  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.
