Waiting for $m$ mutations
نویسندگان
چکیده
منابع مشابه
The waiting time 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 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 applicatio...
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IN the Abstract of their recent article, ‘‘Waiting for Two Mutations: With Applications to Regulatory Sequence Evolution and the Limits of Darwinian Evolution’’ (Genetics 180: 1501–1509, 2008), Durrett and Schmidt write that one of their aims is ‘‘to expose flaws in some of Michael Behe’s arguments concerning mathematical limits to Darwinian evolution.’’ Their effort, however, is itself serious...
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This paper presents a novel method for the calculation of the waiting time distribution function for the M=M=m queue. It is shown that the conditional waiting time obeys an Erlang distribution with rate m , where is the service rate of a server. Explicit closed form solution is obtained by means of the probability density function of the Erlang distribution. It turns out that the derivation of ...
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We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations fo...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2008
ISSN: 1083-6489
DOI: 10.1214/ejp.v13-540