Number of adaptive steps to a local fitness peak

TL;DR

This paper analyzes how the number of steps a population takes to reach a local fitness peak varies depending on the statistical properties of the fitness landscape, with implications for understanding evolutionary dynamics.

Contribution

It provides an analytical framework for understanding how the distribution of fitness values influences the length of adaptive walks on rugged landscapes.

Findings

Walk length cumulants grow with sequence length when fitness distribution has finite mean.

Walk length approaches a constant when the fitness distribution has infinite mean.

Analytical results have implications for experimental studies of evolutionary processes.

Abstract

We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed.