The Arrival of the Frequent: How Bias in Genotype- Phenotype Maps Can Steer Populations to Local Optima

Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The total number of genotypes NG is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies Fp~Np=NG, with Np the number of genotypes mapping onto phenotype p, is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype p scales to first order as Fp, although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time Tp of a phenotype p similarly scales to first order as 1=Fp for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger Fp is therefore be much more likely to arise than variation with a small Fp. We show, using the RNA model, that frequent phenotypes (with larger Fp) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never ‘arrive ’ o