Why and how genetic canalization evolves in gene regulatory networks

Abstract

BackgroundGenetic canalization reflects the capacity of an organism’s phenotype to remain unchanged in spite of mutations. As selection on genetic canalization is weak and indirect, whether or not genetic canalization can reasonably evolve in complex genetic architectures is still an open question. In this paper, we use a quantitative model of gene regulatory network to describe the conditions in which substantial canalization is expected to emerge in a stable environment.ResultsThrough an individual-based simulation framework, we confirmed that most parameters associated with the network topology (complexity and size of the network) have less influence than mutational parameters (rate and size of mutations) on the evolution of genetic canalization. We also established that selecting for extreme phenotypic optima (nil or full gene expression) leads to much higher canalization levels than selecting for intermediate expression levels. Overall, constrained networks evolve less canalization than networks in which some genes could evolve freely (i.e. without direct stabilizing selection pressure on gene expression).ConclusionsTaken together, these results lead us to propose a two-fold mechanism involved in the evolution of genetic canalization in gene regulatory networks: the shrinkage of mutational target (useless genes are virtually removed from the network) and redundancy in gene regulation (so that some regulatory factors can be lost without affecting gene expression).Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-016-0801-2) contains supplementary material, which is available to authorized users.

Modelling the influence of parental effects on gene‐network evolution

“…One of the mechanisms by which mutational robustness evolves is through the reduction in the network size (the reduction in the number of expressed genes in the network, Rünneburger & Le Rouzic, ). To understand the impact of NGI on genetic canalization, we investigated its effect on gene‐expression level distribution (Fig.…”

“…Steiner, ). In parallel, despite its side effects on canalization (Elena et al ., ; Elena & Sanjuán, ; Rünneburger & Le Rouzic, ), the population size was reduced to N = 1000 for long‐term simulations used for the study of canalization (50 000 generations), but was kept larger when the focus was on adaptation (5000 individuals and 10 000 generations). The size of gene networks was limited to L = 6 genes for the same reason.…”

“…The simulation framework was derived from Rünneburger & Le Rouzic (). The software was written in C++, the simulation pipeline in Bash and the statistical analysis in R [v3.2.3 (R Core Team, )].…”

Theoretical Study of the 1 Self-Regulating Gene in the Modified Wagner Model

“…We first provide some rationales about the sigmoid function usually considered in the variant of the Wagner gene-network model studied here [14]. They will be used in the next section, when studying the one self-regulating gene system.…”

“…Recent implementations of the model consider continuous gene expressions, and the step function was turned into a sigmoid, scaling gene expressions between -1 and 1 ( f (x) = 2/(1 + e −x ) − 1, [12], see [13] for a mathematical analysis). For more realism, the sigmoid function can also be further modified to ensure that genes are only weakly expressed in absence of regulators, by considering that f (0) = a < 1/2, as in [14], and which is the model studied below.…”