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| Richard Durrett |
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| Professor of Mathematics |
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Web Site www.math.cornell.edu/~durrett/ Contact Information
Courses & Office Hours |
Education
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 Simon Levin that was begun in the late 80’s and produced 10 pages on the use of stochastic spatial models in ecology.
In 1997 I began a collaboration with Chip Aquadro in Molecular Biology and Genetics at Cornell. Our first paper on the evolutionary dynamics of DNA repeat sequences (e.g., CA repeated 15 times in a row) was published in the Proceedings of the National Academy of Science. Subsequent work with two graduate students has shown that the dependence of mutation rates on length of repeat is not simple and selection acts to reduce the length of long repeats.
With Rasmus Nielsen in Biological Statistics and Computational Biology, I have developed stochastic methods for studying the evolution of genomes due to large-scale processes: inversions within chromosomes, translocations between chromosomes, chromosomal fissions and fusions, and gene duplication. This work has led to a surprising new result on the behavior of the distance from the origin for random walk on the transposition group.
Joint work with Ted Cox and Iljana Zahle has studied the influence of spatial structure on genealogies. With Jason Schweinsberg, we developed a simple approximation for the effect of fixation of advantageous mutations on the variability of nearby nucleotides. Gene duplication is another topic that I have considered in three papers that are joint work with REU student Rachel Ward, with Deena Schmidt, and with Jason Schweinsberg.
Recently I have become interested in random graphs. Notes from a course I taught in fall 2004 will end up as a short book or long paper on the subject. In addition, I have done research on this topic with REU student Jonah Balisak and with Paul Jung.
Selected Publications
Microsatellite models: Insights from a comparison of humans and chimpanzees (with R. Sainudiin, C. F. Aquadro, and R. Nielsen), Genetics 168 (2004), 383–395.
Bayesian estimation of genomic distance (with R. Nielsen and T. L. York), Genetics 166 (2004), 621–629.
Subfunctionalization: How often does it occur? How long does it take? (with R. Ward), Theor. Pop. Biol. 66 (2004), 93–100.
Adaptive evolution drives the diversification of zinc-finger binding domains (with D. Schmidt), Mol. Biol. Evol. 21 (2004), 2326–2339.
Approximating selective sweeps (with J. Schweinsberg), Theor. Pop. Biol. 66 (2004), 93–100; Ann. Appl. Probab. (to appear).
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 (to appear).
Power laws for family sizes in a gene duplication model (with J. Schweinsberg), Annals of Probability (to appear).
Random Oxford graphs (with J. Blasiak), Stochastic Process and their Applications (to appear).
Two phase transitions for the contact process on small worlds (with P. Jung), Ann. Appl. Probab. (to appear).
Last modified: May 2, 2005