Dynamics of emerging functional shifts in cooperative systems

Abstract

Hypercycles are cyclic catalytic systems formed by replicating species, conceived in the 1970’s as a solution to the so-called information crisis or Eigen’s paradox. So far, hypercycles have considered only cooperation, together with the emergence of so-called catalytic short-circuits and parasites. More recently, the impact of functional shifts (the change from cooperation to degradation or predation by one of the species) has been investigated in both discrete- and continuous-time systems. These previous models, however, included these shifts in an implicit manner, assuming that some species or a given fraction of them changed cooperation. Here a simple model for a two-species hypercycle is proposed, in which one of the species explicitly produces a degrader phenotype due to mutational processes, where the effects of cleavage and predation have been studied. We have identified a saddle-node bifurcation separating coexistence from co-extinctions, involving bistable dynamics before the bifurcation occurs. Although the effects of predation have been found to be damaging, cleavage turns out to be, to some extent, beneficial