Relationship among phenotypic plasticity, phenotypic fluctuations, robustness, and evolvability; Waddington's legacy revisited under the spirit of Einstein.

Questions on possible relationship between phenotypic plasticity and evolvability, and that between robustness and evolution have been addressed over decades in the field of evolution-development. Based on laboratory evolution experiments and numerical simulations of gene expression dynamics model with an evolving transcription network, we propose quantitative relationships on plasticity, phenotypic fluctuations, and evolvability. By introducing an evolutionary stability assumption on the distribution of phenotype and genotype, the proportionality among phenotypic plasticity against environmental change, variances of phenotype fluctuations of genetic and developmental origins, and evolution speed is obtained. The correlation between developmental robustness to noise and evolutionary robustness to mutation is analysed by simulations of the gene network model. These results provide quantitative formulation on canalization and genetic assimilation, in terms of fluctuations of gene expression levels.