Published August 30, 2016

RESEARCH

Introduction to a Special Issue on Genotype by Environment Interaction Natalia de Leon,* Jean-Luc Jannink, Jode W. Edwards, and Shawn M. Kaeppler

ABSTRACT Expression of a phenotype is a function of the genotype, the environment, and the differential sensitivity of certain genotypes to different environments, also known as genotype by environment (G ´ E) interaction. This special issue of Crop Science includes a collection of manuscripts that reviews the long history of G ´E research, describes new and innovative ideas, and outlines future challenges. Improving our understanding of these complex interactions is expected to accelerate plant breeding progress, minimize risk through improved cultivar deployment, and improve the efficiency of crop production through informed agriculture. Achieving these goals requires the integration of broad and diverse science and technology disciplines.

N. de Leon, Dep. of Agronomy, UW-Madison, Madison, WI 53706; J.-L. Jannink, USDA-ARS, Cornell Univ., Ithaca, NY, 14853; J.W. Edwards, Dep. of Agronomy, Iowa State Univ., Ames, IA 50011; S.M. Kaeppler, Dep. of Agronomy, UW-Madison, Madison, WI 53706. Received 18 July 2016. *Corresponding author ([email protected]). Abbreviations: CGM, crop growth models; G ´ E, genotype by environment; GGE, genotype main effects and G ´ E; QTL, quantitative trait locus.

Overview The ability of an individual to achieve the maximum potential encoded in its genome is a function of the environment in which it completes its life cycle. Evolution provides numerous examples of exquisite adaptations that allow species and individuals within species to excel in specific environmental contexts. Polar bears (Ursus maritimus), as an example, are a relatively new subspecies derived from brown bears (Ursus arctos). As a mechanism to adapt to the harsh Arctic environments, polar bears have developed specializations such as pigment-free and hollow core fur (Miller et al., 2012). While beneficial in some environments, these adaptations may be detrimental in others. In humans, for example, it is hypothesized that when food is scarce, people with a taste for sweet and fatty foods may have higher survival rates than others, whereas when food is plenty, the reverse may be true. Humans have noticed and managed these adaptations for agricultural production of crops and animals. For example, the terroir of wine is a term used to describe the specific flavors that are a component of specific vintages due to factors such as soil, plants in the vineyard, and the specific season. These unique characteristics can result in tremendous differences in the value of bottles of wine produced from the same variety of grape.

Published in Crop Sci. 56:2081–2089 (2016). doi: 10.2135/cropsci2016.07.0002in © Crop Science Society of America | 5585 Guilford Rd., Madison, WI 53711 USA This is an open access article distributed under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). crop science, vol. 56, september– october 2016 

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Expression of a phenotype is a function of the genotype, the environment and differential phenotypic response of genotypes to different environments, also known as genotype by environment (G ´ E) interaction. This term formally refers to a statistical decomposition of variance and provides a measure of the relative performance of genotypes grown in different environments. Plant breeders have managed and leveraged these interactions throughout the history of crop domestication, crop improvement, and dispersal, and within recent history through the formalized procedures of plant breeding. This issue of Crop Science contains a collection of articles focusing on the topic of G ´ E interactions. This special issue is spurred by the exciting emerging potential of more efficiently adapting genotypes to current and future environmental contexts due to the confluence of extensive genome sequence, advanced environmental monitoring, new tools to monitor crop growth throughout the life cycle, and unprecedented computational capacity allowing the wealth of new information to be incorporated in predictive models of ever-increasing detail and value. The topic of G ´ E has been of continued interest throughout the history of this journal. In fact, four of the top 30 most-cited articles in the history of the journal are related to this topic indicating its long-standing importance in crop breeding and production (in order of citation number: Eberhart and Russell, 1966; Allard and Bradshaw, 1964; Lin et al., 1986; Rosielle and Hamblin, 1981). The review article by Allard and Bradshaw (1964) stated that “aside from the satisfaction that would accompany understanding of the biochemical, physiological, or morphological basis of the interplay between genotype and environment, the question arises whether studies of basic causes have anything to offer the practicing breeder whose primary responsibility is to develop and identify superior varieties.” Advances in the identification of loci affecting quantitative traits (QTL) and in the use of crop growth models (CGM) lead us to posit the answer is “yes.” The applied breeder now has unprecedented ability to manipulate genes identified as mechanistically involved in G ´ E. Likewise, interactions that are understood at morphological and physiological levels can be predicted using CGM, leading to target ideotypes defined phenotypically, as promoted for many years (Donald, 1968), or genetically as in new approaches (Technow et al., 2015).

