Abstract
Regardless of genome polarity, intermediaries of complementary sense must be synthesized and used as templates for the production of new genomic strands. Depending on whether these new genomic strands become themselves templates for producing extra antigenomic ones, thus giving rise to geometric growth, or only the firstly synthesized antigenomic strands can be used to this end, thus following Luria's stamping machine model, the abundances and distributions of mutant genomes will be different. Here we propose mathematical and bit string models that allow distinguishing between stamping machine and geometric replication. We have observed that, regardless the topology of the fitness landscape, the critical mutation rate at which the master sequence disappears increases as the mechanism of replication switches from purely geometric to stamping machine. We also found that, for a wide range of mutation rates, large-effect mutations do not accumulate regardless the scheme of replication. However, mild mutations accumulate more in the geometric model. Furthermore, at high mutation rates, geometric growth leads to a population collapse for intermediate values of mutational effects at which the stamping machine still produces master genomes. We observed that the critical mutation rate was weakly dependent on the strength of antagonistic epistasis but strongly dependent on synergistic epistasis. In conclusion, we have shown that RNA viruses may increase their robustness against the accumulation of deleterious mutations by replicating as stamping machines and that the magnitude of this benefit depends on the topology of the fitness landscape assumed.