TANGLED WEBS Evolutionary Dynamics on Fitness Landscapes with Neutrality

3 After a while your adversaries and competitors will give up trying to think of alternative hypotheses, or else will grow old and die, and then your hypothesis will become accepted. Sounds crazy, we know, but that's how science works!-Numerical Recipes in C Abstract The bulk of research on the dynamics of populations of genotypes evolving on fitness landscapes has concentrated on the rôle of correlation and landscape ruggedness as a putative indicator of the qualitative dynamics. There is, however, a small but growing awareness amongst population geneticists (through Motoo Kimura's Neutral Theory of molecular evolution [16, 3]) and molecular biologists (Eigen, Schuster, et. al.[5, 2, 18]) of the importance of neutral mutation as a significant factor in evolutionary dynamics. This awareness has thus far not extended to the GA community. Of particular interest is the notion of neutral networks of selectively neutral genotypes which percolate a fitness landscape-recent work on RNA folding landscapes characterises their structure in terms of There is at present a lack of computationally tractable abstract models demonstrating neutrality. In this paper we introduce two parametrised families of abstract landscapes: the NKp landscapes, based on the NK family of abstract landscapes [15], allow tuning of the degree of neutrality whilst leaving invariant the auto-correlation function [24, 23, 15]. The RNN (Random Neutral Network) landscapes, constructed by mutually-avoiding random walks, feature percolating neutral networks of specifiable size and neutral dimension. The statistical structure of these landscapes is examined and related to the characteristic dynamics of populations evolving on them. Several conjectures regarding the auto-correlation function on NKp landscapes (relevant also to NK landscapes) are raised. Attention is drawn to the very different nature of population dynamics on landscapes with percolating neutral networks as compared to the dynamics on rugged multi-peaked landscapes. Qualitative similarities between population dynamics on RNN landscapes and RNA folding landscapes are highlighted. Finally, implications for biological research and for the application of GA's to optimisation problems are discussed.