## Electronic Journal of Probability

### Waiting for $m$ mutations

Jason Schweinsberg

#### 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

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

Rights

#### 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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