Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#243543] of Richard T. Durrett

Papers Published

  1. Zähle, I; Cox, JT; Durrett, R, The stepping stone model. II: Genealogies and the infinite sites model, The annals of applied probability : an official journal of the Institute of Mathematical Statistics, vol. 15 no. 1 B (2005), pp. 671-699, ISSN 1050-5164 [MR2114986 (2006d:60157)], [doi]
    (last updated on 2018/03/18)

    This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman's coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by recent studies of the human genome. © Institute of Mathematical Statistics, 2005.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320