Hypercycles versus Parasites in a Two Dimensional Partial Differential Equations Model

Hypercycles have been proposed as a means for a simple self-replicating system to increase its information content. They are, however, in general vulnerable to parasites: an established hypercycle system may decay if a deficient molecule appears. Recently, spatial spiral structures have been shown to provide some stability against parasites in two-dimensional cellular automaton models. In this paper a partial differential equations model system is simulated with finite difference equations. Spatially and temporally ordered spiral or cluster states arise. When parasites are inserted, the outcome depends on the spatial structure of the system as well as on the parameters of the parasites: the hypercycle may be killed by the parasites, co-exist with them, or the parasites may die without doing any harm to the system. Highly irregular, chaotic states are observed to emerge under special conditions. Contrary to previous results, the hypercycle is ruinerable to parasites in this model system regardless of spirals. Clusters may under certain conditions save the hypercycle from being killed by parasites.