Pervasive robustness in biological systems.

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Pervasive robustness in biological systems Marie-Anne Félix1 and Michalis Barkoulas2

Abstract | Robustness is characterized by the invariant expression of a phenotype in the face of a genetic and/or environmental perturbation. Although phenotypic variance is a central measure in the mapping of the genotype and environment to the phenotype in quantitative evolutionary genetics, robustness is also a key feature in systems biology, resulting from nonlinearities in quantitative relationships between upstream and downstream components. In this Review, we provide a synthesis of these two lines of investigation, converging on understanding how variation propagates across biological systems. We critically assess the recent proliferation of studies identifying robustness-conferring genes in the context of the nonlinearity in biological systems. Robustness Invariance or low variation of a given phenotype when faced with a given incoming variation. Used synonymously with insensitivity.

Sensitivity Variation of a given phenotype when faced with a given incoming variation.

Variance A measure of variation in a distribution, defined as the sum of squared deviations of individual points to the mean.

Institute of Biology of the Ecole Normale Supérieure, CNRS UMR8197, INSERM U124, ENS, 46 rue d’Ulm, 75005 Paris, France. 2 Imperial College London, Department of Life Sciences, Sir Alexander Fleming Building, South Kensington Campus, London SW7 2AZ, UK. Correspondence to M-A.F. e‑mail: [email protected] doi:10.1038/nrg3949 1

The robustness of a phenotypic trait is characterized by its absence, or low level, of variation in the face of a specific environmental or genetic perturbation. The opposite of robustness is sensitivity, which corresponds to large variation of the phenotypic trait in the face of the perturbation. A continuum of possible responses exists between complete robustness and high sensitivity, and robustness is best used in a relative manner, compared to a more sensitive case1. Historically, there have been two major, and frequently distinct, approaches that have dealt with the degree of robustness and sensitivity of biological traits. The first concerns the field of evolutionary quantitative genetics, in which variance in a phenotype is quantified and partitioned into distinct causative sources of variation (FIG. 1): microenvironmental variance (also called stochastic variance); macroenvironmental variance (for example, temperature or food); and genetic variance2–8. Lack of phenotypic variance is often called canalization and is primarily studied for its effects in masking genetic variation6,9–15. Waddington2,9 used the term canalization to designate either a developmental process restricting available cell fate choices over developmental time, or an evolutionary process reducing phenotypic variance under selection. Canalization is also often used as a synonym of robustness, to describe a lack of variance. The second line of enquiry regarding robustness stems from studies in physics and progressed through the field of systems biology 16–19. Here, robustness is defined as the insensitivity to variation in one system parameter, analysed using computational and experimental systems16,17,20. In these studies, genetic variation and evolution of the system are not typically considered.

A related line of enquiry derived from engineering considers robustness to all possible variation in the lifetime of a system by summing over the probabilities of different perturbations19,21–23. Previous authors have reviewed robustness mechanisms at different levels of integration12,16–19,21–23. In this Review, we present both lines of enquiry into robustness, evolutionary genetics and systems biology, and their interactions. Following early seminal work by Waddington9, Kacser 24 and Rendel25, these two views are starting to merge on a theoretical level26–29. On the experimental side, the rise of quantitative approaches in cellular and developmental biology and identification of the genetic bases of variational features are providing the opportunity to unify the field based on a more precise characterization of robustness within real biological systems. We first define robustness and argue against a generic use of the term without precise specification of the feature that is robust and of a specific perturbation. We present experimental designs to measure robustness and to study its evolutionary variation through genetic analysis. Based on recent studies that use controlled perturbations to precisely quantify robustness, it appears that downstream phenotypes are often robust to a wide range of variation in major upstream developmental regulators, matching the expectations of both Waddington9 and Rendel25. Such nonlinearities in dose–response curves are pervasive in biological systems, which makes some robust features easy to explain. In this context, we critically assess the recent proliferation in the literature of reports of robustnessconferring genes, many of which simply affect the

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REVIEWS phenotype mean level in a condition-dependent manner. Finally, we caution against an uncritical adaptationist view of robustness, as robust features are not necessarily the consequence of an evolutionary advantage.

Stochastic variance Variation of the phenotype when faced with uncontrollable noise; also called microenvironmental variance.

Defining a robust feature Robustness has become a commonly used term in biological studies, often generically used without defining the phenotype of interest, the perturbation or the degree of robustness. As has been argued before12,24, when using the term robustness, it is important to specify which trait is robust, to which perturbation, and to provide a quantification. Once properly defined in this way, one can

Genetic variance Variation of the phenotype when faced with a given set of genetic variation.

Canalization A process by which the phenotypic variance of a trait is reduced when faced with a given perturbation.

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What is robust? Many phenotypes can be monitored for a given system at different organizational levels and developmental time points — for example, the level of a signalling pathway in a given cell or the final fate of this cell. Each of these phenotypes may be assayed for its robustness to a perturbation. For example, a specific environmental change may induce a threefold activation of a signalling pathway, but no variation in a downstream output such as cell fate. Generally, the phenotype upon

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refer to this as a robust feature. However, this precise specification has often been neglected in studies reporting robust features, including the examples given below.

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Figure 1 | Robustness of a phenotype to an incoming variation. a | Schematic showing the relationship between levels of variation in individual development (genotype and environmental parameters, noise, endophenotypes or intermediate developmental phenotypes, and focal phenotypes), in a population and in evolution. Sources of variation are marked with an asterisk. Here, variation is represented in an environmental parameter (E1 versus E2), as shown with black versus green dots, for a given genotype G. The spread of dots of one colour in the endophenotype space represents sensitivity to noise within an environment. In the example, the output phenotype is robust to the incoming environmental variation. A phenotypic distribution (dotted orange curve) could be limited by stabilizing selection in a genetically diverse population (solid blue curve), influencing next-generation genotypes. b | Variational feature. The incoming variation and the focal phenotype may be chosen at any level within the brackets. c–e | Low or high robustness to different types of variation. Variables x, y and z may be environmental, genetic, or correspond to a model parameter. Individual phenotypes are represented as dots. Robustness to a controlled variation between x1 and x2 (part c) is shown with high-robustness (y1) and low-robustness (y2) cases represented in blue and orange, respectively. y2 shows in condition x2 a different mean (left) or variance (middle). Concerning the latter case, the right graph highlights a non-isogenic population, varying at a relevant z locus. In all three cases, the effect corresponds to a non-additive interaction between two variables. Robustness to a natural distribution of incoming variation is shown in parts d (noise) and e (random genetic variation). In part e, each dot is the mean phenotype of a mutation accumulation line, and controls are lines without the mutation treatment. Nature Reviews | Genetics

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REVIEWS which one focuses is the most downstream output, but in many studies the choice of the focal phenotype remains unclear and often inconsistent, with multiple phenotypes being considered across the same study. For example, it is often stated that plasticity underlies robustness or that robustness is compatible with plasticity. When the perturbation is environmental, phenotypic plasticity is the opposite of robustness; thus such statements are false when considering the same phenotype under the same perturbation. What is usually meant is that an intermediate phenotype (also termed an endophenotype; FIG. 1a) is sensitive to the environmental variation, whereas the output phenotype is robust to it: robustness and plasticity are here applied to different phenotypes. Alternatively, in the case of plasticity, a given environmental perturbation can give rise to a consistent phenotypic change. The phenotype is then robust to stochastic noise within a given environment, leading to a consistent phenotypic response across environments. Here, ‘robustness’ and ‘plasticity’ correspond to different sources of perturbation, within environments versus between environments, respectively.

Variational features A specific instance of the propagation of variation from an incoming variation to a given phenotype. The incoming variation may be stochastic, environmental or genetic.

Robust features A particular case of variational feature where the phenotype is robust to the incoming variation.

Plasticity Variation of a phenotype when faced with a given environmental variation.

Intermediate phenotype Also known as endophenotype. An intermediate developmental trait in the construction of the phenotype of interest.

Standing genetic variation Allelic variation that is currently segregating in a given population, in contrast to alleles that arise by new mutation events.

Incoming variation The perturbation that is considered for a given variational feature.

Cryptic genetic variation Genetic variation that is silent for the trait of interest but is not silent for some variables in the underlying system.

Perturbation or incoming variation. In studies characterizing a robust feature, the perturbation of interest needs to be clearly defined. The perturbation may be either a discrete change, or an experimentally controlled and continuous variation from A to B, or a natural distribution, such as noise or standing genetic variation within a population. The term ‘perturbation’ as used in physics and engineering implies the existence of a norm and refers to a deviation from this norm that might not be realistic in natural systems, in which, for example, noise cannot be added or removed at will. The term ‘perturbation’ is therefore not a generally applicable term, and especially does not address the types of variation studied in quantitative genetics. We therefore coin the term incoming variation to refer to the source of variation considered in a robust feature, or more generally in any variational feature. Note that the incoming variation may not affect the input of the system as defined in systems biology terms (FIG. 1b). For example, in a biochemical system with defined upstream inputs and downstream outputs, such as nutrient concentration and a downstream enzymatic activity, the incoming variation may correspond to variation in the concentration of an internal system component, such as another enzyme30,31. In quantitative genetics, the classification of incoming variation has often been limited to genetic versus environmental sources, without further characterization within each of these categories, which limits mechanistic insights. In addition, many studies have attempted to globally compare robustness to genetic versus environmental variation, whereas experimentally one can only compare specific cases of each, such as a given set of mutations and environments. Another ambiguous example concerns cryptic genetic variation and its meaning relative to robustness. By definition, genetic variation that is cryptic implies that the focal phenotype is fully robust to this cryptic genetic variation. Yet it does not imply its robustness to other incoming variations15.

