Evolutionary accessibility of random and structured fitness landscapes

TL;DR

This paper analyzes the accessibility of evolutionary paths in different fitness landscape models, highlighting how structure and correlations influence the likelihood of accessible evolutionary routes.

Contribution

It introduces a probabilistic framework for understanding accessibility in both random and structured fitness landscapes, revealing how certain features affect evolutionary pathways.

Findings

Accessible paths exist above a fitness difference threshold in uncorrelated landscapes.

Structured landscapes with tradeoffs have many accessible paths to local maxima.

Global constraints in models lead to increased accessibility of evolutionary routes.

Abstract

Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length $L$ becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotype, which can be explicitly computed for large classes of genotype graphs. The behaviour in uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.