  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.
