Electronic Journal of Probability
- Electron. J. Probab.
- Volume 13 (2008), paper no. 52, 1442-1478.
Waiting for $m$ mutations
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.
Electron. J. Probab., Volume 13 (2008), paper no. 52, 1442-1478.
Accepted: 28 August 2008
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
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)
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