Robustness as a quantitative trait. Robustness of a phenotype to a perturbation is itself a quantitative trait. BOX 1 describes methods that can be used to quantify the extent of robustness, or sensitivity, of a phenotype to a given perturbation. Robustness is most often used as a relative measure — for example, for comparison of the same phenotype across different incoming environmental variations. The phenotype standard deviation can be scaled to the mean value to obtain dimensionless values that are in some cases comparable across different phenotypes (BOX 1). Under a given perturbation, variation in the flux of an upstream metabolic step can, for example, be compared to that in a downstream step32. The propagation of variation across cascades and hierarchical levels of organization can be amplified or reduced, and this constitutes the variational properties of a biological system. Another type of robustness measure, derived from engineering, uses the probability density of perturbations relative to a norm, summing the effects over the (rare) occurrence of each of the perturbations33. This measure is operationally useful for optimization and risk assessment 21,34. Applications to biological systems require an understanding of the ecological context and the corresponding probabilistic pattern of environmental change. Although integration over multiple types of variation is highly relevant for evolutionary questions, we focus our discussion below on the dissection of one specific incoming variation and its propagation across the system. The evolution of a robust feature. In contrast to engineered systems, biological systems have unique evolutionary histories, and their properties have evolved following the dynamics of evolutionary change. A robust feature, similar to a plastic one, must not be considered a priori to have arisen as a result of selection operating on robustness. In addition, at least for multicellular organisms with moderate population sizes, a robust feature is unlikely to have evolved in response to selection based on its robustness to mutation (BOX 2). To study the evolution of any variational feature, whether on the robust or sensitive side of the spectrum, one needs to consider three types of variation: the incoming variation, the focal phenotype distribution (these two define the variational feature; FIG. 1b) and the genetic variation affecting their relationship. Genetic approaches can thus be used both to uncover evolutionarily relevant natural genetic variation and to explore robustness mechanisms. Below, we present designs to study robustness, successively for different types of incoming variation, using induced mutants or natural genetic variation.

Experimental designs Noise. Microenvironmental or stochastic variation is, in practice, noise that cannot be controlled in experiments. It may originate from inhomogeneity in growth conditions, or from noise at the molecular level — for example, the uneven distribution of rare molecules in daughter cells or the stochastic nature of molecular interactions35.



REVIEWS Fluctuating asymmetry Measure of variation between the right and left sides of the body, taken as a measure of sensitivity to developmental noise.

Norm of reaction (Also known as reaction norm). Function or plot linking the phenotype (y‑axis) to the environmental variable (x‑axis), for a given genotype.

Coefficient of variation Dimensionless measure of variation in a distribution corresponding to the square root of the variance (standard deviation) over the mean.

Robustness to noise is assessed by constraining both the environment and the background genotype to be as constant as experimentally possible. Phenotypic variation is measured either among individuals of the same genotype, or within a single individual (FIG. 1c). Within an individual, repeated measurements are possible for physiological or behavioural traits or for repeated developmental structures, such as the left and right sides of the body (fluctuating asymmetry)36 or different cells of a multicellular organism37. The use of isogenic populations is critical when the goal is to isolate sources of incoming variation affecting a phenotypic distribution: in a non-isogenic population, the variance could result from a hidden interaction with genetic variation (FIG. 1c, right panel)38. Studying isogenic populations is feasible in clonal or selfing organisms such as bacteria, yeasts, or Caenorhabditis elegans, but problematic in organisms (such as flies, mice or humans) that are subject to inbreeding depression, which itself may increase susceptibility to noise.

The existence of standing genetic variation that affects robustness to noise was first demonstrated by Mather in a study using experimental evolution of Drosophila melanogaster, in which he showed that selection could increase the left-right asymmetry in sternopleural bristle number 39. Both natural variation40–43 and induced mutations44–47 have the potential to affect robustness to noise among isogenic individuals. Environmental variation. A given phenotype is not considered to be robust to the specified environmental variation if its distribution varies among tested environments. Such sensitivity to an environmental variation is also called phenotypic plasticity 3. This response can be represented as a norm of reaction, which is the function linking the mean phenotype in the y‑axis to the environmental variable in the x‑axis. Assessing robustness to an environmental variation involves measuring the phenotype in different environments. The phenotype mean or/and variance may

Box 1 | Measuring robustness and variation Robustness is defined as either the lack or low level of phenotypic variation in response to a perturbation. When there is a low level of phenotypic variation, robustness can be expressed as the inverse of a measure of this phenotypic variation. Standard deviation (s.d.) and variance are commonly used measures of variation in quantitative traits. The s.d. is expressed in the unit of the data, whereas the variance is expressed as the squared value of that unit. The advantage of variance is that it can be additively partitioned into components — for example, among genetically distinct groups and environmental treatments. Variance is most useful within a sample and for comparing samples with normal distribution and equal means. As many traits do not have normal distributions, the data may first need to be transformed so as to be normally distributed — for example, using the Box–Cox method122. Owing to this limitation, methods that do not rely on normality of data are useful, such as the Levene’s statistic (L) under its median form, which compares levels of variation. In the Levene’s test, the means of the variable |xindividual − xmedian| (or a log-transformed version) are tested for equality using an F-test6,123. For a given quantitative trait that is experimentally measured across a variety of conditions, the mean as well as the variance, and more generally the distribution, may vary among datasets, thus requiring appropriate measures of the relationship between mean and variance. One way to analyse quantitative trait variation data is to first regress variance over the mean in the dataset and use the residual deviations from this relationship124,125. The figure illustrates nonlinear relationships between mean and variance. Several schematized examples of distinctive nonlinear relationships between mean and variance for specific phenotypes, derived from specific sets of perturbations, are shown: a comprehensive yeast knockout library44 (graphs 1–3) or the quantitative perturbation of a single gene activity in the Caenorhabditis elegans vulva78 (graph 4). Data points (grey circles) represent different knockout strains (phenotypes 1–3), or transgenic lines and mutants modifying vulval induction compared to the wild type where the mean is 3 and variance 0 (phenotype 4). Red lines are best curve fits to data points. To further compare the robustness of different traits, measured with different phenotypic scales, to the same perturbation, one needs dimensionless metrics. A standard dimensionless measure is the coefficient of variation (c.v.): the s.d. over the mean, expressed as a fraction or a percentage. The c.v. only applies well to normal distributions with non-negative values. It may inflate the detection of variance-controlling quantitative trait loci if the shape of the distribution and the relationship of variance as a function of the mean is not accounted for124,125. However, it is possible to compare differences in c.v. without normality assumptions, using non-parametric resampling56. Yet comparing c.v. on different traits remains problematic when they cannot be assumed to be proportional — for example, the case of a length versus a volume126. Another dimensionless measure is the index of dispersion, or Fano factor, corresponding to the variance over the mean. The index of dispersion is commonly used to measure noise in gene expression studies, as a tool to reveal deviations from the Poisson statistic, where the index of dispersion equals 1.

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REVIEWS Box 2 | The evolutionary context of robustness The term robustness does not imply that this robust feature has an evolutionary advantage. The same holds true for plasticity. Alternative scenarios for the evolutionary origin of a robust feature are that it arose neutrally, or via pleiotropy with another character. First, some robust features probably occurred ‘for free’, as byproducts of system architecture12. Although it may be tempting to assume adaptation, especially for complicated network features, these may also arise readily under neutral evolution127. Second, evolution of robust features through pleiotropy occurs because the same genes act in different tissues and processes. This may be especially true when robustness for one incoming variation arises as a pleiotropic effect of selection for robustness for another incoming variation. For example, a system may be robust to a new environment that it has never encountered, if the environmental effect in the quantitative space of the system is similar to that of a previously experienced environment. The ecological history and the congruence between incoming variations are therefore central in assessing the evolutionary origin of robust features128. It is generally difficult to test whether a feature may have evolved under selection, and this can only be tested by indirect inference based on patterns of molecular evolution and genetic architecture129. A test of whether an observed robust feature is maintained under selection in a laboratory environment makes use of mutation accumulation lines in which population size is very small to minimize the effects of selection. If the level of robustness decreases after mutation accumulation and not at higher population size, such as in natural populations, this suggests that selection maintains this robust feature, directly or indirectly through pleiotropic action. The efficacy of selection increases with the proportion of organisms that are concerned by the perturbation and the strength of the deleterious effect. Therefore, stabilizing selection to noise and common environmental fluctuations during individual development is in general stronger than that to infrequent environmental variants or random mutation4,27,128,130,131. Increased robustness to mutation is unlikely to evolve because selection for it is very weak except in regimes where the mutation rate is high, such as that of viruses132–134, or in bounding a high mutational variance for a trait135. In particular, robustness against mutation is not necessary for a phenotype to be maintained in a population. By contrast, robustness to genetic variation occurring through recombination may be more prevalent, especially in cases when outcrossing is frequent128,130. In developmental system models, stabilizing selection in the presence of recombination leads to the survival of compatible alleles and the evolution of mutational robustness and negative epistasis136,137. Thus, population structure, natural environments and the structure of congruence in the genotype/environment to phenotype map need to be integrated to account for the evolution of variational properties of a system.

Pleiotropy Alteration of more than one phenotype by the same genetic variant.

Stabilizing selection Selection that tends to eliminate extreme phenotypic variants. This results in reduced phenotypic variance and robustness of the trait under selection.

Mutational variance A particular case of genetic variance, where the relevant genetic variation is a random mutation.

