The Ornstein-Uhlenbeck process with migration: evolution with interactions

Abstract: The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes drift and stabilizing selection and assumes that species evolve independently. However, especially in plants, there is ample evidence of hybridization and introgression during evolution. In this work we present a statistical approach with analytical solutions that allows for the inclusion of adaptation and migration in a common phylogenetic framework. We furthermore present a detailed simulation study that clearly indicates the adverse effects of ignoring migration. Similarity between species due to migration could be misinterpreted as very strong convergent evolution without proper correction for these additional dependencies. Our model can also be useful for studying local adaptation among populations within the same species. Finally, we show that our model can be interpreted in terms of ecological interactions between species, providing a general framework for the evolution of traits between "interacting" species or populations.