Definition and Importance of G ´ E

A conceptual G ´ E interaction is commonly depicted as the slope of the line when genotype performance is plotted against an environmental gradient (Fig. 1). Non-parallel, but non-intersecting lines indicate that the rank of cultivar performance stays the same across environments. Lines that intersect indicate that there is a change in rank of cultivars across environments, and the optimum cultivar will 2082

be location specific. G ´ E affects virtually every aspect of the decision making process involved in plant breeding programs including identification of the most relevant testing environments, allocation of resources within a breeding program, and choice of germplasm and breeding strategy. G ´ E can also be conceptualized as a measurement of the relative plasticity of genotypes in terms of the expression of specific phenotypes in the context of variable environmental influences. Although a clear divide characterizes the long and rich history of the scientific field concerned with phenotypic plasticity, one foundational understanding has united researchers across disciplines: the ability of genotypes to express different phenotypes when influenced by different environmental signals has a genetic basis. The divide comes from the focus that different groups of researchers have taken to study this phenomenon. On the one hand, phenotypic plasticity has been the focus of much research in the field of molecular and evolutionary biology studying natural populations and model species. Efforts in that area have typically aimed at understanding the biological and genetic fundamentals of this plasticity and its evolution. In the early 1960s the work by Bradshaw (1965) provided much of the foundation to this area of research. Through the use of relevant examples, his pioneer efforts elucidated a fundamental understanding of the genetic basis of phenotypic plasticity and the significance of this phenomenon for adaptation of specific genotypes as a function of the expression of specific traits in response to environmental influences to which they are exposed (Bradshaw, 1965). A somewhat complementary and more pragmatic view of phenotypic plasticity emerged in the field of animal and plant breeding (Pigliucci, 2001). Falconer (1952) introduced the idea that G ´ E could be considered as the pleiotropic effect of particular variants across environments. This concept implies that any given trait when evaluated across more than one environment can be analyzed as genetically correlated traits. In this case, the magnitude of such a correlation indicates the degree of shared genetic control and the sign of the correlation indicates the direction of the allelic effect for the environments being considered. This perspective has provided an important framework for interpreting and handling G ´ E in plant breeding programs (Des Marais et al., 2013). As with most other areas of quantitative genetics, this has led to the development of statistical as opposed to biological parameters to quantify, understand, and interpret G ´ E in plant breeding (Malosetti et al., 2013). The study of the genetic nature of G ´ E is complicated by the fact that such statistics have to be calculated and interpreted in the context of a specified universe of environments: specific assumptions of what constitutes reasonable environments need to be determined before any inferences can be made from G ´ E measurements. This fact calls for the need to establish appropriately-sized field evaluations involving relevant environmental conditions rather than contrasting

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Fig. 1. The G ´ E (VGE) displayed here illustrates two components, homogeneity vs. heterogeneity of the genetic variance (VG) and the correlation between performance across environment. (A) Homogeneity of VG and no correlation between environments; (B) Heterogeneity of VG in different environments and no correlation between environments; (C) Crossover interactions are due to imperfect correlations between genotypic performance across environments (in this case -1) and here homogeneous VG; (D) VGE is due to a combination of heterogeneous VG and an imperfect correlation between genotypic performance across environments.

controlled environment evaluations which by design are expected to provide an overestimation of the variation compared to that found in natural conditions (Anderson et al., 2014). Thus meaningful assessments of G ´ E require long term research as responses are expected to vary significantly from year to year (Agren and Schemske, 2012).

