250106 VO Advanced course in mathematical population genetics (2019W)

This course will be devoted to theory of population-genetic models that describe the evolution of spatially structured populations in heterogeneous environments. This leads to migration-selection models, which are formulated in terms of systems of difference or differential equations if individuals migrate between different patches of the environment. In contrast, if individuals migrate in a continuous environment in which the average dispersal distance is small compared to selectively relevant changes in the environment, the models are formulated in terms of parabolic partial differential equations or, in simplified form, as reaction-diffusion equations. The basic theory of both types of models will be developed. In particular, topics such as the adaptation to new environments, the divergence among subpopulations (often the first step to speciation), and the theory of clines will be highlighted.