Traveling waves of selective sweeps

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, $T_k$, is approximately linear in $k$ and heuristics are used to obtain formulas for $E{T}_k$. Here, we consider the analogous problem for the Moran model and prove that as the mutation rate $\mu \to 0$, $T_k\sim c_k\log (1/\mu )$, where the $c_k$ can be computed explicitly. In addition, we derive a limiting result on a log scale for the size of $X_k(t)=$the number of cells with $k$ mutations at time $t$.

Published in at http://dx.doi.org/10.1214/10-AAP721 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Genetic progression and the waiting time to cancer
• The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation
• A waiting time problem arising from the study of multi-stage carcinogenesis
• Asymptotic behavior of the rate of adaptation

Cited by in corpus (3)

• Evolutionary dynamics of tumor progression with random fitness values
• From Adaptive Dynamics to Adaptive Walks
• Upper bound on the rate of adaptation in an asexual population