250119 VO Migration-selection models in population genetics (2016W)

The population genetics theory of spatially structured populations evolving subject to selection, migration, or random drift will be developed. In introductory chapters, the theory of populations inhabiting discrete niches will be treated. The corresponding models are formulated mainly in terms of systems of difference equations or ordinary differential equations. The main focus will be on models in which individuals disperse in continuous space. In the simplest case, such models can be formulated by reaction-diffusion equations, i.e., parabolic PDEs. Special emphasis will be on the theory of clines, i.e., of stable stationary, spatially inhomogeneous distributions which reflect local adaptation to the heterogeneous habitat. Other special cases include Fisher’s equation for they wave-like advance of advantageous genes. The lecture course will be most suitable for Master or PhD students with a good background in differential equations and a sincere interest in modeling and applications. Lecture notes will be made available in October on my home page.