THE INFLUENCE OF MUTATION ON AUTOCATALYTIC REACTION NETWORKS

A particular class of ordinary differential equations (ODEs) describin g catalyzed, template-induced, and erroneous replication is investigat ed. The ODEs can be split into a replicator part accounting for the co rrect replication and a mutation term accounting for all miscopying pr ocesses. The set of all species is divided into the catalytically acti ve ''viable'' species and an error tail subsuming all other species. N eglecting both the intermutation among the viable species and the refl ux from the error tail allows for an extensive analysis of the autocat alytic network. If mutation rates are small enough, a perturbation app roach is feasible showing that mutation in general simplifies the qual itative behavior of the dynamical system. Special cases, such as Schlo gl's model, the uniform model, and the hypercycle, show that the viabl e species become unstable beyond a critical mutation rate: There is an analogue to the error threshold of the quasi-species model also in no nlinear autocatalytic reaction networks with mutation.