Error threshold in simple landscapes

We consider the quasispecies description of a population evolving in both the "master sequence" landscape (where a single sequence is evolutionarily preferred over all others) and the REM landscape (where the fitness of different sequences is an independent, identically distributed, random variable). We show that, in both cases, the error threshold is analogous to a first order thermodynamical transition, where the overlap between the average genotype and the optimal one drops discontinuously to zero.