Electronic Journal of Probability

Waiting for $m$ mutations

Jason Schweinsberg

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Abstract

We consider a model of a population of fixed size $N$ in which each individual gets replaced at rate one and each individual experiences a mutation at rate $\mu$. We calculate the asymptotic distribution of the time that it takes before there is an individual in the population with $m$ mutations. Several different behaviors are possible, depending on how $\mu$ changes with $N$. These results have applications to the problem of determining the waiting time for regulatory sequences to appear and to models of cancer development.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 52, 1442-1478.

Dates
Accepted: 28 August 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819125

Digital Object Identifier
doi:10.1214/EJP.v13-540

Mathematical Reviews number (MathSciNet)
MR2438813

Zentralblatt MATH identifier
1191.60100

Subjects
Primary: 60J99: None of the above, but in this section
Secondary: 60J85: Applications of branching processes [See also 92Dxx] 92D25: Population dynamics (general) 92C50: Medical applications (general)

Keywords
Waiting times mutations population genetics Moran model

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Schweinsberg, Jason. Waiting for $m$ mutations. Electron. J. Probab. 13 (2008), paper no. 52, 1442--1478. doi:10.1214/EJP.v13-540. https://projecteuclid.org/euclid.ejp/1464819125


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