Methods of Measuring G ´ E Historically breeders have recognized the potentially negative implications of G ´ E in selection and cultivar deployment and have focused on developing tools and resources to quantify it as a first step toward minimizing its detrimental effect and, whenever possible, taking advantage of positive interactions (Freeman, 1973; Cooper, 1999; Cooper et al., 2014; Sadras and Richards, 2014). Commonly, target cultivars are identified for deployment to specific sets of environments (Cooper et al., 1997; Chapman et al., 1997). That identification ideally proceeds from the interpretation of analyses that measure the differential sensitivity of genotypes to environments and that connect that variation to particular biological mechanisms (Sadras and Richards, 2014). A proportion of the G ´ E studies have used managed stress trials to emphasize the effect of particular sources of, generally, abiotic stresses on the performance of diverse crop science, vol. 56, september– october 2016 

genotypes. Although this approach has shown promise for understanding the effects of particular environmental disruptions on phenotypes, they are usually difficult (and therefore expensive) to implement. Most of the evaluations of the effect of the environment on performance in plant breeding have relied on multi-environmental field testing that represent target production environments and those are used to identify and develop cultivars (Comstock, 1977). These multi-location studies provide two-way tables of means for diverse genotypes across different environments. Data from such two-way tables can be initially analyzed using models that incorporate the effect of the genotype, the environment, and also that partition the remaining variation into the effect of the interaction between environments and genotypes and the residual experimental error. This provides a good indication of the proportion of the variance that refers to the main effect of genotype compared to G ´ E, but it is limited in terms of providing insight into the nature of the interaction. Much of that descriptive information, in the context of plant breeding, has been founded on the work by Finlay and Wilkinson (1963) and modified by others (Eberhart and Russell, 1966) which qualified G ´ E based on the slope of the regression of the performance of particular genotypes across an environmental gradient. The most basic

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models determine this quality gradient based on the average performance of all genotypes in that environment. This methodology permits to interpolate the performance of the specific genotypes being investigated across untested environments, as long as the environments are within the range of the gradient in tested locations. This traditional concept of stability is useful for the study of phenotypic plasticity as it provides a single measurement of the slope of the regression line of genotypes along environmental gradients which can be used as the entry phenotype for genotypic-phenotypic associations, for example, to understand the genetic architecture of plasticity itself. Other complementary and well recognized methods developed to assess environmental stability include mean-CV analysis from Francis and Kannenberg (1978) and Shukla’s (1972) stability variance. A significant expansion of traditional methodologies to describe G ´ E involves the incorporation of multidimensional environmental characterizations to statistical models. The additive main effects and multiplicative interaction (AMMI) model was one of the initial implementations of this strategy (Gollob, 1968; Gauch, 1988). In this context, G ´ E is modeled as the product of the effect of the specific sensitivity of a genotype to a latent (unobservable) environmental variable. A principal components strategy maximizes the variation explained by the products of the resulting genotype sensitivities by environmental variables (Gabriel, 1978). Another variant to this overall strategy came through the development of modeling strategies that incorporated not only the G ´ E variation but also the combined effect of the genotypic main effect and the G ´ E as a sum of the multiplicative terms. This general set of methods are called “genotype main effects and G ´ E” or GGE model (Yan et al., 2000). These multiplicative strategies are particularly useful because they provide meaningful graphical displays of performance which allows direct interpretation of the relationship between specific environments and between particular genotypes, and, in the case of GGE, direct interpretation of the effect of specific genotypes in particular environments. From the standpoint of improving the interpretation of the effect of particular environmental effects on performance, another advancement came from the incorporation of explicit quantification of environmental components to statistical models as explanatory variables. These so-called factorial regression models connect the differential sensitivity of genotypes to observed environmental variables (e.g., rainfall in May) which could be chosen based on what is needed for crop growth (van Eeuwijk et al., 1996). Since overall performance is what breeders are interested in, this type of analysis facilitates direct biological interpretation of performance and therefore has direct utility for practical breeding programs. Several mixed model applications have also been proposed to analyze and interpret G ´ E primarily for multi-environment analysis that involves a large number of genotypes (Smith et al., 2005). In this context, genotypes can be modeled as random effects and their potential 2084

heterogeneity of variances (and co-variances) can be interpreted as an indication of differential genotypic sensitivity to certain environmental cues. A more in-depth description of this and other similar and related methodological approaches can be found in Malosetti et al. (2013).

