Simple quasispecies models for the survival-of-the-flattest effect: The role of space

The survival-of-the-flattest effect postulates that under high mutation rates natural selection does not necessarily favor the faster replicators. Under such conditions, genotypes which are robust against deleterious mutational effects may be favored instead, even at the cost of a slower replication. This tantalizing hypothesis has been recently proved using digital organisms, subviral RNA plant pathogens (viroids), and an animal RNA virus. In this work we study a simple theoretical system composed by two competing quasispecies which are located at two widely different fitness landscapes that represent, respectively, a fit and a flat quasispecies. The fit quasispecies is characterized by high replication rate and low mutational robustness, whereas the flat quasispecies is characterized by low replication rate but high mutational robustness. By using a mean field model, in silico simulations with digital replicons and a two-dimensional spatial model given by a stochastic cellular automata (CA), we predict the presence of an absorbing first-order phase transition with critical slowing down between selection for replication speed and selection for mutational robustness, where the surpassing of a critical mutation rate involves the outcompetition of the fit quasispecies by the flat one. Furthermore, it is shown that space, which involves a lower critical mutation rate, broadens the conditions at which the survival-of-the-flattest may occur.