Cornell Math - MATH 777, Fall 2000

MATH 777 — Fall 2000
Stochastic Processes:
Using Probability Models to Understand DNA Sequence Evolution

In this course we will develop some results in probability theory that are useful for the study of molecular evolution. We will begin with models of neutral evolution in a homogeneously mixing population and then investigate what happens when the model is modified to include important complications such as: selection, recombination, and population subdivision. We will be interested not only in the evolution of nucleotide sequences due to substitutions, insertions, deletions, etc., but also in whole genome processes such as translocations and inversions, chromosome fissions and fusions, local gene duplications, and polyploidization.

My plan is to hand out notes each week that will be posted in PDF on my web page (www.math.cornell.edu/~durrett/GB/).

My idea, of course, is to use these notes to develop a short book (250-300 pages). The book will also discuss models of microsatellite evolution but we will not touch on those topics in the course. Most of the modelling involves only simple applications of probability, so a basic course in that subject should be sufficient. Of course, since this is math course, no knowledge of genetics will be assumed. I will do my best to briefly explain the details as they arise. Questions about the course can be sent to me via email. Watch the web page for more information about the course and the first set of notes.

Outline

I. Neutral Mutation in a Homogeneously Mixing Population

1. Two alleles: Wright-Fisher model
2. Infinitely many alleles: coalescent, and Ewens sampling formula
3. Infinite sites model: heterozygosity, segregating sites, etc.
4. Stepwise mutation

II. Complications to the Basic Models

5. Selection
6. Recombination
7. Hitchhiking
8. Population subdivision: island model
9. Balancing and background selection
10. Spatial structure: stepping stone model

III. Genome Evolution

11. Inversions
12. Translocations
13. Whole genome duplication
14. Local gene duplication