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2008 Waiting for $m$ mutations
Jason Schweinsberg
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Electron. J. Probab. 13: 1442-1478 (2008). DOI: 10.1214/EJP.v13-540

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.

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Jason Schweinsberg. "Waiting for $m$ mutations." Electron. J. Probab. 13 1442 - 1478, 2008. https://doi.org/10.1214/EJP.v13-540

Information

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

zbMATH: 1191.60100
MathSciNet: MR2438813
Digital Object Identifier: 10.1214/EJP.v13-540

Subjects:
Primary: 60J99
Secondary: 60J85, 92C50, 92D25

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