Organisms often show robustness to genetic or environmental perturbations. Whether these two components of robustness can evolve separately is the focus of the paper by Le Rouzic . Using theoretical analysis and individual-based computer simulations of a gene regulatory network model, he shows that multiple aspects of robustness can be investigated as a set of pleiotropically linked quantitative traits. While genetically correlated, various robustness components (e.g., mutational, developmental, homeostasis) of gene expression in the regulatory network evolved more or less independently from each other under directional selection. The quantitative approach of Le Rouzic could explain both how unselected robustness components can respond to selection on other components and why various robustness-related features seem to have their own evolutionary history. Moreover, he shows that all components were evolvable, but not all to the same extent. Robustness to environmental disturbances and gene expression stability showed the largest responses while increased robustness to genetic disturbances was slower. Interestingly, all components were positively correlated and remained so after selection for increased or decreased robustness.
This study is an important contribution to the discussion of the evolution of robustness in biological systems. While it has long been recognized that organisms possess the ability to buffer genetic and environmental perturbations to maintain homeostasis (e.g., canalization ), the genetic basis and evolutionary routes to robustness and canalization are still not well understood. Models of regulatory gene networks have often been used to address aspects of robustness evolution (e.g., ). Le Rouzic  used a gene regulatory network model derived from Wagner’s model . The model has as end product the expression level of a set of genes influenced by a set of regulatory elements (e.g., transcription factors). The level and stability of expression are a property of the regulatory interactions in the network.
Le Rouzic made an important contribution to the study of such gene regulation models by using a quantitative genetics approach to the evolution of robustness. He crafted a way to assess the mutational variability and selection response of the components of robustness he was interested in. Le Rouzic’s approach opens avenues to investigate further aspects of gene network evolutionary properties, for instance to understand the evolution of phenotypic plasticity.
Le Rouzic also discusses ways to measure his different robustness components in empirical studies. As the model is about gene expression levels at a set of protein-coding genes influenced by a set of regulatory elements, it naturally points to the possibility of using RNA sequencing to measure the variation of gene expression in know gene networks and assess their robustness. Robustness could then be studied as a multidimensional quantitative trait in an experimental setting.
 Le Rouzic, A (2022) Gene network robustness as a multivariate character. arXiv: 2101.01564, ver. 5 peer-reviewed and recommended by Peer Community in Evolutionary Biology. https://arxiv.org/abs/2101.01564
 Waddington CH (1942) Canalization of Development and the Inheritance of Acquired Characters. Nature, 150, 563–565. https://doi.org/10.1038/150563a0
 Draghi J, Whitlock M (2015) Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks. Evolution, 69, 2345–2358. https://doi.org/10.1111/evo.12732
 Wagner A (1994) Evolution of gene networks by gene duplications: a mathematical model and its implications on genome organization. Proceedings of the National Academy of Sciences, 91, 4387–4391. https://doi.org/10.1073/pnas.91.10.4387
DOI or URL of the preprint: https://arxiv.org/abs/2101.01564
Version of the preprint: 3
Dear Dr Le Rouzic,
Thank you for submitting a revision of your work on "Gene network robustness as a multivariate character". The two previous reviewers and a newer one were satisfied with the most recent version of your work and with your answers their comments. All of them ask for some corrections in the text and more clarifications, especially of the new figures. I recommend that you address their comments, and mine below before we can continue with the recommendation. A new revision will most likely not go to reviewers again.
I welcome the addition of the details about the genetic correlation of the robustness traits. It shows more precisely how different aspects of robustness may evolve more or less independently from each others. It thus greatly improves the quality of the paper. However, it can be argued that the way the evolutionary constraints have been assessed is far from the way networks may evolve in natural systems in the sense that we hardly expect robustness traits to be under direct selection. Indeed, as stressed at different places in the manuscript, robustness is an emergent property of the topology of the networks, which determine the expression phenotypes under selection. Therefore, as also asked by the third reviewer, I would like to see a more thorough justification for the purpose of this approach (imposed direct selection on robustness traits) to guide the reader and avoid misinterpretations about the nature of selection on robustness you expect to see in nature. My interpretation is that you use direct selection as a device to understand the evolutionary properties of the robustness traits. This should be made clearer in the text. What should also be clarified is whether and when you'd expect direct selection on robustness traits to act in natural populations.
A discussion on that very same topic is thus also awaited, especially in the light of the difference of your model with existing models. It is not yet clear from your manuscript how the genetic constraints among robustness traits bear on the evolution of the genetic networks themselves when populations are challenged by the environment but in absence of such artificial direct selection on the robustness traits. I think this is a legitimate question since it is generally expected that robustness is a trait under second-order selection. Thus, I would like to see a general discussion on that topic to help us better understand the significance of your findings in a broader evolutionary context. Such a discussion is missing at the moment but would greatly improve the impact of your paper.
(line numbers refer to the latex-diff version)
l58 : hypotheses -> hypothesis
ll122-123, 136-137 : please verify if assumptions about constitutive expression are the same as in Ciliberti et al. 2007. Seems to me that their S(0) is similar to your P_0. Also amend accordingly comments about constitutive expression in your vs other models elsewhere in the text.
ll385-387 : is it 1000 generations or 5000 as in the legend of Figure 4?
Caption: illstrated -> illustrated;
A legend for the meaning of the gray arrows in the top-right figure representing join selection on the two traits should be given to better link with the text (ie. "bivariate selection" is used in the text) (see Mullon's comment).
The hyphenated line in the predicted-observed evolvability graph gives the wrong impression that the two evolvabilities match, while they don't. A 1-1 line would rightly show that the observed evolvability is larger than its predicted value. This should be stressed in the text as well.
The direction of change as function of direction of selection is very hard to find, maybe split the graphs to make the patterns more discernible?
ll457-459 : avoid repetition of "cumulative"; specify that the cumulative effect is on the phenotype (=gene expression level); maybe specify that evolution is "gradual"?
l468 : dfferent -> different
ll507-508 : not sure which mathematical model is referred to here
l511 : catch -> capture
DOI or URL of the preprint: https://arxiv.org/abs/2101.01564
Version of the preprint: 2
Thank you for submitting your work for a recommendation at PCI Evol Biol. The research you present highlights very important points regarding the evolvability of robustness, a long standing and fundamental question in evolutionary biology. The responses of two reviewers are attached to my evaluation. You will see that both are positive about your manuscript but ask for a few clarifications and possible expansions, which I summarize below. In light of those comments, and my own as well, I recommend to have a round of revision before recommendation. I would thus encourage you to resubmit a revised version of your manuscript.