Epistasis Non-additive effect of two genetic variations on the phenotype.

change upon environmental variation (FIG. 1c), and it is important to distinguish these two cases by reporting both phenotypic mean and variance when studying robustness to an environmental variation. The change in mean corresponds to the plasticity of the phenotype between the tested environments, whereas the change in variance reflects higher sensitivity to noise in one of the macroenvironments. As detailed below, changes in mean and in variance may occur concomitantly when changing a single system variable. Similar to the analysis of robustness to noise, experiments to assess robustness to environmental variation are best performed with isogenic populations to separate the effect of the environmental variation from its interaction with residual genetic variation (FIG. 1c, right panel). Screens for temperature-sensitive mutations are an example of screens for genetic variation in trait mean between two environments. Here, a phenotypic effect is observed at the restrictive but not the permissive temperature, a form of genotype-by‑environment (GxE)

interaction in which the environmental effect is silent in one genetic background. As best demonstrated using the yeast knockout library in different culture environments48, many laboratory mutants are conditiondependent. Many instances of natural genetic variation for which the phenotypic effect depends on the environment have now been identified49. Of those, many loci affect sensing or transport of the environmental input, whereas some affect downstream signal transduction or destruction of an active substance resulting from the environmental input. Genetic variation. Incoming genetic variation for a robust feature may be a random mutation, a given set of mutations, transgenic manipulations50,51 or a standing genetic variation in a population. The effect of a random mutation can be measured in the laboratory using spontaneous mutation accumulation lines or by induced mutagenesis (FIG. 1e). One can measure the mutational variance of comparable traits52, such as the developmental fate of different cells53, reflecting their potential for phenotypic evolution. Searching for genetic variation in the effect of an incoming genetic variation corresponds to screening for a form of genetic epistasis. For example, the genetic perturbation may have an effect in one genetic background (synergistic epistasis) and none in the other (masking epistasis). One relevant experimental design is to compare the effect of the same induced mutation in different wild-type genetic backgrounds51,54,55. Another approach compares the mutational variance of a trait in mutation accumulation lines derived from different ancestor genetic backgrounds56 or a wild-type versus a mutant background57. Computational perturbations. In models of biological systems, the incoming variation for a robust feature may be simulated noise, quantitative variation in system parameters, or variation in network topology. Pioneering work on robustness often proceeded by systematically altering all parameter values in order to assess the system parameter space in which the target phenotype was obtained17,58. The components of such models are often genes or simplified pathways whose full inactivation has a phenotypic effect. However, because the model equations are highly nonlinear, the phenotypic output from the system may be robust to wide variations in parameters19,22 and/or to structural changes59. A twofold change in gene dosage using heterozygotes20,60 is a particularly meaningful perturbation that can be experimentally tested. The relationship between the parameter variation specified within a model and genetic and environmental variation within real biological systems is often not simple. One model parameter may map to several genetic loci — for example, if some regulators are not included in the model26,28. Conversely, variation in a regulatory gene or an environmental parameter may change a suite of model parameters. The similarity between the responses to different sources of variation is called congruence.



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System parameter space Multidimensional space of quantitative parameters characterizing a system.

Congruence Similarity between the responses to different sources of variation — for example, environmental and genetic.

Nonlinearity Relationship between two variables (input and output) that is not proportional.

Coherent feedforward motifs Networks in which the downstream effects of a gene reinforce each other.

Incoherent feedforward motifs Networks in which the downstream effects of a gene antagonize each other.

Paradoxical regulation A two-component network in which the downstream effects of a gene antagonize each other.

Probit Distance to the mean in standard deviations of a frequency distribution, computed as the inverse of the standard normal cumulative distribution function.

Comparing the effects of different perturbations. Specific environmental and genetic variations may be congruent. For example, variation in the nutritional input (an environmental source) may act through a signalling pathway, which is encoded by multiple genes, which are in turn subject to genetic variation. Such congruence between different perturbations is intricate, and the detailed matrix of congruence is specific for each system. Congruence is important because robustness to one perturbation may evolve ‘for free’ after selection for robustness of the same phenotype to another perturbation (BOX 2). Many experimental studies have attempted to assess the congruence between environmental and genetic variation, and reached mixed conclusions. This is not surprising because these experimental tests inevitably have made use of specific sets of environmental and genetic variation, and so they have only examined a small subset of possible congruent relationships50,51,61. Therefore, although congruence has not been detected in many of these studies, this negative result only reflects the specific tested perturbation and conditions. A more extensive test of congruence between random noise and random mutation was conducted in one study on one yeast mutant, which also did not detect congruence57. By contrast, a meta-analysis of global datasets using the yeast knockout library found significant — although not full — congruence between genetic, environmental and stochastic sources of variation on growth ability 62. Overall, the detailed matrix of congruence is likely to be specific for each system and set of perturbations. Computational modelling studies can be more systematic and have been more apt for detecting congruence between environmental and genetic variation, using various systems such as chemical reactions24, RNA folding 63, or transcriptional developmental networks27,29,64,65.

Propagation of variation When taking a ‘norm of reaction’ view of variation, the focal phenotype is plotted as a function of the incoming variable. Although this relationship can be completely flat (in the case of complete robustness), if it varies, it often does so in a nonlinear manner. For example, the phenotype may be invariable from 10–20 °C but change above 20 °C. Or if a pheromone is added, the response phenotype may plateau beyond a certain pheromone concentration. These examples of nonlinear dose– response curves are ubiquitous in biology, and can result, for example, from enzyme saturation, feedback loops or mechanical and geometric constraints in developmental systems. Nonlinearity in single gene to phenotype mapping. Relevant to the evolutionary process is the sensitivity of the phenotype to genotypic changes. A small genetic step may either result in a phenotypic change or not. Wild-type alleles have been observed to be generally dominant to reduced-function or null alleles66. Dominance is a simple example of the robustness of the focal phenotype to halving the genetic dose of a critical component while being sensitive to its full loss

of function. Dominance thus represents nonlinearity in genotype-phenotype mapping. From a mechanistic viewpoint, Wright 66 and Haldane67,68 argued that a twofold decrease in gene dosage may often remain phenotypically silent because the wild-type level of gene activity is well above the required threshold. They proposed that simple chemical reactions could entail such insensitivity to enzyme gene dosage and that this high activity could have evolved under selection, as a safety factor 67,68. Later, Kacser and Burns69 showed that, at least under some conditions70, overall flux through a series of chemical reactions was insensitive to twofold variation in most enzyme concentrations. In developmental genetics, dominance of the wildtype allele over laboratory-induced mutations is also common. For example, a developmental signalling pathway frequently must be activated over a threshold in a receiving cell for this cell to adopt the induced fate. Signal amplification, such as in kinase cascades, may yield a steep sigmoidal response, measured by a high Hill coefficient, with a robust behaviour over a large concentration range of the upstream ligand, below and above the threshold71. Specific network motifs such as positive and negative feedback loops, coherent feedforward motifs and incoherent feedforward motifs, cross-inhibition and paradoxical regulation may buffer variation in regulatory input by enhancing nonlinearities in quantitative relationships between variables, thereby ensuring threshold-like behaviours30,31,72–75. Such regulatory features frequently contain a limited number of network configurations, which makes them easy to evolve76. Saturation curves in which a given phenotypic output is reached at any concentration above a threshold are commonplace, and entail robustness to dose variation in the plateau region (FIG. 2a, left panel). The mechanistic basis of robust features may therefore often be a trivial outcome of the underlying biochemistry (FIG. 3a). Also common are cases in which the robust range in the dose–response curve is bounded by two thresholds, leaving an intermediate plateau along which the dose can be altered without causing any phenotypic change (FIG. 2a, right panel). Before studies were able to directly measure gene activity, Rendel invented an intermediate variable between genotype and phenotype, called ‘Make’25, corresponding hypothetically to the activity of one major controlling gene (FIG. 2b). In the absence of direct measurements of gene activity, Rendel estimated this hypothetical variable Make using the probit (in units of standard deviation) of the frequency distribution of the phenotype, from a set of different allelic combinations at a major gene locus with variable expressivity 25. From this, he was able to deduce an intermediate plateau in Make values to which the phenotype was robust. Developments in molecular biology now allow for direct routine experimental measurement of gene activity and dose–response dependency (FIGS 2b,c). One example comes from the analysis of vulva development in the nematode C. elegans. Of the six ventral cells that are potentially competent for vulval development, a subset of three cells acquire their vulval fates through induction by



REVIEWS EGF (epidermal growth factor)–RAS–MAPK (mitogenactivated protein kinase) and Notch signalling. A critical parameter is the amount of the upstream signal LIN‑3/ EGF sent by the gonadal anchor cell77. A recent experimental study 78 perturbed and directly measured the number of lin‑3/egf mRNA molecules within the anchor a One threshold

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cell and explored the consequence of this on vulval fates. The resulting curve of the vulval induction index as a function of lin‑3/egf transcript abundance strikingly resembles Rendel’s curves (FIG. 2b), with two thresholds bounding an intermediate plateau. The mechanistic reasons for this shape are easy to understand and lie in the

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Figure 2 | Nonlinear relationships between gene activity and phenotype. a | Two common examples of nonlinear relationships between gene activity and phenotype. Red arrows denote the zone of high robustness of the phenotype to variation in the corresponding gene activity, and ‘T’ denotes thresholds (grey dashed lines) beyond which the phenotype varies. Adapted from REF. 154, Elsevier. b | Experimental examples of developmental phenotypes with two thresholds. The upper two, number of scutellar bristles and vibrissae, are classical examples, with the x‑axis plotting a hypothetical variable called ‘Make’, which is estimated as the probit of the distribution in phenotypes for several genotypes at the same locus (scute for Drosophila melanogaster bristles155; Tabby for mouse vibrissae)156. Schematic adaptation with permission from REF. 25, Logos Press. The bottom graph similarly plots schematically the mean number of

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Caenorhabditis elegans vulval precursor cells Nature adopting vulval|fates as a Reviews Genetics function of the number of lin‑3/egf mRNA molecules (adapted from REF. 78, Cell Press). Yellow cells represent cells that do not adopt a vulval fate, although they are competent to do so. c | Computational examples of parameter variation, to which the target phenotype is robust over the whole range, or with one or two thresholds, drawn from three typical parameter ranges in a model of the Drosophila segment polarity network. The y‑axis is the goodness-of‑fit score, with lower scores representing better matches of model behaviour to the target phenotype upon parameter perturbation. The thin black dashed line indicates the boundary below which the match is accepted, as in REF. 17. The robustness range is therefore the range in the parameter value with a goodness-of‑fit score below the boundary. Adapted from REF. 17, Nature Publishing Group.



