Robustness and epistasis in mutation-selection models

We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of a 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 mapping to a Schrödinger 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 landscapes and show that diminishing epistasis is a necessary but not sufficient condition for error threshold behaviour.