Mathematical models play a fundamental role in theoretical population
genetics and, in turn, population genetics provides a wealth of mathematical
challenges. In this lecture we illustrate this by using a mathematical
caricature of the evolution of genetic types in a spatially distributed
population to demonstrate the role that the shape of the domain inhabited by
a species can play in mediating the interplay between natural selection,
spatial structure, and (if time permits) so-called random genetic drift (the
randomness due to reproduction in a finite population).