  In evolution, the effects of a single deleterious mutation can sometimes be
compensated for by a second mutation which recovers the original phenotype.
Such epistatic interactions have implications for the structure of genome space
- namely, that networks of genomes encoding the same phenotype may not be
connected by single mutational moves. We use the folding of RNA sequences into
secondary structures as a model genotype-phenotype map and explore the neutral
spaces corresponding to networks of genotypes with the same phenotype. In most
of these networks, we find that it is not possible to connect all genotypes to
one another by single point mutations. Instead, a network for a phenotypic
structure with $n$ bonds typically fragments into at least $2^n$ neutral
components, often of similar size. While components of the same network
generate the same phenotype, they show important variations in their
properties, most strikingly in their evolvability and mutational robustness.
This heterogeneity implies contingency in the evolutionary process.