Genetic and Physiological Mechanisms of G ´ E The differential expression of certain genotypes in the presence of distinctive environmental factors has been assessed using condition-dependent mutants such as those presenting specific sensitivity to light, water, and hormones. The primary goal of such studies is to identify genetic models that could describe pathways directly affected by those environmental interactions (Kim et al., 2009; Cutler et al., 2010). More recently, genomewide transcriptional studies have also assessed the responses of contrasting genotypes when exposed to various types of environmental stresses. In those studies, numerous transcripts appear to be up or downregulated and the combination of that information has proven useful in terms of identifying relevant regulatory networks associated with that response (e.g., Zou et al., 2011). However, specific characteristics of the natural variants regulating those pathways is still largely unknown (Des Marais and Juenger, 2010; Juenger, 2013). In a recent study, DesMarais et al. (2013) have attempted to gain insight about the most important genomic regions associated with G ´ E through a meta-analysis of available studies that have evaluated the association of phenotypes and genotypes across multiple environmental conditions. This meta-analysis included crop species and natural populations and assessed a variety of traits. A number of interesting patterns and mechanisms associated with G ´ E were identified across the diversity of traits, species and environmental treatments assessed. Overall, the control of G ´ E appears to involve multiple genetic regions. Although the summary provided in this review is very enlightening, the majority of the studies involved natural populations or model species evaluated in contrasting conditions within controlled environments. An expansion to include studies involving crop species in natural production conditions will provide an additional perspective on these findings. Several potential mechanisms have been proposed to explain the genetic basis of G ´ E (reviewed by El-Soda et al., 2014). These interactions have been associated with pleiotropic effects that can range from antagonistic effects to, what is most commonly observed, a differential sensitivity of alleles across environments (Scheiner, 1993; DeWitt et al., 1998; Agrawal, 2001; Pigliucci, 2005). Several examples of these types of relationships are available in the literature for naturally and artificially selected populations (Hall et al., 2010; Hancock et al., 2011, Brekke et al., 2011a, 2011b; Anderson et al., 2013). A complementary mechanism invoked to help explain G ´ E involves the effect of the genetic background, which can differentially affect a trait in distinct environments. Although it is intuitively easy to imagine that this

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epistatic relationship should frequently occur, the ability to empirically demonstrate this relationship has been challenging, due to the limited power most studies have to detect statistically significant interaction effects (Alcazar et al., 2009) in the context of multi-environment testing. Additionally, the complex relationship of alleles within a locus has been suggested to affect G ´ E: the presence of more than one allele at a locus is directly associated with phenotypic plasticity in outbred species or in the comparison of inbreds and hybrids involving self-pollinated species. This property is especially relevant for transient environmental conditions to which different alleles confer adaptation. It is also well recognized that environmental factors can influence levels of DNA methylation and alter chromatin states. Such epigenetic modulation has been proposed as a mechanism affecting plasticity levels of specific plant genotypes across environments (Reinders et al., 2009; Bossdorf et al., 2010; Mirouze and Paszkowski, 2011; Pecinka and Mittelsten-Scheid, 2012; Zhang et al., 2013). The relative contribution of the diverse set of mechanisms just described is an active field of study in evolutionary science. It is important to highlight, however, that most of the molecular characterizations conducted to date focused on plant model species or combinations of naturally occurring populations evaluated in controlled conditions and frequently involved pairs of discrete and contrasting environments rather than a more realistic continuous array of complex and interactive climatic factors such as those present in production environments.

Content of this Special Issue Greater gain from selection will come from greater ability to predict the performance of specific genotype-environment combinations. Prediction of future combinations in turn depends on a deeper understanding of performance of past combinations, as determined by detailed data on each component and the ability to meaningfully analyze that data. Plant breeders and geneticists are now poised to collect that detailed data in ways unimagined even 5 yr ago. Three types of information are needed to train prediction models: genotypic, phenotypic, and “envirotypic,” the latter neologism, with its cognate “envirotyping,” meaning comprehensive measurement of environmental characteristics (e.g., weather and soil characteristics). The cost of collecting all three types continues to decline, thanks to innovations in sequencing, and automated field recording of phenotypes and weather.

