Su-Chan Park and Joachim Krug J. Stat. Mech. (2008) P04014 doi:10.1088/1742-5468/2008/04/P04014
Evolution in random fitness landscapes: the infinite sites model
FREE ARTICLE Topical articles on Disorder, Fluctuations and UniversalitySu-Chan Park and Joachim Krug
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We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w). This is the finite population version of Kingman's house of cards model (Kingman 1978 J. Appl. Probab. 15 1). In contrast to Kingman's work, the focus here is on unbounded distributions g(w) which lead to an indefinite growth of the population fitness. The model is solved analytically in the limit of infinite population size 
and simulated numerically for finite N. When the genome-wide mutation probability U is small, the long-time behavior of the model reduces to a point process of fixation events, which is referred to as a diluted record process (DRP). The DRP is similar to the standard record process except that a new record candidate (a number that exceeds all previous entries in the sequence) is accepted only with a certain probability that depends on the values of the current record and the candidate. We develop a systematic analytic approximation scheme for the DRP. At finite U the fitness frequency distribution of the population decomposes into a stationary part due to mutations and a traveling wave component due to selection, which is shown to imply a reduction of the mean fitness by a factor of 1−U compared to the 
limit.
- Keywords
- PACS
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87.23.Cc Population dynamics and ecological pattern formation
- MSC
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92D15 Problems related to evolution
62P10 Applications to biology and medical sciences
92B15 General biostatistics (See also 62P10)
92D10 Genetics (For genetic algebras, see 17D92)
- Subjects
- Dates
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Issue 04 (April 2008)
Received 13 November 2007, accepted for publication 14 March 2008
Published 14 April 2008
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Evolution in random fitness landscapes: the infinite sites model
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