Spatial dynamics and the evolution of enzyme production.

We re-examine the problem of the evolution of protein synthesis or enzyme production using a stochastic cellular automaton model, where the replicators are fixed in the sites of a two-dimensional square lattice. In contrast with the classical chemical kinetics or mean-field predictions, we show that a small colony of mutant, protein-mediated (enzymatic) replicators has an appreciable probability to take over a resident population of simpler, direct-template replicators. In addition, we argue that the threshold phenomenon corresponding to the onset of invasion can be described quantitatively within the physics framework of nonequilibrium phase transitions. We study also the invasion of a resident population of enzymatic replicators by more efficient replicators of the same kind, and show that although slightly more efficient mutants cannot invade, invasion is a likely event if the productivity advantage of the mutants is large. In this sense, the establishment of a population of enzymatic replicators is not a 'once-forever' evolutionary decision.