Journal
ANNALS OF APPLIED PROBABILITY
Volume 21, Issue 2, Pages 699-744Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AAP721
Keywords
Moran model; selective sweep; rate of adaptation; stochastic tunneling; branching processes; cancer models
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Funding
- NSF [DMS-07-04996]
- NSF RTG [DMS-07-39164]
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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 ET(k). Here, we consider the analogous problem for the Moran model and prove that as the mutation rate mu -> 0, T(k) similar to 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.
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