Evolving Dynamical Systems: nearly neutral regions in continuous fitness landscapes

Neutrality arises from the many to one mapping between genotypes and phenotypes. Several studies have demonstrated that in the presence of selective neutrality evolution is qualitatively different from that on the more common rugged fitness landscapes which are often (implicitly) assumed by artificial evolution practitioners. Almost all of such work has been based on discrete genotype fitness landscapes. However, in many artificial evolutionary problems the most natural way to encode the parameters of the systems being evolved is using real valued genotypes. The notion of neutrality in continuous landscapes has been very little discussed. Dynamical systems, with their parameter space as genotype and their dynamical behaviour determining fitness, generate a redundant mapping. In this sense, changes in parameter settings most of the times produce only slight changes in the dynamical behaviour; but for certain parameter values, even infinitesimal changes will cause the behaviour of the system to change radically. In many real world evolutionary tasks, the fitness of the individuals is considerably related to the behaviour of the underlying system. It is the argument of this thesis that when evolving dynamical systems on such tasks, the evolutionary process may exhibit features which are reminiscent of neutral evolution. We explore the characteristics of the evolutionary process through the use of computer simulations on two families of landscapes. Special attention is paid to the existence and usefulness of regions of equal or nearly equal fitness in these continuous fitness landscapes. Supervisor: Dr. Inman Harvey Submitted for the degree of M.Sc. University of Sussex September, 2004