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Traveling waves of selective sweeps

Publication ,  Journal Article
Durrett, R; Mayberry, J
Published in: Annals of Applied Probability
April 1, 2011

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 . © Institute of Mathematical Statistics, 2011.

Duke Scholars

Published In

Annals of Applied Probability

DOI

EISSN

1050-5164

ISSN

1050-5164

Publication Date

April 1, 2011

Volume

21

Issue

2

Start / End Page

699 / 744

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Durrett, R., & Mayberry, J. (2011). Traveling waves of selective sweeps. Annals of Applied Probability, 21(2), 699–744. https://doi.org/10.1214/10-AAP721
Durrett, R., and J. Mayberry. “Traveling waves of selective sweeps.” Annals of Applied Probability 21, no. 2 (April 1, 2011): 699–744. https://doi.org/10.1214/10-AAP721.
Durrett R, Mayberry J. Traveling waves of selective sweeps. Annals of Applied Probability. 2011 Apr 1;21(2):699–744.
Durrett, R., and J. Mayberry. “Traveling waves of selective sweeps.” Annals of Applied Probability, vol. 21, no. 2, Apr. 2011, pp. 699–744. Scopus, doi:10.1214/10-AAP721.
Durrett R, Mayberry J. Traveling waves of selective sweeps. Annals of Applied Probability. 2011 Apr 1;21(2):699–744.

Published In

Annals of Applied Probability

DOI

EISSN

1050-5164

ISSN

1050-5164

Publication Date

April 1, 2011

Volume

21

Issue

2

Start / End Page

699 / 744

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics