An evolutionary version of the random energy model

We consider Eigen's quasispecies model (1971) of molecular evolution in the case in which the reproduction rates of different molecular species are quenched independent random variables. We show, by analogy with the random energy model, the existence of two phases: a 'neutral' phase, where no adaptation effects are exhibited, and a (pathological) 'adapted' phase, where the population is made of identical, optimally adapted molecules, and does not evolve.