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Figure 3 | Mechanisms of developmental robustness. a | Pervasive such Nature mechanisms Reviews | Genetics as nonlinearities and redundancy underlie the robustness of biological systems to incoming variations. Participating in these mechanisms but also relating to phenotype construction, specific examples of molecular players are shown. b | A simple three-gene network buffering variability in bone morphogenetic protein (BMP) signalling, as quantified by antibody staining of the phosphorylated form of the signal transducer MAD (pMAD) in Drosophila melanogaster embryos along the dorsoventral (D/V) axis. The branches with crossveinless 2 (cv‑2) and eiger (egr) form an incoherent feedforward loop, with an additional feedback motif onto the egr branch. Double egr cv‑2 mutants show an increase in the coefficient of variation with no overall change in mean intensity of staining along the dorsoventral axis. c | An example of feedback loops buffering network output at the level of gene expression. Expression of the Hox family gene mab‑5 quantified at the single-molecule level in the Caenorhabditis elegans Q neuroblast becomes more variable when loops are weakened. miRNA, microRNA; zen, zerknullt. Part b adaptated with permission from REF. 100, Cell Press. Part c adapted with permission from REF. 107, Cell Press.

characteristic cell geometry and structure of the signalling network77,78. Of note, robustness in this study refers to the genetic dose of lin‑3/egf — a relevant feature in evolution — and not the mRNA level in a single individual, as considered in most computational models77. This distinction matters because of stochastic variation in lin‑3/egf mRNA number among individuals. Such quantitative perturbation approaches allow genotypes and phenotypes to be partially linked through intermediate variables or endophenotypes (FIG. 1a). In the case of Make, Rendel was referring to the activity of a gene whose variation has a major influence on the phenotype of interest. Thus, Make represents a variable close to the genotype at this locus. With modern quantitative methods, one can also consider perturbing variables that are more remote from genotype, such as cell position, and measuring multiple phenotypic consequences within the developing system. Nonlinearity in multiple genes to phenotype mapping. The examples above concern variation in one gene. When considering phenotypic perturbations generated by the joint effect of variation in multiple genes, the phenotype may not be linearly related to genotype. For example, in C. elegans vulva development, knockout of one negative regulator of EGF signalling may be silent for the focal phenotype, whereas knocking out two of them provokes hyperinduction79–84. This results from the nonlinear relationship between EGF pathway activity and vulval index (FIG. 2b), as well as, in some cases, from gene duplication80. Such cases of synthetic genetic interactions are common in developmental and metabolic systems. Redundancy of elements acting in a given system, such as genes, transcriptional enhancers, pathways or cells, tends to make systems resilient to genetic or environmental perturbations85–90. It is usually unclear whether redundancy is maintained in evolution because of redundancy per se or because of the pleiotropic effects of the elements showing redundancy. Molecular (DNA replication, translation), cellular (spindle formation) and developmental events can fail but proofreading mechanisms and checkpoints such as those in cell cycle regulation or developmental milestones91 provide further safety mechanisms that protect against failure at these critical steps. Signalling gradients. A category of developmental systems where robust features may be challenging to explain are those that rely on long-range molecular gradients. Several robust features may be relevant, including: robustness of the signal dose to upstream variation (such as noise, embryo size, gene dosage, and upstream regulators), robustness of the spatial position of downstream regulators to variation in signal dose, and sharpness of the spatial boundary of downstream regulators (robustness to within-organism noise). Many experimental and modelling studies have been devoted to such systems, especially to the Drosophila melanogaster early embryo and imaginal discs20,60,92. Fast degradation and turnover of components — for example, via negative



REVIEWS feedback loops (self-enhanced degradation) — allow for higher robustness to variation in morphogen concentration than simple exponential decay 20,60. A sharp boundary may be established through additional mechanisms, such as cell rearrangements enforced by gene expression93 or an intercellular signalling network with cross-inhibitory feedback and temporal integration94,95. One emblematic example is the bicoid (bcd) gradient along the anteroposterior axis of the syncytial Drosophila melanogaster embryo, which first sets the position of hunchback (hb) transcription, then of the cephalic furrow. When the bcd genetic dose is varied, the cephalic furrow position varies linearly 96,97. The embryo remains viable with different furrow positions via compensatory mechanisms such as localized cell death96. A nonlinearity arises, with embryo survival thereby remaining high for bcd doses between one to four gene copies (the wild-type having two copies), followed by a sharp decrease at six copies96,97. In addition, hb expression boundary and cephalic furrow positions display low variance among individuals when expressed as a fraction of the egg long-axis. It is as yet unclear how the maternal bcd gradient remains robust to variations in egg length and how the limit of hb expression sharpens over time98,99. An exemplary study concerns amnioserosa patterning along the dorsoventral axis of the Drosophila mela‑ nogaster embryo100, which depends on diffusible bone morphogenetic protein (BMP) signalling. A network containing an incoherent feedforward motif (zerknüllt (zen) on BMP signalling) and a positive feedback loop buffers BMP signalling to noise among embryos (FIG. 3b). In double mutants of network components, the variance in BMP signalling is increased without a change in its mean. Interestingly, evolutionary loss of the upstream network component in Drosophila santomea correlates with variable dorsal fate patterning in this species100. Stochastic variation in gene expression. These examples illustrate that a key intermediate developmental phenotype is the cell-specific expression level of a relevant gene. Transcript abundance is now quantifiable through single-molecule imaging, and its stochastic variation among individuals can be quantified. This noise is higher when transcription occurs by bursts and when the bursts are large101. Interestingly, it can be tuned independently of the mean expression level, through cis-regulatory changes that affect transcriptional burst frequency and not burst size102. Such gene expression noise may or may not propagate to variation in downstream phenotypes such as cell fates. Propagation of noise in a trancriptional103 or metabolic32,104 cascade can be modelled. In the wild type, cell fates are usually robust to noise in the expression of developmental regulators. By contrast, when there are mutations in upstream regulators that affect the mean level of downstream gene expression, cell fates are often sensitive to noise, resulting in partial penetrance of the mutant phenotypes. For example, mutations in C. elegans endoderm specification genes such as skinhead‑1 (skn‑1) or in the Drosophila melanogaster gap genes tailless (tll),

Krüppel (Kr) and knirps (kni) increase variation in downstream gene expression and in cell fates105,106. Similarly, WNT pathway mutants show increased Hox family gene expression noise in the C. elegans Q neuroblast 107. In this system, interlocked positive and negative feedback loops normally cooperate to minimize Hox family gene expression variability in the wild type (FIG. 3c). WNT signalling has been proposed to generally reduce noise propagation to downstream gene expression108. The example of C. elegans vulva development (FIG. 4d) also shows an increased cell fate variance outside the normal range of EGF pathway activity. In conclusion, the experimental analysis of the propagation of variation following fine-scale perturbations and noise is now feasible in developmental systems. Displacing the mean activity of some system components may result in large changes in variance for downstream components owing to simple dose–response relationships and noise.

Genetic variation of robust features Genetic effects on trait mean and variance. As mentioned above, if a robust feature is a property of the developmental system that has evolved under natural selection, it should be possible to identify genetic variation that affects such robustness, particularly loci whose knockdown affects a robust feature. While heat shock protein 90 (HSP90) is such a gene, it remains unclear whether this phenomenon is common (BOX 3). Bergman and Siegal109 used simulations to evolve model transcriptional networks, which showed extensive loss of robustness to standing genetic variation in the face of mutations in a single gene. This result led them to predict that genes whose knockout increases phenotypic variance should be prevalent 109. Various experimental questions arise; for instance, how common are the genes whose variation affects robust features? Do they map to core phenotype construction processes or represent regulators that are superimposed on developmental networks? Are they specific for a given robust feature? Are they subject to natural genetic variation and environmental regulation? And, finally, how do they evolve? Recently, many such examples of supposed robustnessconferring genes have appeared in the literature. Expressions such as the ‘canalizing gene’ or describing a gene or mechanism that ‘confers robustness’ have become commonplace (for examples, see REFS 110,111). For any gene activity, it is generally difficult to determine whether the gene evolved under selection for this specific activity. For robustness, the case is even more problematic: we argue below that, at least in some instances, mutation of the ‘robustness gene’ affects the mean activity of key system components and thereby their variance when confronted with another incoming variation. With this wide classification, any gene directly involved in the system may be referred to as a ‘robustness-conferring gene’. The major concern with these studies is that the effects of a mutation on the phenotype mean and variance are rarely compared in detail. Displacement of the mean represents the sensitivity to the studied



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Figure 4 | Two definitions of robustness-conferring genes, with and without change of the phenotypic mean. a | Increase in variance through unidirectional phenodeviants versus through strict variance increase. Genotype G1 Nature Reviews | Genetics represents a wild type, with the quantitative trait of interest showing low microenvironmental variance among individuals. Genotypes G2/G3 represent mutations that change the trait mean, with phenodeviants on one side of this norm. Individuals of genotype G4 display the same mean but an increased variance, with phenodeviants in both directions. Most robustness studies do not distinguish these two cases. Error bars indicate standard deviation. b | Signalling pathways in Caenorhabditis elegans vulval induction: EGF (epidermal growth factor)–RAF–MAPK (mitogen-activated protein kinase) pathway shown in blue; Delta–Notch shown in red; crosstalk shown using grey arrows. c | Example of increase in variance through unidirectional phenodeviants. Red bars indicate the mean phenotype. The wild type has a mean vulval index of 3, with undetectable variance in both environments86. Hypomorphic mutations in genes coding for RAF and MAPK slightly lower the vulval index and result in higher variance. A null mutation in a negative regulator (unc‑101/clathrin subunit) results in a low-penetrance hyperinduction phenotype in environment E2 (starvation at the L2 stage), thus a loss of robustness to variation between E1 and E2 and to noise in E2. These three gene products are classically called signal transducers and regulators, and not robustness-conferring genes. Data from REF. 86 (original figures S4 and S5) replotted in a box plot. d | Using a modulation in lin‑3/egf dose, any weak departure from the wild-type induction index (in black) results in an increase in variance (in red). Grey dots correspond to data points of transgenic lines and mutants changing the lin‑3 mRNA dose. Data from REF. 78 (original figures 2C and S2), replotted from our raw data with different x- and y-axes.

