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Hansen (2006) in his review uses the concept of environmental robustness independently of the other concepts of robustness (at pages 139 and 140) without defining it.

How is the term environmental robustness usually defined?

The concept of robustness (aka genetic robustness) can be further decoupled into mutational robustness, developmental robustness and maybe some others. I think envirnmental robustness is one of these sub-categories of (genetic) robustness.

Intuitively, I understand environmental robustness as something that is very close to plasticity in the broad sense. What I call plasticity in the broad sense is any phenotypic response to an environment whether or not the response is adaptive or not. Therefore, plasticity in the broad sense is adaptive plasticity + non-adaptive plasticity. I would intuitively think that a genotype is environmentally robust if the phenotype it produces varies little with environment, that is if this genotype has low plasticity (in the broad sense). Am I using a more or less standard definition of environmental robustness?

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I think robustness and plasticity are different concepts, although related to each other.

I would define plasticity as the property of a system to adapt to external changes. As defined in the wikipedia page for phenotypic plasticity:

Phenotypic plasticity is the ability of an organism to change its phenotype in response to changes in the environment.

I think this definition agrees with the one in your question.

Robustness in biological systems, however, is defined as (wikipedia article):

Robustness of a biological system (also called biological or genetic robustness) is the persistence of a certain characteristic or trait in a system under perturbations or conditions of uncertainty.

From this article three references are cited, all of which give some definition of robustness in their introductions/abstracts:

Felix and Wagner (Heredity 2008):

Robustness, the persistence of an organismal trait under perturbations, is a ubiquitous property of complex living systems.

Kitano (Nature Reviews Genetics 2004):

Robustness is a property that allows a system to maintain its functions despite external and internal perturbations.

Stelling et al. (Cell 2004):

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is a long-recognized key property of living systems.

All these definitions imply that robustness is the ability to remain unperturbed under external or environmental perturbations. In a sense this looks like the opposite to plasticity, which is the ability to change under external perturbations. Personally, I think that robustness is accomplished because biological plasticity allows organisms to compensate (with some limits) the external perturbation in order to maintain their state.

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  • $\begingroup$ This is sort of how I understand Hansen as well. The problem here is that robust is a rather vague word, similar to the observation by Pimm (1991) that ecologists had been using stability in at least five different ways when discussing population and community stability (he mentions: mathematical stability, resilience, persistence, resistance, variability) $\endgroup$ – fileunderwater Dec 16 '14 at 14:49
  • $\begingroup$ @ddiez Thanks for your answer. The concept of (genetic) robustness is further decoupled into subconcepts that are mutational robustness, developmental robustness and environmental robustness (and maybe some others). My question is about environmental robustness. I don't think Hansen meant genetic robustness when saying environmental robustness, but I think he rather meant some subset of robustness. I might be wrong though. I'll edit my question to clarify my understanding of the subconcepts of robustness. $\endgroup$ – Remi.b Dec 16 '14 at 19:46
  • $\begingroup$ @fileunderwater completely agree robustness is defined in a vague way. I think we all understand the concept, but how to quantify it? For example, it makes sense to imagine some system to be more robust than another to perturbations, but for me there is no clear way to measure it. $\endgroup$ – ddiez Dec 17 '14 at 3:16
  • $\begingroup$ @Remi.b thank you for showing us Hansen's review- looks interesting. I will read it (only skimmed over it a bit) and think a bit more about your comments (and maybe modify my answer accordingly). I think the source of confusion is, as fileunderwater mentioned, that usually the term is just vaguely defined. $\endgroup$ – ddiez Dec 17 '14 at 3:20
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I am just summarizing ddiez's answer with a small addition.

Robustness is the ability of the system to maintain its steady state or at the very least qualitative nature of the steady state with minor changes in the parameters of the system.

This is different from stability which actually means the ability of the system to return to its steady state when it is slightly displaced from there. A stable system will reach the steady state irrespective of the initial condition. In multistable systems the state where the system eventually converges, will depend on the initial condition.

So stability is meant in the sense of perturbation in the state and robustness, of perturbation in the system parameters.

So, if you have a model and you do a random sampling of parameters drawn from a uniform distribution of lets say ±2×mean, you will end up with a many sets of parameters with fluctuations from the mean values. Now, if you solve for the steady state at each parameter value you will get a distribution. Less the variance of this distribution, more robust is the system (based on the model).

We had discussed plasticity in this post. Plasticity may be in a way synonymous with adaptive; if a system takes an input and gives an output then how plastic a system is can be defined as how fast or easily does a system reach the new steady state. In this case the input is a parameter of the model and only that is changed.

If I put these concepts in the perspective of an organism's metabolism then:

  • Robustness would refer to how (in)sensitive the metabolic flux is to the minor changes in rates of different reactions (by changes in the enzyme structures perhaps).
  • Stability would refer to whether the system gets back (or how fast it gets back) to its original state if you add some extra or remove a metabolite.
  • Plasticity would refer to how fast would the system adapt or reach the new steady state when there is a change of diet/available nutrients.

Having said that I also feel, as fileunderwater said, that definitions are not universal and different people mean different things. Mathematically speaking environment is an extrinsic parameter i.e. Input. Environmental robustness should mean the maintenance of the steady state response to changes in the input. This makes sense for example in the case of maintenance of body temperature in homeotherms. Environmental plasticity is also important in certain situations.

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  • $\begingroup$ thanks for your answer. I copy-paste here the comment I made to ddiez "The concept of (genetic) robustness is further decoupled into subconcepts that are mutational robustness, developmental robustness and environmental robustness (and maybe some others). My question is about environmental robustness. I don't think Hansen meant genetic robustness when saying environmental robustness, but I think he rather meant some subset of robustness. I might be wrong though. I'll edit my question to clarify my understanding of the subconcepts of robustness." $\endgroup$ – Remi.b Dec 16 '14 at 19:52
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    $\begingroup$ Also, it is a bit counter-intuitive to me to define plasticity as the speed at which phenotypic changes occur, rather than the magnitude of the change or the range of environment toward which phenotypic response occurs. $\endgroup$ – Remi.b Dec 16 '14 at 19:53
  • $\begingroup$ @Remi.b Not really the speed but response time is one way of quantifying a plastic response. How quickly you adjust is important. The magnitude of the perturbation cannot be controlled by the system and you would want to adjust to the new environment without making a great change in your system composition. So magnitude of change has to be minimized and response time too. I think you can define all subsets of robustness depending on what kinds of parameters you perturb. $\endgroup$ – WYSIWYG Dec 17 '14 at 4:11

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