Monotonicity of Fitness Landscapes and Mutation Rate Control

TL;DR

This paper explores how mutation rates can be optimally controlled in finite DNA sequence spaces, showing that mutation rates tend to increase as fitness decreases, especially in less monotonic landscapes, with implications for evolutionary biology.

Contribution

It introduces a theoretical framework for mutation rate control in discrete DNA spaces and empirically validates the relationship between landscape monotonicity and mutation rate increase.

Findings

Optimal mutation rate functions increase as fitness decreases.

Less monotonic (more rugged) landscapes exhibit more rapid mutation rate increases.

Theoretical results apply to landscapes that are continuous and open at the optimum.

Abstract

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.