Phenodeviants Individuals with a phenotype outside a defined normal range within a reference population.

perturbation, whereas the variance represents sensitivity to noise, or to any genetic and environmental variation in the population. As mentioned, mutant strains tend to be more variable than the wild type, because the system leaves the plateau region of a dose–response curve (FIG. 4). In many systems, departure from the wild-type mean phenotype due to unidirectional phenodeviants; (FIG. 4a), even if subtle, results in de facto increased sensitivity to noise and further perturbations. For example, in C. elegans, any vulval mutation that alters the mean vulval induction index, even mildly, also increases variance (FIG. 4c). Using such mutations to define ‘robustnessconferring genes’ would lead to the odd conclusion

that the EGF–RAS–MAPK pathway confers robustness to vulval induction, whereas it actually induces vulval fates. A strict definition of robustness-conferring genes requires an increase in variance without a change in the mean (strict variance increase; FIG. 4a), or at least an unexpectedly high variance for a given mean level44. A striking example concerns the proposed role of microRNAs (miRNAs) in developmental buffering 111. miRNAs are genome-encoded small RNAs that posttranscriptionally downregulate gene expression by binding sequence-specifically to mRNAs112. miRNAs, as well as other small RNAs, establish thresholds of targeted mRNA levels below which protein output is insensitive



REVIEWS Box 3 | On HSP90 as a robustness factor and evolutionary capacitor Heat shock protein 90 (HSP90) is a chaperone that assists the maturation of many proteins. In a seminal paper, Rutherford and Lindquist showed that genetic or pharmacological impairment of Hsp90 in Drosophila melanogaster identifies low-penetrance developmental abnormalities, which seem to depend on the genetic background120. The authors suggested that HSP90 suppresses phenotypic variation, leading to the accumulation of cryptic genetic variation. They further proposed that a novel stressing environment in the wild may reduce available HSP90 proteins owing to catastrophic protein unfolding. As a result, new phenotypic variants would arise, specifically in some genetic backgrounds, which could be selected in this new environment. This proposed scenario underlies the hypothesis that HSP90 may act as an ‘evolutionary capacitor’. This initial connection between molecular mechanism and control of phenotypic variability sparked enthusiasm in studying HSP90. However, subsequent work in different organisms found a buffering role for HSP90 to standing genetic variation for some traits138, but not all44,139–142, and not to tested environmental variation. Whether HSP90 can be considered as a general ‘robustness factor’ and ‘evolutionary capacitor’ is questionable for several reasons. First, the scoring of phenotypes upon HSP90 inhibition in many studies was qualitative. Studies including quantitative scoring of phenotypes have found that HSP90 depletion generally induces aberrant phenotypes on one side of the spectrum only — for example, by failing to activate a signalling pathway at a sufficient level in one tissue140,141,143. Only one study143 has found an increase in the phenotype variance without a change in mean, similar to the strict increase in variance shown in FIG. 4a. Second, these studies on Hsp90 impairment generally have not provided comparisons to other genes. Thus, there may be nothing special about Hsp90 downregulation revealing the effect of genetic variation46,142, compared to, for example, other chaperones144,145, network hubs44 or translation termination regulated by the yeast [PSI] prion146. Geneticists have long noticed that mutants often display low-penetrance phenotypic defects in diverse tissues, and that the genetic background affects penetrance. One study55 showed that mutations in standard components of pleiotropic signalling pathways display a differential penetrance among tissues that depends on the genetic background, as shown for HSP90. Third, the mechanisms through which HSP90 may buffer genetic variation remain unclear. HSP90 interacts with diverse proteins, including kinases, ubiquitin ligases and transcription factors147,148. A direct link between HSP90 and Pol II transcriptional pausing has also been made149. Fourth, it has been controversial to what extent phenotypes observed upon HSP90 depletion are due to standing genetic variation or to other mechanisms, such as transposition, aneuploidization or epigenetic variation150–152. Finally, the evolutionary significance of HSP90‑mediated buffering is unclear. HSP90 is almost certainly under selection chiefly for its chaperone activity rather than for its putative role as an evolutionary capacitor. Consistent with this, naturally occurring derived HSP90 alleles with decreased expression have a lower competitive fitness and are deleterious upon heat stress153. How such naturally occurring alleles are maintained remains unclear. For example, although surface populations of the cavefish Astyanax mexicanus harbour selectable cryptic genetic variation affecting eye size upon HSP90 inhibition, as may have occurred in the cave environment143, it has not been tested whether the effect is specific to HSP90.

Phenotypic capacitors Genes that, when mutated or deleted, lead to an increase in phenotypic variance in response to a given perturbation.

to variation in transcript concentration113,114. In principle, one can distinguish the expression-tuning effect of miRNAs that reduces mean transcript level from their expression-buffering effect that reduces variance110. However, their effects on variance and mean are rarely distinguished. Drosophila melanogaster miR‑7 was shown to be necessary for specifying sensory organ cell fates upon environmental fluctuations and thus shown to impart robustness. Yet the miR‑7 mutation affected both the mean and variance of the cell fate phenotype115. Similarly, miR‑9a‑mediated regulation of the transcription factor senseless (sens) is important to stabilize bristle number in the Drosophila melanogaster scutellum upon

natural genetic variation, and miR‑9a mutations affect both phenotypic variance and mean116. Therefore, strictly speaking, it is unclear whether miRNAs evolved to confer developmental robustness. Moreover, miRNAs may also contribute to plasticity phenotypes, as shown by recent studies in plants reporting a link between age-dependent miRNA levels and flowering responses to cold117,118. For miR‑7 mutants115 and other reported genetic variants (such as those reported in REFS 90,119), a mean phenotypic value is not attained in one of the tested environments. Classical ways to express such a change in phenotypic mean are the environmental dependence of the mutation effect (as in developmental genetics), or a statistical interaction between the genotype and environment (as in quantitative genetics, then known as GxE) (FIG. 1b). In the C. elegans vulva development example, it could be said that the unc‑101 gene confers robustness to a change of environment (FIG. 4c), whereas what it actually does is lower epidermal growth factor receptor (EGFR) activity, which becomes limiting in the new environment. The same holds true in the hsp90 and miR‑9 examples116,120 with genetic (GxG) interactions. In other words, what used to be called a synthetic interaction is now often labelled as robustness, which is not particularly relevant for two reasons. First, it remains doubtful and difficult to test whether the gene actually evolved to confer robustness to this change (BOX 2). Second, in many cases the mutation results in a change in mean phenotype, even if subtle, and thus only corresponds to a defect in phenotypic construction. Searching for genes affecting trait variance. Laboratory screens for an increase in phenotypic variance without a change in the mean phenotype (FIG. 4a) are difficult and have rarely been performed, even for intensely studied systems such as C. elegans vulval patterning. Nevertheless, experiments using Drosophila melanogaster deficiency lines have identified multiple genomic regions encompassing loci that are involved in buffering wing shape to genetic variation or sensory bristle traits to environmental variation46,121. Unbiased screens used to identify phenotypic capacitors have only been performed in the yeast Saccharomyces cerevisiae44,45. Levy and Siegal44 used a high-dimensional morphological phenotyping approach, with stochastic noise as the incoming variation and the yeast knockout library as the source of genetic variation for gene identification. Using these screens, they identified over 300 haploid single-gene knockouts with reduced robustness to noise. The gene set was enriched in chromosome organization, cell cycle and transcriptional regulators, all of which are highly connected network hubs. The authors did not require that phenotype means be unaffected to define a capacitor, but instead took into account the variance-to‑mean relationship for the particular trait in their dataset (BOX 1). Their study nicely exemplifies that this relationship must be studied to test whether the variance observed for a given mean level significantly differs from the expectation. More recently, Rinott et al.45 studied gene expression noise with a similar design and identified a set of



REVIEWS similarly highly connected genes, including transcriptional regulators. They monitored the expression of two reporter constructs driven by different promoters, thereby distinguishing local (with variable expression of one reporter) versus global variation (with variable expression of both reporters). Most relevant to evolution is the molecular identification of natural genetic variation underlying trait variance. A recent effort identified, down to the nucleotide level, variation among wild S. cerevisiae genetic backgrounds with effects on the expression noise of a reporter gene42. Unlike laboratory variants, these naturally varying loci displayed a high degree of specificity for this reporter gene. One was a frameshift mutation in a transmembrane receptor, whereas another was a common cis-regulatory variant in a permease gene. Interestingly, both genes are putative environmental sensors, potentially connecting noise with plasticity to a macroenvironmental variation42.

