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    Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process

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    Author
    Kessler, David A.; Levine, Herbert
    Date
    2015
    Abstract
    One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size NN is large and mutation rates are low, but not necessarily small compared to 1/N1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy αα-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form
    Citation
    Kessler, David A. and Levine, Herbert. "Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process." Journal of Statistical Physics, 158, no. 4 (2015) Springer: 783-805. http://dx.doi.org/10.1007/s10955-014-1143-3.
    Published Version
    http://dx.doi.org/10.1007/s10955-014-1143-3
    Keyword
    Luria-Delbruck; alpha-stable distribution; growth; mutants
    Type
    Journal article
    Publisher
    Springer
    Citable link to this page
    https://hdl.handle.net/1911/94865
    Rights
    This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer.
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map