Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in terms of Phenotypic Variances

TL;DR

This study explores how phenotypic variances related to noise and genetic mutation influence robustness and adaptability in gene regulatory networks, revealing proportional relationships and optimal noise levels for evolution under environmental changes.

Contribution

It demonstrates proportionality between phenotypic variances of different origins and shows how phenotypic fluctuations facilitate robustness and adaptability during evolution.

Findings

Proportionality between epigenetic and genetic phenotypic variances confirmed.

Optimal phenotypic noise level enhances adaptability and robustness.

Robustness and adaptability coexist at a critical noise level.

Abstract

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.