Quicklinks: General Information, Lecture Notes, Final Assignment

Math 833: Topics in Probability

Stochastic Processes in Evolution and Genetics

Fall 2012


The main theme of this course is the rigorous mathematical analysis of probabilistic and combinatorial structures arising from biology, mostly in the study of evolution and genetics. No biology background is required. The course should be of interest to probabilists, combinatorialists, applied mathematicians, theoretical computer scientists, computational biologists, and biostatisticians.

Various stochastic processes on combinatorial structures will be considered, including random trees, Markov models on trees, multitype branching processes, finite Markov chains, random walks, exchangeable partitions, and Kingman's coalescent. Here is a tentative list of topics:

Mathematical Phylogenetics (a.k.a. the mathematics behind the Tree of Life)

Mathematical Population Genetics

General Information

Lectures Notes

UPDATE [Sep 1, 2015]: The latest version of the lecture notes can be found here.



Population genetics



The optional homework is here. It covers only the phylogenetics part of the course. It is due during class on December 14.

Final Assignment

For your final assignment, choose a research paper to present in class. Examples of possible papers follow. Check with me when you have made your choice. The assignment is to give a short presentation in class. Some of the papers below also contain simulations and empirical results, but I expect you to focus on the theoretical parts of the paper. The rules for the presentation are as follows:

Partial list of possible papers (a [X] indicates the paper has already been assigned):

Other useful references

Supported partly by NSF grant DMS-1248176.
Last updated: Dec 14, 2012.