Theory and Practice of Optimal Mutation Rate Control in Hamming Spaces of DNA Sequences

We investigate the problem of optimal control of mutation by asexual self-replicating organisms represented by points in a metric space. We introduce the notion of a relatively monotonic fitness landscape and consider a generalisation of Fisher’s geometric model of adaptation for such spaces. Us-ing a Hamming space as a prime example, we derive the prob-ability of adaptation as a function of reproduction parameters (e.g. mutation size or rate). Optimal control rules for the pa-rameters are derived explicitly for some relatively monotonic landscapes, and then a general information-based heuristic is introduced. We then evaluate our theoretical control func-tions against optimal mutation functions evolved from a ran-dom population of functions using a meta genetic algorithm. Our experimental results show a close match between theory and experiment. We demonstrate this result both in artifi-cial fitness landscapes, defined by a Hamming distance, and a natural landscape, where fitness is defined by a DNA-protein affinity. We discuss how a control of mutation rate could oc-cur and evolve in natural organisms. We also outline future directions of this work