Complex Systems

Evolution of Bit Strings II: A Simple Model of Co-Evolution Download PDF

Harald Freund
Robert Wolter
Physics Department, University of Wuppertal,
Gauss-Strasse 20, 42097 Wuppertal, Germany


In this paper we present the results of simple co-evolutionary models that simulate the temporal development of a population of interacting bit strings. Each bit string is decoded into functional groups called "genes.'' The individuals participate in a procedure similar to the Darwinian principle, that is, random interaction (in which the genes determine the fitness of an individual) followed by deterministic selection including random errors during reproduction. We use three selection models: selection by sorting and replacing, tournament selection, and energy flow.

We compare the results for each model to those of a random-selection model to ensure that "emergent'' (non-trivial) features are really caused by evolutionary processes. The influence of selection is clearly evident when comparing the age distributions of individuals and species to those of the random-selection case. While the age distribution of the individuals shows a systematic deviation from an exponential behavior in the selection case, the species ages tend to follow a power law when applying non-random selection. The species show a dynamic of "punctuated equilibria'' that is similar to the behavior of natural systems.