Woven through both the collection and analysis of these data are new computer technologies that, through power and miniaturization, enable automated data collection (e.g., highly sensitive detectors in small drones to regularly scan fields) and large scale analyses (e.g., statistical models incorporating millions of genotypic data points). Naturally, having the data does not equate with knowing how best to analyze and interpret it. Contributions on G ´ E analysis in this issue are gathered to assess what tools plant breeders have, what opportunities are becoming available, some analysis ideas, and some initial attempts at applying the wealth of new data becoming available. The issue starts with four reviews. The first reflects on the history of G ´ E analyses providing references to the giants on whose shoulders we now stand (Elias et al., 2016, this issue). The second gives an excellent overview and perspective for junior researchers about G ´ E analyses, giving them a learning program of practical approaches using modern but by now well-tested tools (van Eeuwijk et al., 2016, this issue). For practicing breeders, Yan et al. (2016, this issue) provide a worked example of a useful selection tool in GGE biplot analysis. Finally, Hayes et al. (2016, this issue) give an animal breeding perspective and suggest that animal and plant breeders are in a process of converging on common solutions to the analysis of G ´ E. From there, articles in the issue address development of new methods to design and analyze multi-environment trials. Regardless of new technologies, running such trials is expensive, and therefore they should be optimally designed. Kleinknecht et al. (2016, this issue) provide a simulation approach, conditioning on parameters such as the number of entries and the variance components to be expected in the trials. In the analysis of trials, separating signal from noise is the initial goal, one for which the AMMI model has shown good properties. Paderewski et al. (2016, this issue) extend that analysis to four-way factorials including entries, locations, years, and management practices. We then come to the focal task of performance estimation or prediction. The issue collects several reports on method development for this purpose. A useful taxonomy of prediction challenges has developed in the context of G ´ E research that we describe here in an attempt to categorize methods. Given a matrix of individuals observed in environments, different types of information may be available for prediction (Table 1).

Table 1. Taxonomy of prediction challenges. Validation environments

Validation individuals

Tested for some individuals

Not tested

Tested in some environments

CV2†/(G ;E )§

CV3‡/(Gt;Eu)§

Not tested

CV1†/(Gu;Et)§

CV4/(Gu;Eu)§

t

t

† Defined in Burgueno et al. (2012). ‡ Used in Heslot et al. (2014). § Defined in Malosetti et al. (2016, this issue), where the superscript t and u indicate tested and untested, respectively. crop science, vol. 56, september– october 2016 

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Among these cross-validation schemes, CV2 is clearly the “easiest” in the sense that cross-validation accuracies are most likely to be high. From there, CV1 and CV3 present different challenges: as the difference between validation and training individuals increases, CV1 accuracies will decrease. Likewise, as the difference between validation and training environments increases, CV3 accuracies will decrease. Logically, CV4 should prove to be the most challenging. Three papers in this issue dissect the overall G ´ E to the marker level, applying models that estimate marker by environment interaction. Crossa et al. (2016, this issue) work through a durum wheat (Triticum turgidum ssp. durum) dataset using this approach to improve accuracies in environments that have been observed for some individuals. Jarquín et al. (2016, this issue) develop a Bayesian implementation of the problem. Lado et al. (2016, this issue) address the issue of unbalanced datasets common in practical breeding programs showing how estimating performance covariance across environments can improve accuracy. To move from prediction for past to future environments, that is, to go from the first to the second column in the Table above, it is necessary to consider the nature of the information available about environments. Environments are characterized by many biotic (e.g., pathogens, insects, weeds, beneficial microbes) and abiotic factors (e.g, temperature, rainfall, insolation, soil quality). Each of these factors can, in turn, be split myriad ways (e.g., pathogen variants or timing or rainfall quantities in different time slices). The challenge is to discover, among all these quantities, which are important. As suggested by Heslot et al. (2013), the problem has some parallels to that of quantitative trait locus (QTL) identification or prediction in that we need phenotypes to sort through potentially numerous predictors. In effect, these phenotypes represent the translation of environmental inputs into observable traits, that is, actual plants process the inputs from “the plant’s eye view.” The clever device of using probe genotype performance to characterize environments also recognizes the value of allowing plants to “interpret” the effects of environmental inputs (Cooper and Fox, 1996). The task of crop physiology is to enable scientists to do something similar, and the sum total of its lessons are instantiated in CGM. Two further method development articles take up the use of CGM in predicting G ´ E. In Cooper et al. (2016, this issue) the CGM is the actual prediction model, run with physiological parameters determined by iterations of random sampling of marker effects on the parameters and retaining only iterations with model outputs close to observed data. A challenge of this approach is that the CGM needs multiple parameter values, but only one trait is observed: final yield. Extrapolating from one trait to multiple parameters seems akin to locating a point in a high-dimensional space based solely on its projection in a low-dimensional space. We might envision data from 2086

