In evolutionary biology, phenotypic plasticity (PP) and reaction norm (RN) are two central concepts connected to the fact that the phenotype of an organism is affected by the environment where development occurs (Fusco and Minelli 2010). PP may be defined as the ability of a given genotype to respond to environmental variation producing different phenotypes (Pigliucci 2005); and RN is the curve that describes the phenotypic response of a given genotype as a function of the environment, thus referring to a phenotypic trait and an environmental factor which are (or can be represented as) continuous variables (Chevin et al. 2010). Thus, RNs show if and how genotypes respond to a given environmental variation.

From a biometric analysis perspective, the variation in phenotypic responses of different genotypes submitted to diverse environments—the variation in RN response—is statistically represented as a nonadditive effect of genotype and environment in an analysis of variance (ANOVA), that is, a genotype–environment interaction (G×E) (Via and Lande 1985). Hence, we may establish the following relationship among these concepts:

Despite this correspondence, the “analysis of phenotypic variance is not a sufficient substitute for knowing the actual norms of reaction of genotypes” (Gupta and Lewontin 1982). Therefore, the understanding of G×E and its many evolutionary implications—from the evolution of adaptive PP to the maintenance of genetic variation for quantitative traits—requires the ability to describe the variation of RNs in a comprehensible manner, that is, describe G×E not only as a factor in an ANOVA, but in terms of RNs that may cross each other in a predictable manner. Ideally, this description should be made with a model, thus allowing for outcome predictions of natural selection acting on different genotypes occurring in diverse environments.

In this sense, many efforts have been made toward describing actual RNs. Often, such studies have used a simple experimental design: individuals of each genotype are allowed to develop at two, or a maximum of three different environments; and the RNs are described as the lines that are traced connecting the phenotypic values of each genotype (Thomas and Barker 1993; Noach et al. 1997; Bitner-Mathé and Klaczko 1999; Pérez and Garcia 2002; Elberse et al. 2004; Andrade et al. 2005; Gutteling et al. 2007; Ellers and Driessen 2011). This two/three-point-curve experimental design has already been used to produce a variety of empirical data which led to the emergence of different views on G×E, RN, and PP. For clarity, here we will characterize the two ends of a continuum which contains these different views. We named these epistemological views as “optimistic” and “pessimistic,” referring to their attitude toward the possibility of describing and understanding RN variation. The optimistic view seeks the understanding of G×E through the use of a simple model to describe RN variation. The pessimistic view, however, states that RNs vary in such complex ways that it becomes impossible to model and generalize G×E.

Additionally to the use of a model, the optimistic view is characterized by the belief that the simplest possible RN model—the linear equation—is a legitimate simplification of actual RNs. Thus, RN variation would be summarized by the parameters *b*_{0} (intercept or elevation) and *b*_{1} (slope) in the RN function *P*=*b*_{0}+*b*_{1}*E*, where *P* is the phenotypic value and *E* the environment. Thus, genotypes with different elevations but with the same slope would have RNs that run side to side, keeping the same rank order along the environmental axis (Fig. 1A); whereas genotypes with varying slopes but constant elevation would have different responses to the same environmental variation (different PPs), and their curves would cross each other, leading to predictable changes in rank order as the environment varies (Fig. 1B). Hence, the optimistic view promotes the building of models of RN and PP evolution (de Jong 1990; Gavrilets and Scheiner 1993; Scheiner 1993; de Jong 2005; Zhang 2006; Ghalambor et al. 2007; Nussey et al. 2007; Aubin-Horth and Penn 2009; Lande 2009; King and Roff 2010; Reed et al. 2010) by feeding characteristic RN parameters into models.

On the other hand, the pessimistic view is characterized by the lack of an attempt to adjust any model, due to the perception that RNs show complex variation, crossing each other more frequently than expected by the linear model (Byers 2005) (Fig. 1C). Consequently, under this view it is not possible to build models to predict the evolution of RN shape (PP), and G×E is a synonym of unpredictable and ubiquitous rank order changes among environments. Thus, it perceives RN complexity as leaving no hope for further understanding, leading to the classical aphorism “it is impossible to say which genotype is better or worse” (Lewontin 1974; Gottlieb 2007; Vale et al. 2008).

