Document Type
Article
Publication Title
Annals of Applied Probability
Department
Mathematics
ISSN
1050-5164
Volume
21
Issue
2
DOI
10.1214/10-AAP721
First Page
699
Last Page
744
Publication Date
4-1-2011
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.
Recommended Citation
Durrett, R.,
&
Mayberry, J.
(2011).
Traveling waves of selective sweeps.
Annals of Applied Probability, 21(2), 699–744.
DOI: 10.1214/10-AAP721
https://scholarlycommons.pacific.edu/cop-facarticles/871
