Adaptive walks and extreme value theory

TL;DR

This paper analyzes biological evolution as an adaptive walk in high-dimensional genotype space, revealing that the mean walk length depends logarithmically on beneficial mutations and is influenced by the fitness distribution's tail.

Contribution

It provides an analytical and numerical study of adaptive walks, linking walk length to the tail behavior of fitness distributions in high-dimensional spaces.

Findings

Mean walk length is logarithmic in beneficial mutations.

Walk length depends on the tail of the fitness distribution.

Analytical results are confirmed by simulations.

Abstract

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.