Evolutionary dynamics on strongly correlated fitness landscapes

TL;DR

This paper investigates the evolutionary dynamics of populations on strongly correlated fitness landscapes, revealing how correlations influence mutation effects, jump patterns, and record distributions, with exact analytical results provided.

Contribution

It introduces a model of fitness landscapes with block correlations and derives exact dynamical properties, including jump statistics and record distributions, in this correlated setting.

Findings

Number of jumps in population dynamics follows a predictable pattern.

Distribution of the last jump time exhibits an inverse square law.

Exact results for record and extreme value distributions in correlated variables.

Abstract

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables.