Spatio-temporal dynamics in simple asymmetric hypercycles under weak parasitic coupling

Hypercycles represent an example of cooperation at the molecular level suggested to be involved in the evolution of the first autonomous, self-reproducing molecular living-like systems. However, they are vulnerable to parasites: an established hypercycle may decay if a selfish replicator appears i.e. one that receives catalytic help but does not reciprocate catalysis. In this work we study the dynamics of a two-member hypercycle with an attached, weak parasite. We are using a mean field model and a stochastic cellular automaton (CA) focusing on the role of the kinetic properties of both hypercycle replicators, exploited by the parasite. Both approaches show three possible, parameter-dependent outcomes: (i) hypercycle stability and parasite extinction; (ii) extinction of the entire system; and (iii) coexistence between the hypercycle and the parasite. Scenario (iii) is shown to be structurally unstable in the mean field model but the addition of space allows a wider coexistence phase. Moreover the CA model also indicates that the degree of hypercycle’s asymmetry may be relevant in the survival of the catalytic replicators, being also responsible for qualitatively different dynamics e.g. if the parasite is attached to the fittest hypercycle unit, low-dimensional chaos arises. The coexistence phase is characterized by the emergence of hypercyclic aggregates with a broad distribution of cluster sizes and mixed patterns of replicators able to provide the hypercycle with resistance against the parasites. Nevertheless the resistance to the parasite is shown to reduce with increase of diffusion. The role of the kinetic properties of the hypercycle and of diffusion in the survival of the hypercycle is discussed in the context of prebiotic evolution.