Abstract
We simulate a deterministic population genetic model for the coevolution of genetic codes and protein-coding genes. We use very simple assumptions about translation, mutation, and protein fitness to calculate mutation-selection equilibria of codon frequencies and fitness in a large asexual population with a given genetic code. We then compute the fitnesses of altered genetic codes that compete to invade the population by translating its genes with higher fitness. Codes and genes coevolve in a succession of stages, alternating between genetic equilibration and code invasion, from an initial wholly ambiguous coding state to a diversified frozen coding state. Our simulations almost always resulted in partially redundant frozen genetic codes. Also, the range of simulated physicochemical properties among encoded amino acids in frozen codes was always less than maximal. These results did not require the assumption of historical constraints on the number and type of amino acids available to codes nor on the complexity of proteins, stereochemical constraints on the translational apparatus, nor mechanistic constraints on genetic code change. Both the extent and timing of amino-acid diversification in genetic codes were strongly affected by the message mutation rate and strength of missense selection. Our results suggest that various omnipresent phenomena that distribute codons over sites with different selective requirements--such as the persistence of nonsynonymous mutations at equilibrium, the positive selection of the same codon in different types of sites, and translational ambiguity--predispose the evolution of redundancy and of reduced amino acid diversity in genetic codes.