Conclusions and future perspectives Robustness to perturbations is prevalent in biological systems as a consequence of the prevalence of nonlinear dose–response curves. However, some robust

Levy, S. F. & Siegal, M. L. in Evolutionary Systems Biology (ed. Soyer, O. S.) 431–452 (Springer, 2012). Gibson, G. & Wagner, G. Canalization in evolutionary genetics: a stabilizing theory? Bioessays 22, 372–380 (2000). 3. Debat, V. & David, P. Mapping phenotypes: canalization, plasticity and developmental stability. TREE 16, 555–561 (2001). 4. Meiklejohn, C. D. & Hartl, D. L. A single mode of canalization. TREE 17, 468–473 (2002). 5. de Visser, J. A. et al. Perspective: evolution and detection of genetic robustness. Evolution 57, 1959–1972 (2003). 6. Dworkin, I. in Variation: A Central Concept in Biology (eds Hallgrimsson, B. & Hall, B. K.) 131–158 (Elsevier, 2005). 7. Flatt, T. The evolutionary genetics of canalization. Q. Rev. Biol. 80, 287–316 (2005). 8. Lehner, B. Genotype to phenotype: lessons from model organisms for human genetics. Nat. Rev. Genet. 14, 168–178 (2013). 9. Waddington, C. H. The strategy of the genes (Allen & Unwin, 1957). 10. Scharloo, W. Canalization: genetic and developmental aspects. Ann. Rev. Ecol. Syst. 22, 65–93 (1991). 11. Gibson, G. & Dworkin, I. Uncovering cryptic genetic variation. Nat. Rev. Genet. 5, 681–690 (2004). 12. Wagner, A. Robustness and Evolvability in Living Systems (Princeton Univ. Press, 2005). This book represents the most detailed recent analysis related to definitions, mechanisms and evolution of biological robustness. 13. Masel, J. & Siegal, M. L. Robustness: mechanisms and consequences. Trends Genet. 25, 395–403 (2009). 14. Masel, J. & Trotter, M. V. Robustness and evolvability. Trends Genet. 26, 406–414 (2010). 15. Paaby, A. B. & Rockman, M. V. Cryptic genetic variation: evolution’s hidden substrate. Nat. Rev. Genet. 15, 247–258 (2014). 16. Barkai, N. & Leibler, S. Robustness in simple biochemical networks. Nature 387, 913–917 (1997). This paper reports on modelling of signal transduction in bacterial chemotaxis, and provides one of the first examples of an analysis of the robustness of the response to changes in individual reaction rates. 17. von Dassow, G., Meir, E., Munro, E. M. & Odell, G. M. The segment polarity network is a robust developmental module. Nature 406, 188–192 (2000). This computational study provides evidence that the segment polarity gene network topology in 1. 2.

features, such as the response to long-range morphogen gradients, are complex and require careful attention to underlying mechanisms. An increase in phenotypic variance in mutants labelled as ‘robustness-conferring’ may be commonly generated by a broad failure of phenotypic construction, rather than being indicative of a distinct robustness mechanism. Analysis of the mean and variance along dose–response curves would facilitate interpretation of an observed change in variance. Propagation of variation across whole systems is a natural point of linkage between evolutionary and systems biology, and is a particularly fruitful avenue for future research. The amount and distribution of phenotypic variation at different points in a system is another important area for continuing study. The congruence and other non-additive effects of different sources of variation are particularly fascinating. Another key challenge is to identify the variational properties of biological systems that are particularly relevant to natural variation, and their evolution. Future work for both experimentalists and theoreticians should include explicit connections between systems biology with models of quantitative variation and population genetics.

Drosophila melanogaster is the main source of the robustness of pattern formation to parameter change. 18. Gutenkunst, R. N. et al. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3, e189 (2007). 19. Whitacre, J. M. Biological robustness: paradigms, mechanisms, and systems principles. Front. Genet. 3, 67 (2012). 20. Eldar, A. et al. Robustness of the BMP morphogen gradient in Drosophila embryonic patterning. Nature 419, 304–308 (2002). 21. Carlson, J. M. & Doyle, J. Highly optimized tolerance: robustness and design in complex systems. Phys. Rev. Lett. 84, 2529–2532 (2000). 22. Kitano, H. Biological robustness. Nat. Rev. Genet. 5, 826–837 (2004). This influential review on the biological robustness provides an alternative view on this topic, integrating principles from systems biology and engineering. 23. Stelling, J. et al. Robustness of cellular functions. Cell 118, 675–685 (2004). 24. Kacser, H. in The Strategy of the Genes (ed. Waddington, C. H.) 191–249 (Routledge Library Editions, 1957). 25. Rendel, J. M. Canalisation and Gene Control (Logos Press, 1967). Rendel’s work anticipates key aspects of nonlinearity in genotype to phenotype mapping, before the molecular biology era. 26. Nijhout, H. F. The nature of robustness in development. Bioessays 24, 553–563 (2002). 27. Siegal, M. L. & Bergman, A. Waddington’s canalization revisited: developmental stability and evolution. Proc. Natl Acad. Sci. USA 99, 10528–10532 (2002). 28. Landry, C. R. & Rifkin, S. A. in Evolutionary Systems Biology (ed. Soyer, O. S.) 371–398 (Springer, 2012). 29. Kaneko, K. in Evolutionary Systems Biology (ed. Soyer, O. S.) 249–278 (Springer, 2012). 30. Shinar, G., Milo, R., Martinez, M. R. & Alon, U. Input output robustness in simple bacterial signaling systems. Proc. Natl Acad. Sci. USA 104, 19931–19935 (2007). 31. Hart, Y. & Alon, U. The utility of paradoxical components in biological circuits. Mol. Cell 49, 213–221 (2013). 32. Anderson, D. F., Mattingly, J. C., Nijhout, H. F. & Reed, M. C. Propagation of fluctuations in biochemical systems, I: linear SSC networks. Bull. Math. Biol. 69, 1791–1813 (2007).


33. Kitano, H. Towards a theory of biological robustness. Mol. Syst. Biol. 3, 137 (2007). 34. Kitano, H. Violations of robustness trade-offs. Mol. Syst. Biol. 6, 384 (2010). 35. Tsimring, L. S. Noise in biology. Rep. Prog. Phys. 77, 026601 (2014). 36. Leamy, L. J. & Klingenberg, C. P. The genetics and evolution of fluctuating asymmetry. Annu. Rev. Ecol. Evol. Syst. 36, 1–21 (2005). 37. Yvert, G. ‘Particle genetics’: treating every cell as unique. Trends Genet. 30, 49–56 (2014). 38. Pare, G., Cook, N. R., Ridker, P. M. & Chasman, D. I. On the use of variance per genotype as a tool to identify quantitative trait interaction effects: a report from the Women’s Genome Health Study. PLoS Genet. 6, e1000981 (2010). 39. Mather, K. Genetical control of stability in development. Heredity 7, 297–336 (1953). 40. Fraser, H. B. & Schadt, E. E. The quantitative genetics of phenotypic robustness. PLoS ONE 5, e8635 (2010). 41. Shen, X., Pettersson, M., Ronnegard, L. & Carlborg, O. Inheritance beyond plain heritability: variancecontrolling genes in Arabidopsis thaliana. PLoS Genet. 8, e1002839 (2012). 42. Fehrmann, S. et al. Natural sequence variants of yeast environmental sensors confer cell‑to‑cell expression variability. Mol. Syst. Biol. 9, 695 (2013). This study identifies, down to the nucleotide level, the natural genetic variation underlying reporter gene expression noise in yeast. 43. Ziv, N., Siegal, M. L. & Gresham, D. Genetic and nongenetic determinants of cell growth variation assessed by high-throughput microscopy. Mol. Biol. Evol. 30, 2568–2578 (2013). 44. Levy, S. F. & Siegal, M. L. Network hubs buffer environmental variation in Saccharomyces cerevisiae. PLoS Biol. 6, e264 (2008). This paper represents the most comprehensive survey of genetic loci buffering noise in yeast, using morphological phenotypes. 45. Rinott, R., Jaimovich, A. & Friedman, N. Exploring transcription regulation through cell‑to‑cell variability. Proc. Natl Acad. Sci. USA 108, 6329–6334 (2011). 46. Takahashi, K. H. Multiple capacitors for natural genetic variation in Drosophila melanogaster. Mol. Ecol. 22, 1356–1365 (2012). 47. Debat, V. et al. Developmental stability: a major role for cyclin G in Drosophila melanogaster. PLoS Genet. 7, e1002314 (2011).


