Data from: The robustness and evolvability of continuously-varying traits

Theoretical work on the evolution of simple phenotypes with discrete states, such as RNA and protein structures, has shown that the most evolvable phenotypes have intermediate levels of mutational robustness, so long as we let neutral mutations cause the diversification of a population's mutationally-accessible phenotypic neighborhood. But whether this applies to more complex phenotypes is unclear. Here, I predict that for quantitative traits, intermediate levels of mutational robustness should boost evolvability whenever (i) the adaptive landscape changes after a period of stabilizing selection, and (ii) the phenotypic neighborhood of a genotype is determined in large part by the accumulation of cryptic alleles, the effects of which can be exposed to selection by epistatic mutations. I present evolutionary simulation models that support these predictions, provided that cryptic allele effects are not too large. Genetic diversity can also be concealed and exposed by incomplete environmental robustness (i.e., plasticity). With additional simulations, I show that evolvability can also be maximized with intermediate levels of environmental robustness, although in a more restrictive parameter space. So, as for discrete traits, quantitative trait robustness can be good for evolvability.