Phenotypic cliffs in the RNA genotype-phenotype map

Point mutations of a genotype can leave the phenotype unchanged, or change it, in some cases radically. The extent of this phenotypic change can critically impact fitness. To investigate the range of possible phenotypic changes that result from point mutations, we analyse the structure of the well-established RNA genotype-phenotype (GP) map for sequences of length 12 by developing a general phenotypic distance framework. Our analysis reveals that phenotypes are more likely to be surrounded by similar phenotypes than would be expected by chance. Furthermore, we see that generalised versions of the GP map metrics of frequency, robustness, and evolvability that take phenotypic distance into account still exhibit the same fundamental structural relationships that are observed in many GP maps. We also develop site-specific quantities for robustness, evolvability, and accessible phenotypic distance, which reveal a key insight: RNA secondary structure (SS) sites that are more likely to be neutral and access fewer new phenotypes tend to produce larger changes in phenotype when a change does occur. Robust sites therefore produce cliffs in the landscape (flat in some directions, steep in others) whereas non-robust sites give rise to more gently undulating landscapes.