  All possible phenotypes are not equally accessible to evolving populations.
In fact, only phenotypes of large size, i.e. those resulting from many
different genotypes, are found in populations of sequences, presumably because
they are easier to discover and maintain. Genotypes that map to these
phenotypes usually form mostly connected genotype networks that percolate the
space of sequences, thus guaranteeing access to a large set of alternative
phenotypes. Within a given environment, where specific phenotypic traits become
relevant for adaptation, the replicative ability of a phenotype and its overall
fitness (in competition experiments with alternative phenotypes) can be
estimated. Two primary questions arise: how do phenotype size, reproductive
capability and topology of the genotype network affect the fitness of a
phenotype? And, assuming that evolution is only able to access large
phenotypes, what is the range of unattainable fitness values? In order to
address these questions, we quantify the adaptive advantage of phenotypes of
varying size and spectral radius in a two-peak landscape. We derive analytical
relationships between the three variables (size, topology, and replicative
ability) which are then tested through analysis of genotype-phenotype maps and
simulations of population dynamics on such maps. Finally, we analytically show
that the fraction of attainable phenotypes decreases with the length of the
genotype, though its absolute number increases. The fact that most phenotypes
are not visible to evolution very likely forbids the attainment of the highest
peak in the landscape. Nevertheless, our results indicate that the relative
fitness loss due to this limited accessibility is largely inconsequential for
adaptation.
