MINIMUM OF INFORMATION DISTANCE CRITERION FOR OPTIMAL CONTROL OF MUTATION RATE IN EVOLUTIONARY SYSTEMS

Evolutionary dynamics studies changes in populations of species, which occur due to various processes such as replication and mutation. Here we consider this dynamics as an example of Markov evolution on a simplex of probability measures describing the populations, and then define optimality of this evolution with respect to constraints on information distance between these measures. We show how this convex programming problem is related to a variational problem of optimizing Markov transition kernel subject to a constraint on Shannon's mutual information. This relation is represented by the Pythagorean theorem in information geometry considered on the simplex of joint probability measures. We discuss the application of this variational approach to optimization of a stochastic search in metric spaces, and in particular to optimization of mutation rate parameter during the search for optimal DNA sequences in evolutionary systems.