The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 21, Number 2 (2011), 699-744.
Traveling waves of selective sweeps
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.
Ann. Appl. Probab. Volume 21, Number 2 (2011), 699-744.
First available in Project Euclid: 22 March 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Durrett, Rick; Mayberry, John. Traveling waves of selective sweeps. Ann. Appl. Probab. 21 (2011), no. 2, 699--744. doi:10.1214/10-AAP721. https://projecteuclid.org/euclid.aoap/1300800986