Positiv e-sense, single-stranded RN A viruses are im portant pathogens infecting almost all types of organ- isms. Experimental evidence from distributions of mutations and from viral RN A ampli¿cation suggest that these pathogens may follow different RN A replication modes, r anging from the stamping machine replication (SMR) to the geo metric replication (GR) mode. Although previous theoretical work has focuse d on the evolutionary dynamics of RNA viruses amplifying their genomes with dif fer ent strategies, little is known in ter ms of the bifurcations and transitions invol ving the so-called error threshold (mutation- induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation ac- cumulation and demographic stochasti city). Here we analyze a dynamical system describing the intracel- lular ampli¿cation of viral RN A genomes e volving on a single-peak ¿tness landscape focusing on thr ee cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and err or thr eshold, governe d by transcritical bifurcations that depend on parameters a (paramet er introducing the mode of replication), repl icat ive ¿tness of mutants ( k 1 ), and on the spontaneous degradation rate s of the sequences ( ¿ ). Our re sults re late the error catastrophe with lethal mutag enesis in a model with continuous populations of viral genome s. The form er case invol ves dominance of the mutant sequences, while the latter , a deterministic extinction of the viral RNAs during replication due to increased mutation. Fo r the lethal case the critical mutation ra te involving lethal mu- tagenesis is µ c = 1 - e / v a . Here, the SMR involv es lower critical mutation ra tes, being the system more robu st to lethal mutagenesis replicating closer to the GR mode. This resul t is also f ound for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the er r or threshold once the replication mode surpasses a threshold given by v a = ¿ /k 1

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