Parameter Dependence in Cumulative Selection

Cumulative selection is a powerful process in which small changes accumulate over time because of their selective advantage. It is central to a gradualist approach to evolution, the validity of which has been called into question by proponents of alternative approaches to evolution. An important question in this context concerns how the efficiency of cumulative selection depends on various parameters. This dependence is investigated as parameters are varied in a simple problem where the goal is to find a target string starting with a randomly generated guess. The efficiency is found to be extremely sensitive to values of population size, mutation rate and string length. Unless the mutation rate is sufficiently close to a value where the number of generations is a minimum, the number of generations required to reach the target is much higher if it can be reached at all.