  The characterization of plasticity, robustness, and evolvability, an
important issue in biology, is studied in terms of phenotypic fluctuations. By
numerically evolving gene regulatory networks, the proportionality between the
phenotypic variances of epigenetic and genetic origins is confirmed. The former
is given by the variance of the phenotypic fluctuation due to noise in the
developmental process; and the latter, by the variance of the phenotypic
fluctuation due to genetic mutation. The relationship suggests a link between
robustness to noise and to mutation, since robustness can be defined by the
sharpness of the distribution of the phenotype. Next, the proportionality
between the variances is demonstrated to also hold over expressions of
different genes (phenotypic traits) when the system acquires robustness through
the evolution. Then, evolution under environmental variation is numerically
investigated and it is found that both the adaptability to a novel environment
and the robustness are made compatible when a certain degree of phenotypic
fluctuations exists due to noise. The highest adaptability is achieved at a
certain noise level at which the gene expression dynamics are near the critical
state to lose the robustness. Based on our results, we revisit Waddington's
canalization and genetic assimilation with regard to the two types of
phenotypic fluctuations.
