IMA Complex Systems Seminar

2:30 Wednesday, November 12, 2003

 

 

Infinite population models in population genetics

 

Tom Kurtz

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.