optimum within subpopulations, and ongoing migration that pulls the mean phenotype away from that optimum. Traditionally, macro phenotypic evolution with selection has been modelled by Ornstein-Uhlenbeck (OU) processes, but these models have ignored the role of migration within species. Here, our goal is to reconcile the processes of micro and macroevolution by modelling migration during speciation. More precisely, we introduce an OU model where migration happens between two subpopulations within a branch of a phylogeny and this migration decreases over time as it happens during speciation. We then use this model to study the evolution of trait means along a phylogeny, as well as the way phenotypic disparity between species changes with successive epochs. We show that ignoring the effect of migration in sampled time-series data leads to a significant underestimation of the selective forces acting upon it. We also show that migration decreases the expected phenotypic disparity between species and we show the effect of migration in the particular case of niche filling. We further introduce a method to jointly estimate selection and migration from time-series data. Our model extends standard results of interactions selection-migration in a microevolutionary time frame across multiple speciation events at a macroevolutionary scale. Our results further proof that not accounting for gene flow has important consequences in inferences at both the micro and macroevolutionary scale.