Open Access
April 2011 Traveling waves of selective sweeps
Rick Durrett, John Mayberry
Ann. Appl. Probab. 21(2): 699-744 (April 2011). DOI: 10.1214/10-AAP721


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, Tkck 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.


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Rick Durrett. John Mayberry. "Traveling waves of selective sweeps." Ann. Appl. Probab. 21 (2) 699 - 744, April 2011.


Published: April 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1219.92037
MathSciNet: MR2807971
Digital Object Identifier: 10.1214/10-AAP721

Primary: 60J85, 92D25
Secondary: 92C50.

Keywords: branching processes , cancer models , Moran model , rate of adaptation , selective sweep , stochastic tunneling

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.21 • No. 2 • April 2011
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