REVIEWS 48. Hillenmeyer, M. E. et al. The chemical genomic portrait of yeast: uncovering a phenotype for all genes. Science 320, 362–365 (2008). 49. Martin, A. & Orgogozo, V. The loci of repeated evolution: a catalog of genetic hotspots of phenotypic variation. Evolution 67, 1235–1250 (2013). 50. Stearns, S. C., Kaiscr, M. & Kawecki, T. J. The differential genetic and environmental canalization of fitness components in Drosophila melanogaster. J. Evol. Biol. 8, 539–557 (1995). 51. Dworkin, I. A study of canalization and developmental stability in the sternopleural bristle system of Drosophila melanogaster. Evolution 59, 1500–1509 (2005). 52. Houle, D., Morikawa, B. & Lynch, M. Comparing mutational variabilities. Genetics 143, 1467–1483 (1996). 53. Braendle, C., Baer, C. F. & Félix, M.-A. Bias and evolution of the mutationally accessible phenotypic space in a developmental system. PLoS Genet. 6, e1000877 (2010). 54. Gibson, G., Wemple, M. & van Helden, S. Potential variance affecting homeotic Ultrabithorax and Antennapedia phenotypes in Drosophila melanogaster. Genetics 151, 1081–1091 (1999). 55. Milloz, J., Duveau, F., Nuez, I. & Félix, M.‑A. Intraspecific evolution of the intercellular signaling network underlying a robust developmental system. Genes Dev. 22, 3064–3075 (2008). 56. Baer, C. F. Quantifying the decanalizing effects of spontaneous mutations in rhabditid nematodes. Am. Nat. 172, 272–281 (2008). 57. Richardson, J. B., Uppendahl, L. D., Traficante, M. K., Levy, S. F. & Siegal, M. L. Histone variant HTZ1 shows extensive epistasis with, but does not increase robustness to, new mutations. PLoS Genet. 9, e1003733 (2013). 58. Meir, E., von Dassow, G., Munro, E. & Odell, G. M. Robustness, flexibility, and the role of lateral inhibition in the neurogenic network. Curr. Biol. 12, 778–786 (2002). 59. Li, F., Long, T., Lu, Y., Ouyang, Q. & Tang, C. The yeast cell-cycle network is robustly designed. Proc. Natl Acad. Sci. USA 101, 4781–4786 (2004). 60. Eldar, A., Rosin, D., Shilo, B.‑Z. & Barkai, N. Self-enhanced ligand degradation underlies robustness of morphogen gradients. Dev. Cell 5, 635–646 (2003). 61. Debat, V., Debelle, A. & Dworkin, I. Plasticity, canalization, and developmental stability of the Drosophila wing: joint effects of mutations and developmental temperature. Evolution 63, 2864–2876 (2009). 62. Lehner, B. Genes confer similar robustness to environmental, stochastic, and genetic perturbations in yeast. PLoS ONE 5, e9035 (2010). 63. Fontana, W. Modelling ‘evo-devo’ with RNA. Bioessays 24, 1164–1177 (2002). This review uses the example of RNA secondary structure to explore various aspects of the genotype–phenotype map, including robustness properties. 64. Ciliberti, S., Martin, O. C. & Wagner, A. Robustness can evolve gradually in complex regulatory gene networks with varying topology. PLoS Comput. Biol. 3, e15 (2007). 65. Kaneko, K. Evolution of robustness to noise and mutation in gene expression dynamics. PLoS ONE 2, e434 (2007). 66. Fisher, R. A. The possible modification of the wild type to recurrent mutations. Am. Nat. 62, 115–126 (1928). 67. Wright, S. Molecular and evolutionary theories of dominance. Am. Nat. 63, 24–53 (1934). 68. Haldane, J. B. S. The theory of the evolution of dominance. J. Gen. 37, 365–374 (1939). 69. Kacser, H. & Burns, J. A. The molecular basis of dominance. Genetics 97, 639–666 (1981). 70. Bagheri, H. C. Unresolved boundaries of evolutionary theory and the question of how inheritance systems evolve: 75 years of debate on the evolution of dominance. J. Exp. Zool. Mol. Dev. Evol. 306, 329–359 (2006). 71. Nijhout, H. F. & Berg, A. M. A mechanistic study of evolvability using the mitogen-activated protein kinase cascade. Evol. Dev. 5, 281–294 (2003). This paper combines the modelling of a protein kinase cascade and the exploration of possible evolutionary variation in response phenotypes upon change in parameters. 72. Prill, R. J., Iglesias, P. A. & Levchenko, A. Dynamic properties of network motifs contribute to biological network organization. PLoS Biol. 3, e343 (2005).

73. Ebert, M. S. & Sharp, P. A. Roles for microRNAs in conferring robustness to biological processes. Cell 149, 515–524 (2012). 74. Lander, A. D. How cells know where they are. Science 339, 923–927 (2013). 75. Posadas, D. M. & Carthew, R. W. MicroRNAs and their roles in developmental canalization. Curr. Opin. Genet. Dev. 27, 1–6 (2014). 76. Tsang, J., Zhu, J. & van Oudenaarden, A. MicroRNA-mediated feedback and feedforward loops are recurrent network motifs in mammals. Mol. Cell 26, 753–767 (2007). 77. Hoyos, E. et al. Quantitative variation in autocrine signaling and pathway crosstalk in the Caenorhabditis vulval network. Curr. Biol. 21, 527–538 (2011). 78. Barkoulas, M., van Zon, J. S., Milloz, J., van Oudenaarden, A. & Félix, M.-A. Robustness and epistasis in the C. elegans vulval signaling network revealed by pathway dosage modulation. Dev. Cell 24, 64–75 (2013). This study quantifies the robustness of the C. elegans vulval cell fate pattern to the expression of its upstream inducer at the single-molecule level. 79. Hopper, N. A., Lee, J. & Sternberg, P. W. ARK‑1 inhibits EGFR signaling in C. elegans. Mol. Cell 6, 65–75 (2000). 80. Ohmachi, M. et al. C. elegans ksr‑1 and ksr‑2 have both unique and redundant functions and are required for MPK‑1 ERK phosphorylation. Curr. Biol. 12, 427–433 (2002). 81. Rocheleau, C. E., Ronnlund, A., Tuck, S. & Sundaram, M. V. Caenorhabditis elegans CNK‑1 promotes Raf activation but is not essential for Ras/Raf signaling. Proc. Natl Acad. Sci. USA 102, 11757–11762 (2005). 82. Canevascini, S., Marti, M., Fröhli, E. & Hajnal, A. The Caenorhabditis elegans homologue of the proto-oncogene ect‑2 positively regulates RAS signalling during vulval development. EMBO Rep. 6, 1169–1175 (2005). 83. Walser, C. B., Battu, G., Hoier, E. F. & Hajnal, A. Distinct roles of the Pumilio and FBF translational repressors during C. elegans vulval development. Development 133, 3461–3471 (2006). 84. Nakdimon, I., Walser, M., Fröhli, E. & Hajnal, A. PTEN negatively regulates MAPK signaling during Caenorhabditis elegans vulval development. PLoS Genet. 8, e1002881 (2012). 85. Nowak, M. A., Boerlijst, M. C., Cooke, J. & Smith, J. M. Evolution of genetic redundancy. Nature 388, 167–171 (1997). 86. Braendle, C. & Félix, M.‑A. Plasticity and errors of a robust developmental system in different environments. Dev. Cell 15, 714–724 (2008). 87. Delattre, M. & Félix, M.-A. The evolutionary context of robust and redundant cell biological mechanisms. Bioessays 31, 537–545 (2009). 88. Perry, M. W., Boettiger, A. N., Bothma, J. P. & Levine, M. Shadow enhancers foster robustness of Drosophila gastrulation. Curr. Biol. 20, 1562–1567 (2010). 89. Perry, M. W., Boettiger, A. N. & Levine, M. Multiple enhancers ensure precision of gap geneexpression patterns in the Drosophila embryo. Proc. Natl Acad. Sci. USA 108, 13570–13575 (2011). 90. Frankel, N. et al. Phenotypic robustness conferred by apparently redundant transcriptional enhancers. Nature 466, 490–493 (2010). 91. Oliveira, M. M., Shingleton, A. W. & Mirth, C. K. Coordination of wing and whole-body development at developmental milestones ensures robustness against environmental and physiological perturbations. PLoS Genet. 10, e1004408 (2014). 92. Gregor, T., Tank, D. W., Wieschaus, E. F. & Bialek, W. Probing the limits to positional information. Cell 130, 153–164 (2007). 93. Xiong, F. et al. Specified neural progenitors sort to form sharp domains after noisy Shh signaling. Cell 153, 550–561 (2013). 94. Dessaud, E. et al. Dynamic assignment and maintenance of positional identity in the ventral neural tube by the morphogen Sonic Hedgehog. PLoS Biol. 8, e1000382 (2010). 95. Srinivasan, S. et al. A BMP-FGF morphogen toggle switch drives the ultrasensitive expression of multiple genes in the developing forebrain. PLoS Comput. Biol. 10, e1003463 (2014). 96. Namba, R., Pazdera, T. M., Cerrone, R. L. & Minden, J. S. Drosophila embryonic pattern repair: how embryos respond to bicoid dosage alteration. Development 124, 1393–1403 (1997).


