Evolution of learning in subdivided populations that occupy environmentally heterogeneous sites

We study the effects of natural selection and migration on the numbers of individual learners and social learners in subdivided populations that occupy environmentally heterogeneous sites. The island model and the circular stepping model each have four classes of globally stable equilibria (fixation of individual learners, polymorphism of individual and social learners, fixation of social learners, and extinction). The linear stepping stone model has an additional class of equilibria, which are characterized by the complete absence of phenotypes adapted to the interior sites. Low and high rates of migration favor social and individual learners, respectively, in all three models. In addition, we use the stepping stone models to study the range expansion of a species, initially confined to one environmentally homogeneous site, into the spatially heterogeneous world. The successive peaks of the transient spatial distributions of the number of individual learners occur at initially empty sites.