Traveling Waves of Selective Sweeps
Rick Durrett and John Mayberry
Abstract.
The goal of cancer genome sequencing projects is to determine the genetic mutations that cause common cancers. The fact that many malignancies arise during the clonal expansion of a benign tumor motivates the study of recurrent selective sweeps in an exponentially growing population. Simulations of Beerenwinkel et al. show a traveling wave in which the time of the first k-fold mutant, τk$, is approximately linear in k. In addition they used heuristics to obtain formulas for E τk. Here, we prove that as the mutation rate μ goes to 0, τk is asymptotically ck log(1/mu), where the ck can be computed explicitly.
Preprint
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