**IMA Complex Systems Seminar**

**2:30 Wednesday, November 12,
2003**

Infinite population models in population genetics

Departments of Mathematics and Statistics

University of Wisconsin-Madison

Madison, WI 53706-1388

The simplest model of population genetics assumes that each new
generation is obtained by sampling with replacement from the previous
generation. Models including mutation,
selection, and recombination are obtained as perturbations of the basic
sampling model. Population geneticists
noted early on that infinite population approximations simplified
computations. Two radically different
approximations emerged. Diffusion approximations
suggested by Feller provide a model for the evolution of gene or type frequencies
forward in time, and the extension of these models to complex type spaces has
led to the development of measure-valued models. The coalescent models introduced by Kingman describe the
ancestral relationships going backward in time. Models that capture both the coalescent structure and the
diffusion of type frequencies and allow exploitation of one to study the other
will be described.