Spiral Wave Structure in Pre-biotic Evolution: Hypercycles Stable against Parasites*

In the study of pre-biotic evolution self-structuring and evolutionary processes are themes that are usually studied separately. In this paper we demonstrate that spatial self-structuring in incompletely mixed media can profoundly change the outcome of evolutionary processes; for instance, positive selection for “altruistic” features becomes feasible. A spatial cellular automaton model of self-replicative molecules that are linked cyclically by catalysis (i.e. a hypercycle) was studied. Because of the spiral structures that emerge in such a system, the hypercycle becomes resistant to a large class of “parasites”, i.e. molecules that give no catalytic support but receive increased catalytic support.