Richard Durrett
Ph.D. (1976) Stanford University
Research Area
Problems in probability theory that arise from ecology and genetics
My initiation to work at the interface between mathematics and biology came from a collaboration with Kyoto Prize winner Simon Levin that was begun in the late 80’s. This produced 10 joint papers on the use of stochastic spatial models in ecology, and a number of other papers I have written by myself or with students.
In 1997 I began a collaboration with Chip Aquadro in Molecular Biology and Genetics at Cornell. Our first paper concerned the evolutionary dynamics of DNA repeat sequences. Since then I have done work on selective sweeps, the stepping stone model, genome rearrangement, gene duplication, and regulatory seqeunce evolution. Much of this work is summarized in Probability Models for DNA Sequence Evolution, the second edition of which was published by Springer in 2008.
A few years ago, I added in random graphs to my list of interests. In addition to several papers, I have written a book: Random Graph Dynamics, published by Cambridge University Press in 2007. The book and my work concentrate on properties of process that take place on random networks.
Selected Publications
Mutual invadability implies coexistence, Memoris of the AMS 156 (2002), 118 pages.
Bayesian estimation of genomic distance (with R. Nielsen and T. L. York), Genetics 166 (2004), 621–629.
Approximating selective sweeps (with J. Schweinsberg), Theor. Pop. Biol. 66 (2004), 93–100; Ann. Appl. Probab. 15 (2005), 1591–1651.
The stepping stone model, II. Genealogies and the infinite sites model (with I. Zahle and J. T. Cox), Ann. Appl. Probab. 15 (2005), 671–699.
A phase transition in the random transposition random walk (with N. Berestycki), Prob. Theory Rel. Fields 136 (2006), 203–233.
Waiting for regulatory sequences to appear (with Deena Schmidt) Ann. Appl. Probab. 17 (2007), 1–32.