Complex Systems

The NQK Model of Fitness Dynamics: Adaptation by Selective Elimination and Random Replacements Download PDF

Franco di Primio
Electronic mail address: franco.diprimio@ais.fraunhofer.de
Fraunhofer Institute for Autonomous Intelligent Systems (AIS),
53754 St. Augustin, Germany

Abstract

An abstract model of fitness evolution is presented which works on the basis of a form of selection called ranking based elimination (RBE). N refers to the size of a population and Q defines the quota of less fit individuals that are replaced by new ones in each generation. The K parameter makes it possible to take into account dependencies that may lead to the replacement of individuals regardless of their fitness. Unlike the evolution model initially studied by Sneppen et al. in [2], our focus here is not on the asymptotic dynamics of critical fitness values, but rather on how the described parameters affect the average fitness dynamics in a short-range perspective, when there is a limit on the length of the evolutionary time range in question (i.e., the number of generations that can be calculated). The main results are that for every maximum number of generations there is a Q value which yields, on average, a maximum for the average fitness and that even low values of K (1 and 2) have a disruptive effect on the average fitness. Q and K may be used as externally tunable control parameters, but they also can be made to depend on the fitness value of individuals, and thus become internal parameters of the model. An analytical model for the dynamics is given, as well, to complement the experimental results. We also discuss possible applications and argue that, in contrast to Q, K is not scale- and domain-independent.