Error threshold ghosts in a simple hypercycle with error prone self-replication

A delayed transition because of mutation processes is shown to happen in a simple hypercycle composed by two indistinguishable molecular species with error prone self-replication. The appearance of a ghost near the hypercycle error threshold causes a delay in the extinction and thus in the loss of information of the mutually catalytic replicators, in a kind of information memory. The extinction time, τ, scales near bifurcation threshold according to the universal square-root scaling law i.e. τ ∼ (Qhc − Q)−1/2, typical of dynamical systems close to a saddle-node bifurcation. Here, Qhc represents the bifurcation point named hypercycle error threshold, involved in the change among the asymptotic stability phase and the so-called Random Replication State (RRS) of the hypercycle; and the parameter Q is the replication quality factor. The ghost involves a longer transient towards extinction once the saddle-node bifurcation has occurred, being extremely long near the bifurcation threshold. The role of this dynamical effect is expected to be relevant in fluctuating environments. Such a phenomenon should also be found in larger hypercycles when considering the hypercycle species in competition with their error tail. The implications of the ghost in the survival and evolution of error prone self-replicating molecules with hypercyclic organization are discussed.