Effect of robustness on selection of a mutation-rate regulating gene

Abstract

We study the evolution of a population of sequences, where each sequence is divided into a reproduction-rate (fitness) encoding part and a mutation-rate regulating part. Evolutionary selection acts on the sequence both by a direct fitness landscape and by indirect selection on a mutation landscape through which the sequence's mutation rate is determined, thereby providing a model of a mutation-rate-regulating gene. Coupling of the fitness landscape and mutation landscape leads to adaptive evolution of the sequence. We investigate the effects of robustness in the mutation landscape and fitness landscapes on selection of the sequence. We find that the effects of robustness in both the mutation and the fitness landscape can be described by an effective sequence length, defined as the mutational load divided by the per-base mutation rate, and we give expressions for the effective sequence length for various fitness and mutation landscapes. The probability that the sequence with a reduced mutation rate evolves is increased by increasing the robustness of the mutation landscape, and decreased by increasing the robustness of the fitness landscape. However, in the case of the mutation-rate-regulating part making up only a very small part of the total sequence length, we show that selection for a more robust sequence with less-reduced mutation rate is very weak, and therefore we conjecture that robust sequences play little role in selection of error-reducing mechanisms in real populations.