## Genealogical constructions of measure-valued models in population genetics

### Thomas Kurtz Mathematics and Statistics, University of Wisconsin

#### Abstract

Classical population genetics begins with a Markov chain model for the genetic types of the individuals in a finite population and then replaces the discrete model by a diffusion approximation under the assumption that the population is large. "Lookdown" constructions of these models, introduced in work with Peter Donnelly, allow one to retain discrete individuals in the diffusion limit and, in particular, obtain population genealogies coupled to the diffusion approximations. These constructions will be described along with related constructions for spatially distributed populations.