Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability

Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps—a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure—to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.Author Summary: Evolutionary dynamics arise from the interplay of mutations acting on genotypes and natural selection acting on phenotypes. Understanding the structure of the genotype-phenotype (GP) map is therefore critical for understanding evolutionary processes. We address a simple question about structure: Are the genotypes positively correlated? That is, will the mutational neighbours of a genotype be more likely to map to similar phenotypes than expected from random chance? John Maynard Smith and others have argued that the intuitive answer is yes. Here we quantify these intuitions by comparing model GP maps for RNA secondary structure, protein tertiary structure, and protein quaternary structure to a random GP map. We find strong neutral correlations: Point mutations are orders of magnitude more likely than expected by random chance to link genotypes that map to the same phenotype, which vitally increases the potential for evolutionary innovation by generating neutral networks. If GP maps were uncorrelated like the random map, evolution may not even be possible. We also find correlations for non-neutral mutations: Mutational neighbourhoods are less diverse than expected by random chance. Such local heterogeneity slows down the rate at which new phenotypic variation can be found. But non-neutral correlations also enhance evolvability by lowering the probability of mutating to a deleterious non-folding or non-assembling phenotype.