Electronic Journal of Probability

Waiting for $m$ mutations

Jason Schweinsberg

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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)

Waiting times mutations population genetics Moran model

This work is licensed under aCreative Commons Attribution 3.0 License.


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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