Optimal Mutation Rates in Dynamic Environments

Abstract

In this paper, we study the evolution of the mutation rate for simple organisms in dynamic environments. A model based on explicit population dynamics at the gene sequence level, with multiple fitness coding loci tracking a moving fitness peak in a random fitness background, is developed and an analytical expression for the optimal mutation rate is derived. The optimal mutation rate per genome is approximately independent of genome length, something that has been observed in nature. Furthermore, the optimal mutation rate is a function of the absolute, not relative, replication rate of the superior gene sequences. Simulations confirm the theoretical predictions.