An Exploration of NK Landscapes with Neutrality

Abstract

Recent research into the evolution of RNA molecules has raised awareness of the neutral theory of evolution. Several fitness landscape models based upon the NK model have been proposed to investigate the behaviour of populations evolving on neutral landscapes. In this study, Kauffman's results pertaining to the NK fitness landscape model are replicated and a new visualisation technique is developed to illustrate the presence of ruggedness and neutrality across a landscape. These results are extended to the neutral NKp and NKq variants of the NK model. It is shown that these two models of neutrality result in landscapes with significant structural differences. An important goal in evolutionary computation is a greater understanding of the relationship between landscape structure and the optimal choice of evolutionary algorithms. A series of simulations is run comparing the performance of a variety of individual and population-based algorithms on a range of neutral and non-neutral landscapes. It is found that hill-climbing algorithms are generally capable of finding better individual solutions, but population-based algorithms tend to find higher average solutions. Finally, it is shown that crossover allows a population on a neutral landscape to maintain a much higher level of genetic diversity on a neutral layer than a population using mutation alone. Furthermore, populations using crossover suffer a less dramatic loss of diversity when a new fitness level is discovered, and recover diversity more rapidly.

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