Evolving towards the hypercycle: A spatial model of molecular evolution

We extend earlier cellular automata models of spatially extended hypercycles by including an explicit genetic component in the model. This allows us to study the sequence evolution of hypercyclically coupled molecular replicators in addition to considering their population dynamics and spatial organization. In line with previous models that considered either spatial organization or sequence evolution alone, we find both temporal oscillations of the relative concentration of the species forming the hypercycles as well as the formation of spatial organizations including spiral waves. We also confirm the greatly increased robustness of the spatially extended hypercycle against various classes of parasites.We determine how the sequence evolution of each of the hypercyclically coupled populations proceeds (after an initial selection-dominated phase) in a drift-like manner that can be described by a diffusion process in sequence space. Kimura’s theory of neutral evolution is therefore applicable on long timescales despite the fact that the hypercycle exhibits extreme periodic changes in population sizes that are governed solely by frequency-dependent selection.