Monotonicity of Fitness Landscapes and Mutation Rate

The typical view in evolutionary biology is that mutation rates are minimised. Contrary to that view, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control param-eter to optimise the performance of evolutionary algorithms. Ronald Fisher’s work is the basis of much biological theory in this area. He used Euclidean geometry of continuous, infinite phenotypic spaces to study the relation be-tween mutation size and expected fitness of the offspring. Here we develop a general theory of optimal mutation rate control that is based on the alterna-tive geometry of discrete and finite spaces of DNA sequences. We define the monotonic properties of fitness landscapes, which allows us to relate fitness to the topology of genotypes and mutation size. First, we consider the case of a perfectly monotonic fitness landscape, in which the optimal mutation rate control functions can be derived exactly or approximately depending on additional constraints of the problem. Then we consider the general case o