The characterization of plasticity, robustness, and evolvability, animportant issue in biology, is studied in terms of phenotypic fluctuations. Bynumerically evolving gene regulatory networks, the proportionality between thephenotypic variances of epigenetic and genetic origins is confirmed. The formeris given by the variance of the phenotypic fluctuation due to noise in thedevelopmental process; and the latter, by the variance of the phenotypicfluctuation due to genetic mutation. The relationship suggests a link betweenrobustness to noise and to mutation, since robustness can be defined by thesharpness of the distribution of the phenotype. Next, the proportionalitybetween the variances is demonstrated to also hold over expressions ofdifferent genes (phenotypic traits) when the system acquires robustness throughthe evolution. Then, evolution under environmental variation is numericallyinvestigated and it is found that both the adaptability to a novel environmentand the robustness are made compatible when a certain degree of phenotypicfluctuations exists due to noise. The highest adaptability is achieved at acertain noise level at which the gene expression dynamics are near the criticalstate to lose the robustness. Based on our results, we revisit Waddington'scanalization and genetic assimilation with regard to the two types ofphenotypic fluctuations.
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