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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 52 open journal systems 


Waiting for m mutations

Jason Ross Schweinsberg, University of California, San Diego


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 μ. 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 μ 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.


Full text: PDF

Pages: 1442-1478

Published on: August 28, 2008
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Electronic Journal of Probability. ISSN: 1083-6489