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Questions on possible relationship between phenotypic plasticity andevolvability, as well as that between robustness and evolution have beenaddressed over decades in the field of evolution-development. By introducing anevolutionary stability assumption on the distribution of phenotype andgenotype, we establish quantitative relationships on plasticity, phenotypicfluctuations, and evolvability. Derived are proportionality among plasticity asa responsiveness of phenotype against environmental change, variances ofphenotype fluctuations of genetic and developmental origins, and evolutionspeed. Confirmation of the relationships is given by numerical experiments of agene expression dynamics model with an evolving transcription network, whereasverifications by laboratory evolution experiments are also discussed. Theseresults provide quantitative formulation on canalization and geneticassimilation, in terms of fluctuations of gene expression levels.

Relationship among Phenotypic Plasticity, Genetic and Epigenetic  Fluctuations, Robustness, and Evolovability; Waddington's Legacy revisited  under the Spirit of Einstein