Both the optimistic and the pessimistic views find support on empirical data. Part of the two/three-point-curve studies seems to provide empirical support for the optimistic view, showing RNs that seem to be actually linear (e.g., Coyne and Beecham 1987 and Liefting et al. 2009). However, other studies results seem to support the pessimistic view: three-point-curve RNs that vary in a seemingly random manner, with each genotype curve having its maximum and minimum values at any of the three environments, and RNs crossing each other more frequently than expected by the linear model (e.g., Fig. 2 in Lewontin 1974).

Both views are represented and reinforced by studies which have addressed key issues on RN evolutionary genetics, arriving at important conclusions. Using a measure of plasticity derived from the optimistic view, Scheiner and Lyman (1991) performed a selection experiment to test the genetic independence between the mean value and the plasticity of a trait. They found that the response for selection for the mean thorax length of *Drosophila melanogaster* and for its plasticity were independent, and interpreted these results as supporting the epistasis model, that is, that the plasticity of a trait and the trait mean value are determined by different loci. On the other hand, the pessimistic view is clearly present in the work of Gupta and Lewontion (1982), which paradoxically made an emphatic defense of the importance of knowing RNs, against the analysis of phenotypic variance. After analyzing the response of three traits of *D. pseudoobscura* to three temperatures, they stressed that “the essential feature of the norms of reaction” is “that they cross each other so that the large main effect of genotype does not allow one to assume that there are really ‘better’ or ‘worse’ genotypes” (Gupta and Lewontin 1982).

Unmistakably, the results which support the pessimistic view are evidence against the central assumption of the optimistic view: RNs that cross each other more than once are necessarily nonlinear. Indeed, since the pioneer work of Krafka (1920), a number of studies which have described RNs using more than three environments (Thomas 1993; Rocha et al. 2009; and many papers from J. David's group, see below) often show RNs which are clearly nonlinear, even for RNs that had previously been treated as linear (e.g., Coyne and Beecham 1987). Nonetheless, despite the potential consequences of these findings, the two prevailing views on RNs, PP, and G×E seem to remain unchanged.

In a previous work, using 11 different temperatures to test each strain, we have shown that the RNs of the number of dark spots in the abdomen of *D. mediopunctata* are well described by parabolas (Rocha et al. 2009). Using these curves to test the consensus on the independence between the mean value and the plasticity of a trait, we found a significant correlation between the mean number of spots of each strain and its RN shape (curvature). The RNs change from bowed downward to bowed upward parabolas as the mean number of spots across all temperatures of each strain increases (Rocha et al. 2009). Hence, in contrast with Scheiner and Lyman (1991) who favored the epistasis model, our results supported the pleiotropy model (Via 1993), which states that the same locus determines both the plasticity and the mean value of a trait. By using a nonlinear model for RN description, we could find a pattern of genetic association between the mean value and the plasticity of a trait not assessable to linear models, thus highlighting the methods’ power and providing evidence that its use may lead to a different view on RNs.

Taken together, these findings bring up some questions: (1) Are RNs typically linear or nonlinear curves? (2) Is the pessimistic view a consequence of a linear simplification of nonlinear RNs? and (3) What is being lost with the RN linear model that nonlinear models reveal? To address question (1), we described and analyzed a set of 40 RNs of five traits of *D. mediopunctata* in response to 11 temperatures. We tried to find, for each of the 40 curves, the polynomial with best significant fit, that is, the function which would get closest to the underlying RN shape. The generality of our findings was assessed by comparing our results to published RNs with more than three points. To investigate question (2), we have reduced the 11 temperature RNs to three temperature RNs and compared the results of the analysis of these two sets of curves as to the possibility of describing RN variation. Question (3) was addressed by verifying if the conclusions of two published studies based on the linear model may be affected by the nonlinearity of the RNs. Finally, we tried to delineate a view on RN, PP, and G×E which takes into account the nonlinearity of RNs, pointing out methodological issues and questions which would result from the adoption of such view.