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Genotype-phenotype (GP) maps specify how the random mutations that changegenotypes generate variation by altering phenotypes, which, in turn, cantrigger selection. Many GP maps share the following general properties: 1) Thenumber of genotypes $N_G$ is much larger than the number of selectablephenotypes; 2) Neutral exploration changes the variation that is accessible tothe population; 3) The distribution of phenotype frequencies $F_p=N_p/N_G$,with $N_p$ the number of genotypes mapping onto phenotype $p$, is highlybiased: the majority of genotypes map to only a small minority of thephenotypes. Here we explore how these properties affect the evolutionarydynamics of haploid Wright-Fisher models that are coupled to a simplified andgeneral random GP map or to a more complex RNA sequence to secondary structuremap. For both maps the probability of a mutation leading to a phenotype $p$scales to first order as $F_p$, although for the RNA map there are furthercorrelations as well. By using mean-field theory, supported by computersimulations, we show that the discovery time $T_p$ of a phenotype $p$ similarlyscales to first order as $1/F_p$ for a wide range of population sizes andmutation rates in both the monomorphic and polymorphic regimes. Thesedifferences in the rate at which variation arises can vary over many orders ofmagnitude. Phenotypic variation with a larger $F_p$ is therefore be much morelikely to arise than variation with a small $F_p$. We show, using the RNAmodel, that frequent phenotypes (with larger $F_p$) can fix in a populationeven when alternative, but less frequent, phenotypes with much higher fitnessare potentially accessible. In other words, if the fittest never `arrive' onthe timescales of evolutionary change, then they can't fix. We call this highlynon-ergodic effect the `arrival of the frequent'.

The arrival of the frequent: how bias in genotype-phenotype maps can steer populations to local optima