  The prevalence of neutral mutations implies that biological systems typically
have many more genotypes than phenotypes. But can the way that genotypes are
distributed over phenotypes determine evolutionary outcomes? Answering such
questions is difficult because the number of genotypes can be
hyper-astronomically large. By solving the genotype-phenotype (GP) map for RNA
secondary structure for systems up to length $L=126$ nucleotides (where the set
of all possible RNA strands would weigh more than the mass of the visible
universe) we show that the GP map strongly constrains the evolution of
non-coding RNA (ncRNA). Simple random sampling over genotypes predicts the
distribution of properties such as the mutational robustness or the number of
stems per secondary structure found in naturally occurring ncRNA with
surprising accuracy. Since we ignore natural selection, this strikingly close
correspondence with the mapping suggests that structures allowing for
functionality are easily discovered, despite the enormous size of the genetic
spaces. The mapping is extremely biased: the majority of genotypes map to an
exponentially small portion of the morphospace of all biophysically possible
structures. Such strong constraints provide a non-adaptive explanation for the
convergent evolution of structures such as the hammerhead ribozyme. These
results presents a particularly clear example of bias in the arrival of
variation strongly shaping evolutionary outcomes and may be relevant to Mayr's
distinction between proximate and ultimate causes in evolutionary biology.

Populations and Evolution;Biomolecules