The Innuence of Mutation on Autocatalytic Reaction Networks Stadler & Nu~ No: Selection-mutation Equations

A particular class of ordinary diierential equations (ODE) describing catalyzed, template-induced, and erroneous replication is investigated. The ODEs can be split into a replicator part accounting for the correct replication and a mutation term accounting for all miscopying processes. The set of all species is divided into the catalytically active \viable" species and an error-tail subsuming all other species. Neglecting both the inter-mutation among the viable species and the re-ux from the error-tail allows for an extensive analysis of the autocatalytic network. If mutation rates are small enough a perturbation approach is feasible showing that mutation in general simpliies the qualitative behavior of the dynamical system. Special cases, such as Schll ogl's model, the uniform model, and the hypercycle show that the viable species become unstable beyond a critical mutation rate: there is an analogue to the error-threshold of the quasispecies model also in non-linear autocatalytic reaction networks with mutation.