Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations

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 random perturbations and stabilizing selection and assumes that species evolve independently. However, evolving species may interact through various ecological process and also exchange genes especially in plants. This is particularly true if we want to study phenotypic evolution among diverging populations within species. In this work we present a straightforward statistical approach with analytical solutions that allows for the inclusion of adaptation and migration in a common phylogenetic framework, which can also be useful for studying local adaptation among populations within the same species. 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. 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.