Traveling waves of selective sweeps

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Mayberry, J

Published Date

  • April 1, 2011

Published In

Volume / Issue

  • 21 / 2

Start / End Page

  • 699 - 744

Electronic International Standard Serial Number (EISSN)

  • 1050-5164

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/10-AAP721

Citation Source

  • Scopus