Drift, draft and structure: modelling evolution in a spatial continuum.

One of the outstanding successes of mathematical population genetics is Kingman's coalescent. This process provides a simple and elegant description of the genealogical trees relating individuals in a sample of neutral genes from a panmictic population, that is, one in which every individual is equally likely to mate with every other and all individuals experience the same conditions. But real populations are not like this. Spurred on by the recent flood of DNA sequence data, an enormous industry has developed that seeks to extend Kingman's coalescent to incorporate things like variable population size, natural selection and spatial and genetic structure. But a satisfactory approach to populations evolving in a spatial continuum has proved elusive. In this talk we describe the effects of some of these biologically important phenomena on the genealogical trees before describing a new approach (joint work with Nick Barton, IST Austria) to modelling the evolution of populations distributed in a spatial continuum.