Asymptotics of the Luria-Delbrück distribution via singularity analysis
نویسندگان
چکیده
منابع مشابه
Mean field mutation dynamics and the continuous Luria-Delbrück distribution.
The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they ...
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Luria-Delbrück fluctuation analysis provides a method to estimate mutation rates in cell populations. Originally designed for bacterial populations, the method now is widely applied in somatic cell genetics and in cancer biology. However, there are fundamental genetic differences between bacteria and somatic cells, and this together with the inherent mathematical complexity of fluctuation analy...
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The Luria-Delbrück mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes ...
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The Luria-Delbrück experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the past 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far f...
متن کاملImproved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution.
The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values ...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 1996
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s0021900200103924