97. Liu, F., Morrison, A. H. & Gregor, T. Dynamic interpretation of maternal inputs by the Drosophila segmentation gene network. Proc. Natl Acad. Sci. USA 110, 6724–6729 (2013). 98. Lucas, T. et al. Live imaging of bicoid-dependent transcription in Drosophila embryos. Curr. Biol. 23, 2135–2139 (2013). 99. Little, S. C., Tikhonov, M. & Gregor, T. Precise developmental gene expression arises from globally stochastic transcriptional activity. Cell 154, 789–800 (2013). 100. Gavin-Smyth, J., Wang, Y. C., Butler, I. & Ferguson, E. L. A genetic network conferring canalization to a bistable patterning system in Drosophila. Curr. Biol. 23, 2296–2302 (2013). This paper, describing a gene network affecting amnioserosa patterning in Drosophila spp. embryos, provides a good example of a study in which gene effects on trait mean and variance are distinguished. 101. Sanchez, A., Choubey, S. & Kondev, J. Regulation of noise in gene expression. Annu. Rev. Biophys. 42, 469–491 (2013). 102. Dadiani, M. et al. Two DNA-encoded strategies for increasing expression with opposing effects on promoter dynamics and transcriptional noise. Genome Res. 23, 966–976 (2013). 103. Hooshangi, S., Thiberge, S. & Weiss, R. Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc. Natl Acad. Sci. USA 102, 3581–3586 (2005). 104. Nijhout, H. F., Best, J. & Reed, M. C. Escape from homeostasis. Math. Biosci. 257, 104–110 (2014). 105. Janssens, H. et al. Lack of tailless leads to an increase in expression variability in Drosophila embryos. Dev. Biol. 377, 305–317 (2013). 106. Surkova, S. et al. Quantitative dynamics and increased variability of segmentation gene expression in the Drosophila Krüppel and knirps mutants. Dev. Biol. 376, 99–112 (2013). 107. Ji, N. et al. Feedback control of gene expression variability in the Caenorhabditis elegans Wnt pathway. Cell 155, 869–880 (2013). This article shows an example of how gene network architecture influences gene expression variability in C. elegans. 108. Martinez-Arias, A. & Hayward, P. Filtering transcriptional noise during development: concepts and mechanisms. Nat. Rev. Genet. 7, 34–44 (2006). 109. Bergman, A. & Siegal, M. L. Evolutionary capacitance as a general feature of complex gene networks. Nature 424, 549–552 (2003). 110. Wu, C. I., Shen, Y. & Tang, T. Evolution under canalization and the dual roles of microRNAs: a hypothesis. Genome Res. 19, 734–743 (2009). 111. Hornstein, E. & Shomron, N. Canalization of development by microRNAs. Nat. Genet. 38 S20–S24 (2006). 112. Bartel, D. P. MicroRNAs: target recognition and regulatory functions. Cell 136, 215–233 (2009). 113. Siciliano, V. et al. MiRNAs confer phenotypic robustness to gene networks by suppressing biological noise. Nat. Commun. 4, 2364 (2013). 114. Lucchetta, E. M., Carthew, R. W. & Ismagilov, R. F. The endo-siRNA pathway is essential for robust development of the Drosophila embryo. PLoS ONE 4, e7576 (2009). 115. Li, X., Cassidy, J. J., Reinke, C. A., Fischboeck, S. & Carthew, R. W. A microRNA imparts robustness against environmental fluctuation during development. Cell 137, 273–282 (2009). 116. Cassidy, J. J. et al. miR‑9a minimizes the phenotypic impact of genomic diversity by buffering a transcription factor. Cell 155, 1556–1567 (2013). 117. Bergonzi, S. et al. Mechanisms of age-dependent response to winter temperature in perennial flowering of Arabis alpina. Science 340, 1094–1097 (2013). 118. Zhou, C. M. et al. Molecular basis of age-dependent vernalization in Cardamine flexuosa. Science 340, 1097–1100 (2013). 119. Crocker, J. et al. Low affinity binding site clusters confer Hox specificity and regulatory robustness. Cell 160, 191–203 (2015). 120. Rutherford, S. L. & Lindquist, S. Hsp90 as a capacitator for morphological evolution. Nature 396, 336–342 (1998). 121. Takahashi, K. H., Okada, Y. & Teramura, K. Deficiency screening for genomic regions with effects on environmental sensitivity of the sensory bristles of Drosophila melanogaster. Evolution 66, 2878–2890 (2012).


REVIEWS 122. Box, G. E. P. & Cox, D. R. An analysis of transformations. J. Roy. Stat. Soc. B. 26, 211–252 (1964). 123. Schultz, B. B. Levene’s test for relative variation. Syst. Zool. 34, 449–456 (1985). 124. Ronnegard, L. & Valdar, W. Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability. BMC Genet. 13, 63 (2012). This article presents statistical methods for the detection of quantitative trait loci that affect the variance of a phenotype, and points to the relationship with epistatic effects. 125. Geiler-Samerotte, K. A. et al. The details in the distributions: why and how to study phenotypic variability. Curr. Opin. Biotechnol. 24, 752–759 (2013). This article highlights the importance of studying phenotypic distributions and reviews current statistical methods and experimental designs. 126. Lande, R. On comparing coefficients of variation. Syst. Zool. 26, 214–217 (1977). 127. Lynch, M. The evolution of genetic networks by non-adaptive processes. Nat. Rev. Genet. 8, 803–813 (2007). 128. Proulx, S. R. & Phillips, P. C. The opportunity for canalization and the evolution of genetic networks. Am. Naturalist 165, 147–162 (2005). 129. Barrett, R. D. H. & Hoekstra, H. E. Molecular spandrels: tests of adaptation at the genetic level. Nat. Rev. Genet. 12, 767–780 (2011). 130. Wagner, G. P., Booth, G. & Bagheri-Chaichian, H. A population genetic theory of canalization. Evolution 51, 329–347 (1997). 131. Wagner, A. Robustness, evolvability, and neutrality. FEBS Lett. 579, 1772–1778 (2005). 132. Wilke, C. O. Adaptive evolution on neutral networks. Bull. Math. Biol. 63, 715–730 (2001). 133. Sanjuan, R., Cuevas, J. M., Furio, V., Holmes, E. C. & Moya, A. Selection for robustness in mutagenized RNA viruses. PLoS Genet. 3, e93 (2007). 134. Wilke, C. O. Quasispecies theory in the context of population genetics. BMC Evol. Biol. 5, 44 (2005). 135. Masel, J. & Maughan, H. Mutations leading to loss of sporulation ability in Bacillus subtilis are sufficiently frequent to favor genetic canalization. Genetics 175, 453–457 (2007). 136. Azevedo, R. B., Lohaus, R. Srinivasan, S., Dang, K. K. & Burch, C. L. Sexual reproduction selects for

robustness and negative epistasis in artificial gene networks. Nature 440, 87–90 (2006). 137. Kim, K. J. & Fernandes, V. M. Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network. PLoS Comput. Biol. 5, e1000296 (2009). 138. Queitsch, C., Sangster, T. A. & Lindquist, S. Hsp90 as a capacitor of phenotypic variation. Nature 417, 618–624 (2002). 139. Milton, C. C., Huynh, B., Batterham, P., Rutherford, S. L. & Hoffmann, A. A. Quantitative trait symmetry independent of Hsp90 buffering: distinct modes of genetic canalization and developmental stability. Proc. Natl Acad. Sci. USA 100, 13396–13401 (2003). 140. Milton, C. C., Batterham, P., McKenzie, J. A. & Hoffmann, A. A. Effect of E(sev) and Su(Raf) Hsp83 mutants and trans-heterozygotes on bristle trait means and variation in Drosophila melanogaster. Genetics 171, 119–130 (2005). 141. Milton, C. C., Ulane, C. M. & Rutherford, S. Control of canalization and evolvability by Hsp90. PLoS ONE 1, e75 (2006). 142. Debat, V., Milton, C. C., Rutherford, S., Klingenberg, C. P. & Hoffmann, A. A. Hsp90 and the quantitative variation of wing shape in Drosophila melanogaster. Evolution 60, 2529–2538 (2006). 143. Rohner, N. et al. Cryptic variation in morphological evolution: HSP90 as a capacitor for loss of eyes in cavefish. Science 342, 1372–1375 (2013). 144. Fares, M. A., Ruiz-González, M. X., Moya, A., Elena, S. F. & Barrio, E. Endosymbiotic bacteria: groEL buffers against deleterious mutations. Nature 417, 398 (2002). 145. Takahashi, K. H., Daborn, P. J., Hoffmann, A. A. & Takano-Shimizu, T. Environmental stress-dependent effects of deletions encompassing Hsp70Ba on canalization and quantitative trait asymmetry in Drosophila melanogaster. PLoS ONE 6, e17295 (2011). 146. True, H. L. & Lindquist, S. A yeast prion provides a mechanism for genetic variation and phenotypic diversity. Nature 407, 477–483 (2000). 147. Taipale, M., Jarosz, D. F. & Lindquist, S. HSP90 at the hub of protein homeostasis: emerging mechanistic insights. Nat. Rev. Mol. Cell Biol. 11, 515–528 (2010).


148. Taipale, M. et al. Quantitative analysis of HSP90‑client interactions reveals principles of substrate recognition. Cell 150, 987–1001 (2012). 149. Sawarkar, R., Sievers, C. & Paro, R. Hsp90 globally targets paused RNA polymerase to regulate gene expression in response to environmental stimuli. Cell 149, 807–818 (2012). 150. Sollars, V. et al. Evidence for an epigenetic mechanism by which Hsp90 acts as a capacitor for morphological evolution. Nat. Genet. 33, 70–74 (2003). 151. Specchia, V. et al. Hsp90 prevents phenotypic variation by suppressing the mutagenic activity of transposons. Nature 463, 662–665 (2010). 152. Chen, G., Bradford, W. D., Seidel, C. W. & Li, R. Hsp90 stress potentiates rapid cellular adaptation through induction of aneuploidy. Nature 482, 246–250 (2012). 153. Chen, B. & Wagner, A. Hsp90 is important for fecundity, longevity, and buffering of cryptic deleterious variation in wild fly populations. BMC Evol. Biol. 12, 25 (2012). 154. Rendel, J. M. The relationship between gene and phenotype. J. Theor. Biol. 2, 296–308 (1962). 155. Rendel, J. M., Sheldon, B. L. & Finlay, D. E. Canalisation of development of scutellar bristles in Drosophila by control of the scute locus. Genetics 52, 1137–1151 (1965). 156. Dun, R. B. & Fraser, A. S. Selection for an invariant character, vibrissa number, in the house mouse. Austr. J. Biol. Sci. 12, 506–523 (1959).

Acknowledgements

We thank P. Phillips, C. Braendle, V. Orgogozo, V. Debat, E. Andersen, F. Besnard and the reviewers for comments on the manuscript, N. Dostatni and H. Teotonio for discussions, and S. Rifkin for introducing us to Rendel. Work on developmental robustness in the Félix laboratory is funded by the Agence Nationale pour la Recherche (12‑BSV2‑0004‑01) and a Coup d’Elan from the Bettencourt-Schueller Foundation; work in the Barkoulas laboratory is funded by the Biotechnology and Biological Sciences Research Council (BBSRC) in the UK (BB/L021455/1).

Competing interests statement

The authors declare no competing interests.


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