Adaptive walks and extreme value theory

Details Adaptive walks and extreme value theory Adaptive walks and extreme value theory

2011-05-03

arxiv.org/abs/1105.0592v2

Physical Review Letters 107, 178102 (2011)

Biology

Quantitative Biology

Populations and Evolution

4 pages, 2 figures; final version, to appear in Physical Review Letters

Scientific paper

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.

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