a time series generated by high-throughput phenotyping to overcome the data (though not the computational) shortfall of this approach. Malosetti et al. (2016, this issue), in contrast, retain linear mixed models for prediction as is standard. They emphasize the need to estimate the covariance between measurements of the same trait across environments. When trials have been performed in the environments, the translation of environmental inputs to phenotypes has been observed and such covariances can be estimated from the data. Statistical expertise is required to strike a balance between model parsimony and model fit. In the absence of such trials (i.e., for future environments), Malosetti et al. (2016, this issue) suggest estimating the covariances directly from measures or predictions of environmental inputs themselves, as also proposed by Jarquín et al. (2014). Crop growth models, however, are also discussed and, reading between the lines, we again might envision the use of CGM to predict covariances among environments of varying similarity. The issue is completed by three empirical studies of G ´ E that show the breadth of approaches available even under classical analysis methods. Grogan et al. (2016, this issue) analyze the variation of maturity and yield across environments (i.e., the plasticity of these traits) relative to the trait means in wheat. They find that over time selection decreased responsiveness of maturity to environment but increased that of yield: even as wheat varieties are becoming more predictable in their harvest times, their yields are becoming more responsive to favorable environmental opportunities. While a known response to breeding in maize has been an increase in its tolerance to high-density planting, interactions between response to density and environment have not been studied. Edwards (2016) shows that there is indeed G ´ E for response to density such that different hybrids will be at different distances from their optimal densities across environments. This poses an unexplored methodological problem for breeders. Finally, Lee et al. (2016, this issue) dissect the environmental determinants of G ´ E for yield in a phenologically uniform biparental population. Careful model building surprisingly supports the hypothesis that variation in thermal time and solar radiation across years generates more G ´ E than soil water availability.

Taking it to the Next Level Factors such as variable climate conditions, increasing world population, improvements in diets, and a growing demand for alternative uses for agricultural products are expected to increase the need for more efficient agricultural production. Meeting this challenge will largely depend on our ability to generate and manage crop varieties with high productivity in the context of variable environments. Current indicators suggest that traditional breeding techniques are unlikely to meet this demand.

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Plant genome research has generated copious amounts of genomic data and tools. A bottleneck in phenotyping subsists, however, for employing this data to improve agricultural crops. Plant productivity is a direct consequence of how well adapted the genotype of an individual is to the surrounding environment. Useful phenotypic characterization is therefore location-specific and represents the integration of the entire lifecycle of the plant and the local environmental conditions. To truly increase efficiency in agricultural production, a key component will be to predict accurately the performance of specific genotypes across a wide range of variable environments. An overwhelming number of published studies have investigated the role of G ´ E in plant breeding. This wealth of information has mostly focused on developing tools to quantify its magnitude and utilize that information to identify strategies to minimize its potentially negative effect in cultivar advancement and deployment to appropriate environments. While this wealth of information has contributed to our ability to manage G ´ E in a plant breeding context, these studies have also highlighted the complexity of this phenomenon, as the opportunities for genotypes and environments to interact throughout the lifetime of a plant are effectively unlimited. Yield is the single most important measure of plant productivity. Its integration of all environmental conditions over the season, however, obscures the process by which the plant achieved its end of the season state. Technological advances are expected to allow the deployment of small and inexpensive sensors and robotic units for highthroughput field phenotyping. Plants are dynamic living systems that change constantly. Our ability to measure the effect of environmental influences affecting intermediate developmental stages (maybe to the level of daily changes) through the deployment of high-throughput phenotyping tools provide the opportunity to dissect G ´ E into smaller time sensitive components and as such contribute to our understanding of the main factors limiting end of the season productivity. The combination of rich genomic information and detailed environmental assessments allows not only an enhanced ability to quantify and mitigate the unrepeatable portion of G ´ E, but also to genetically characterize it in economically important crops in the context of relevant production conditions. A deeper understanding of the types of genetic architectures and mechanisms controlling G ´ E will provide additional opportunities to engineer crop varieties with enhanced capacity to tolerate and thrive in ever-changing sets of environments. Similarly, a deeper understanding of the specific environmental components that generate crossover G ´ E interactions at specific plant developmental stages is expected to enhance our ability to determine the value of on-the-fly management decisions. crop science, vol. 56, september– october 2016 

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