Linking micro and macroevolution in the presence of migration

Understanding macroevolutionary patterns is central to evolutionary biology. This involves the process of divergence within a species, which 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 the mean trait towards different optima in the different subpopulations, and ongoing migration that pulls the mean phenotype away from that optimum. Traditionally, macro phenotypic evolution is modelled by directional selection processes, but these models usually ignore the role of migration within species. Here, our goal is to reconcile the processes of micro and macroevolution by modelling migration as part of the speciation process. More precisely, we introduce an Ornstein-Uhlenbeck (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 biases significantly the estimation of the selective forces acting upon it. We also show that migration decreases the expected phenotypic disparity between species and we analyse 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 traditional quantitative genetics results of selection and migration from a microevolutionary time frame to multiple speciation events at a macroevolutionary scale. Our results further support that not accounting for gene flow has important consequences in inferences at both the micro and macroevolutionary scale.