Publications [#243522] of Richard T. Durrett

Papers Published

1. Durrett, R; Mayberry, J, Traveling waves of selective sweeps, Annals of Applied Probability, vol. 21 no. 2 (April, 2011), pp. 699-744, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2807971], [doi]
   (last updated on 2024/04/19)

   Abstract:
   The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239- 2246] consider a Wright-Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Simulations show a traveling wave in which the time of the first k-fold mutant, Tk, is approximately linear in k and heuristics are used to obtain formulas for ETk. Here, we consider the analogous problem for the Moran model and prove that as the mutation rate μ →0, Tk ∼ ck log(1/μ), where the ck can be computed explicitly. In addition, we derive a limiting result on a log scale for the size of Xk(t) = the number of cells with k mutations at time t . © Institute of Mathematical Statistics, 2011.