Error Thresholds in Presence of Epistatic Interactions

Models for viral populations with high replication error rates (such as RNA viruses) rely on the quasi-species concept, in which mutational pressure beyond the so-called ``Error Threshold" leads to a loss of essential genetic information and population collapse, an effect known as the ``Error Catastrophe". We explain how crossing this threshold, as a result of increasing mutation rates, can be understood as a second order phase transition, even in the presence of lethal mutations. In particular, we show that, in fitness landscapes with a single peak, this collapse is equivalent to a ferro-paramagnetic transition, where the back-mutation rate plays the role of the external magnetic field. We then generalise this framework to rugged fitness landscapes, like the ones that arise from epistatic interactions, and provide numerical evidence that there is a transition from a high average fitness regime to a low average fitness one, similarly to single-peaked landscapes. The onset of the transition is heralded by a sudden change in the susceptibility to changes in the mutation rate. We use insight from Replica Symmetry Breaking mechanisms in spin glasses, in particular by considering that the fluctuations of the genotype similarity distribution are an order parameter.