MATH 777: Random Topics in Population Genetics (Fall 2006)

Instructor: Richard Durrett

Meeting Time & Room

We will begin with the Wright-Fisher and Moran models for neutral evolution in a homogeneously mixing population of constant size for nonrecombining DNA when the mutations follows the infinite alleles or infinite sites models. We will then see what happens when the various assumptions are removed.

• Recombination, ancestral recombination graph.
• Population complications: growth and bottlenecks, the island and stepping stone models, large family sizes, multiple mergers
• Selection: selective sweeps, hitchhiking, Hill-Robertson interference, balancing selection, background selection

At the beginning these topics will be treated by discrete methods, but then we will take an approach based on diffusion processes.

If time permits we will consider gene duplication and genome rearrangement.

I will use my book Probability Models of DNA Sequence Evolution, but since the rationale for the course is getting the Second Edition done, we will cover a lot of material not in the book as well. DO NOT BUY THE BOOK. Notes will be posted on the course web page.

The only formal prerequisite is a course in stochastic processes such as ORIE 361. A more accurate number for the course would be 477. However, the focus is on insights into genetics that can be obtained from mathematical reasoning so ...

Last modified: August 10, 2006