Nonlinear Dynamics and Cluster Compartmentalization in Two-Member Hypercycles with Parasites

The hypercycle represents an example of cooperation at the molecular level, with different replicators leading to a reciprocal enhancement of their ability to survive and increasing the information content beyond the Eigen's error catastrophe. Hypercycles have been proposed as possible networks of replicators involved in the evolution of the first autonomous self-reproducing molecular living-like systems. However, they are vulnerable to parasites: an established hypercyclic system may decay if a selfish replicator i.e., one that receives catalytic help but does not catalyze the replication of any other member of the hypercycle, appears. In this paper we focus in one of the simplest hypercycles i.e., the symmetric two-member one, studying its dynamics under the presence of parasites by using both mean field and two-dimensional stochastic cellular automata models. Both models show three possible outcomes: (i) hypercycle stability and parasite extinction; (ii) extinction of the entire system; and (iii) coexistence between hypercycles and parasites. Scenario (iii) is shown to be structurally unstable in the mean field model. However, the addition of spatial dimensions enlarges such a scenario over parameter space, showing complex fluctuations and the emergence of clusters able to provide the hypercycle with resistance against the parasites. Such resistance is shown to be reduced with the increase of diffusion. These results are discussed in the context of prebiotic evolution.