Robustness and epistasis in mutation-selection models

TL;DR

This paper analyzes how robustness against mutations affects fitness in mutation-selection models, clarifies previous contradictions, and explores the role of epistasis in error thresholds using analytical and numerical methods.

Contribution

It provides exact analytic results for robustness effects in quasispecies models and clarifies the relationship between epistasis and error thresholds.

Findings

Robustness increases fitness advantage in mutation-selection models.

Diminishing epistasis is necessary but not sufficient for error thresholds.

Analytic results are verified through numerical simulations.

Abstract

We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain analytic results for the robustness effect which become exact in the limit of infinite sequence length. Thereby, we are able to clarify a seeming contradiction between recent rigorous work and an earlier heuristic treatment based on a mapping to a Schr\"odinger equation. We exploit the quantum mechanical analogy to calculate a correction term for finite sequence lengths and verify our analytic results by numerical studies. In addition, we investigate the occurrence of an error threshold for a general class of epistatic landscape and show that diminishing epistasis is a necessary but not sufficient condition for error threshold behavior.