The Paradox of the Plankton: Oscillations and Chaos in Multispecies Evolution

Two theoretical ecologists have recently discovered that even under the simplest models of competition, three species are sufficient to generate permanent oscillations, and five species can generate chaos (Huisman & Weissing, 2001). We can show that these results carry over into genetic algorithm (GA) resource sharing after making one minor change in the “usual” sharing methods. We also bring together previous, scattered results showing oscillatory and chaotic behavior in the “usual” GA sharing methods themselves. Thus one could argue that oscillations and chaos are fairly easy to generate once individuals are allowed to influence each other, even if such interactions are extremely simple, natural, and indirect, as they are under resource sharing. We suggest that great care be taken before assuming that any particular implementation of resource sharing leads to a unique and stable equilibrium.