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We introduce a simple model describing the evolution of a population of information-carrying macromolecules. We discuss the asymptotic dependence of the variability of the population on different parameters, representing the severity or the fluctuations of the environment. We show the existence of a transition separating a neutralist evolutionary regime from a trapped one. We investigate the dependence of the evolutionary behavior of the population on the correlation properties of the fitness landscape.

A spin-1 Ising model with a random crystal field Delta i has been studied within the mean-field approximation. For the particular two-valued distribution P( Delta i)=p delta ( Delta i- Delta )+(1-p) delta ( Delta i), three types of diagrams have been found in the ( Delta ,T) plane, the type depending on the concentration p.

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