Relationship among Phenotypic Plasticity, Genetic and Epigenetic   Fluctuations, Robustness, and Evolovability; Waddington's Legacy revisited   under the Spirit of Einstein
  Questions on possible relationship between phenotypic plasticity and evolvability, as well as that between robustness and evolution have been addressed over decades in the field of evolution-development. By introducing an evolutionary stability assumption on the distribution of phenotype and genotype, we establish quantitative relationships on plasticity, phenotypic fluctuations, and evolvability. Derived are proportionality among plasticity as a responsiveness of phenotype against environmental change, variances of phenotype fluctuations of genetic and developmental origins, and evolution speed. Confirmation of the relationships is given by numerical experiments of a gene expression dynamics model with an evolving transcription network, whereas verifications by laboratory evolution experiments are also discussed. These results provide quantitative formulation on canalization and genetic assimilation, in terms of fluctuations of gene expression levels. 
Kunihiko Kaneko