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The robustness of a genotype is the ability of this genotype to resist (always produce the same phenotype) to various parameters such as mutations and environment. The ability of a genotype to resist to mutations is called mutational robustness while the ability of a genotype to resist to varying environmental variables is called environmental robustness.

Is there a correlation between environmental and mutational robustness?

In other words the above question is: is there a among-species/populations/genotype correlation between mutational robustness and environmental robustness? i.e., Knowing that species $A$ has high mutational robustness, is species $A$ more or less likely than a randomly picked species $B$ to have a high environmental robustness? Or are the concepts of environmental and mutational robustness completely different and involve completely different genes and genetic architecture? Both theoretical and empirical studies that offer insights to this question are welcome.

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Hansen (2006) says (middle of page 140):

A link between genetic and environmental robustness is plausible, because genetic en environmental disturbances may often affect the same functional pathways in the organism, and ny increase in the robustness of a pathway leads to both genetic and environmental canalization. Evidence for a correlation between environmental and genetic robustness has been fund in studies of RNA folding (Ancel & Fontana 2000), in the effects of heat-shock proteins (Stearns et al. 1995).

He also cites Rifkin et al. (2005) who also showed evidence for this correlation. Finally Hansen cites Dworkin (2005) who did not find this link.

Hansen does not cite any theoretical paper and does not offer clear arguments of why this link exist but it is the best I could find

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