  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
number of genotypes $N_G$ 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 $F_p=N_p/N_G$,
with $N_p$ 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 simplified and
general 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 $F_p$, 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 $T_p$ of a phenotype $p$ similarly
scales to first order as $1/F_p$ 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 $F_p$ is therefore be much more
likely to arise than variation with a small $F_p$. We show, using the RNA
model, that frequent phenotypes (with larger $F_p$) 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' on
the timescales of evolutionary change, then they can't fix. We call this highly
non-ergodic effect the `arrival of the frequent'.
