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Phys Rev Lett. 2011 Oct 21;107(17):178102. Epub 2011 Oct 19.

Adaptive walks and extreme value theory.

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Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany.


We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to genotypes, we show that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution. This result is derived analytically in a simplified setting where the mutational neighborhood is fixed during the adaptive process, and confirmed by numerical simulations.

[Indexed for MEDLINE]

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