Drift, draft and structure: some mathematical models of evolution
Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical models we describe a special case of a new model introduced in very recent work with Nick Barton. A number of directions for future research are suggested.