The Experts below are selected from a list of 255 Experts worldwide ranked by ideXlab platform
José Crossa - One of the best experts on this subject based on the ideXlab platform.
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bgge a new package for genomic enabled prediction incorporating Genotype Environment Interaction models
G3: Genes Genomes Genetics, 2018Co-Authors: Italo Stefanine Correia Granato, José Crossa, Juan Burgueño, Jaime Cuevas, Osval A Montesinoslopez, Francisco Javier Lunavazquez, Roberto FritschenetoAbstract:One of the major issues in plant breeding is the occurrence of Genotype × Environment (GE) Interaction. Several models have been created to understand this phenomenon and explore it. In the genomic era, several models were employed to improve selection by using markers and account for GE Interaction simultaneously. Some of these models use special genetic covariance matrices. In addition, the scale of multi-Environment trials is getting larger, and this increases the computational challenges. In this context, we propose an R package that, in general, allows building GE genomic covariance matrices and fitting linear mixed models, in particular, to a few genomic GE models. Here we propose two functions: one to prepare the genomic kernels accounting for the genomic GE and another to perform genomic prediction using a Bayesian linear mixed model. A specific treatment is given for sparse covariance matrices, in particular, to block diagonal matrices that are present in some GE models in order to decrease the computational demand. In empirical comparisons with Bayesian Genomic Linear Regression (BGLR), accuracies and the mean squared error were similar; however, the computational time was up to five times lower than when using the classic approach. Bayesian Genomic Genotype × Environment Interaction (BGGE) is a fast, efficient option for creating genomic GE kernels and making genomic predictions.
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genomic models with Genotype Environment Interaction for predicting hybrid performance an application in maize hybrids
Theoretical and Applied Genetics, 2017Co-Authors: Rocio Acostapech, José Crossa, Gustavo De Los Campos, Simon Teyssedre, Bruno Claustres, Sergio Perezelizalde, Paulino PerezrodriguezAbstract:A new genomic model that incorporates Genotype × Environment Interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids. The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-Environment trials play an important role in the selection of important traits, such as stability across Environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing Genotype × Environment Interaction (G × E), such that the estimated genetic correlations of the performance of individual lines across Environments summarize the joint action of genes and Environmental conditions. This article proposes a genomic statistical model that incorporates G × E for general and specific combining ability for predicting the performance of hybrids in Environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 Environments over 12 years; analyses were performed for each year. On average, genomic models that include the Interaction of general and specific combining ability with Environments have greater predictive ability than genomic models without Interaction with Environments (ranging from 12 to 22%, depending on the trait). We concluded that including G × E in the prediction of untested maize hybrids increases the accuracy of genomic models.
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genomic prediction of Genotype Environment Interaction kernel regression models
The Plant Genome, 2016Co-Authors: Jaime Cuevas, José Crossa, Gustavo De Los Campos, Sergio Perezelizalde, Paulino Perezrodriguez, Victor Soberanis, Osval A Montesinoslopez, Juan BurgueñoAbstract:In genomic selection (GS), Genotype × Environment Interaction (G × E) can be modeled by a marker × Environment Interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-Environment analyses and extended to account for G × E Interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-Environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all Environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single Environment for pairs of Environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific Interaction effects.
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from Genotype Environment Interaction to gene Environment Interaction
Current Genomics, 2012Co-Authors: José CrossaAbstract:Historically in plant breeding a large number of statistical models has been developed and used for studying Genotype × Environment Interaction. These models have helped plant breeders to assess the stability of economically important traits and to predict the performance of newly developed Genotypes evaluated under varying Environmental conditions. In the last decade, the use of relatively low numbers of markers has facilitated the mapping of chromosome regions associated with phenotypic variability (e.g., QTL mapping) and, to a lesser extent, revealed the differetial response of these chromosome regions across Environments (i.e., QTL × Environment Interaction). QTL technology has been useful for marker-assisted selection of simple traits; however, it has not been efficient for predicting complex traits affected by a large number of loci. Recently the appearance of cheap, abundant markers has made it possible to saturate the genome with high density markers and use marker information to predict genomic breeding values, thus increasing the precision of genetic value prediction over that achieved with the traditional use of pedigree information. Genomic data also allow assessing chromosome regions through marker effects and studying the pattern of covariablity of marker effects across differential Environmental conditions. In this review, we outline the most important models for assessing Genotype × Environment Interaction, QTL × Environment Interaction, and marker effect (gene) × Environment Interaction. Since analyzing genetic and genomic data is one of the most challenging statistical problems researchers currently face, different models from different areas of statistical research must be attempted in order to make significant progress in understanding genetic effects and their Interaction with Environment.
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From Genotype × Environment Interaction to Gene × Environment Interaction
Current Genomics, 2012Co-Authors: José CrossaAbstract:Historically in plant breeding a large number of statistical models has been developed and used for studying Genotype × Environment Interaction. These models have helped plant breeders to assess the stability of economically important traits and to predict the performance of newly developed Genotypes evaluated under varying Environmental conditions. In the last decade, the use of relatively low numbers of markers has facilitated the mapping of chromosome regions associated with phenotypic variability (e.g., QTL mapping) and, to a lesser extent, revealed the differetial response of these chromosome regions across Environments (i.e., QTL × Environment Interaction). QTL technology has been useful for marker-assisted selection of simple traits; however, it has not been efficient for predicting complex traits affected by a large number of loci. Recently the appearance of cheap, abundant markers has made it possible to saturate the genome with high density markers and use marker information to predict genomic breeding values, thus increasing the precision of genetic value prediction over that achieved with the traditional use of pedigree information. Genomic data also allow assessing chromosome regions through marker effects and studying the pattern of covariablity of marker effects across differential Environmental conditions. In this review, we outline the most important models for assessing Genotype × Environment Interaction, QTL × Environment Interaction, and marker effect (gene) × Environment Interaction. Since analyzing genetic and genomic data is one of the most challenging statistical problems researchers currently face, different models from different areas of statistical research must be attempted in order to make significant progress in understanding genetic effects and their Interaction with Environment.
Rafael L. Rodríguez - One of the best experts on this subject based on the ideXlab platform.
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Causes of variation in Genotype × Environment Interaction
Evolutionary Ecology Research, 2013Co-Authors: Rafael L. RodríguezAbstract:Questions: What sustains genetic variation in plasticity (Genotype × Environment Interaction, G × E) under selection across Environments? What explains variation among traits and species in the expression of G × E? Hypotheses and methods: I review two hypotheses that seek to explain variation in the expression of G × E. The grain-size hypothesis attempts to elucidate when selection can erode G × E, as it shapes patterns of phenotypic plasticity across Environments. The developmental architecture hypothesis identifies developmental features that make traits vary in the propensity to express G × E. I also review studies that have addressed patterns of geographic variation in G × E, and discuss metrics of the strength of G × E that will facilitate future comparisons across traits and taxa. Conclusions: There is tentative support for both the grain-size and the developmental architecture hypotheses, but further work is required to explain the maintenance of G × E and variation in its expression. I describe scenarios in which, on the one hand, G × E may promote the maintenance of genetic variation and hinder sexual selection, versus on the other, promote evolutionary divergence under natural and sexual selection.
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Grain of Environment explains variation in the strength of Genotype × Environment Interaction
Journal of evolutionary biology, 2012Co-Authors: Rafael L. RodríguezAbstract:Theory predicts that genetic variation in phenotypic plasticity (Genotype × Environment Interaction or G × E) should be eroded by selection acting across Environments. However, it appears that G × E is often maintained under selection, although not universally. This variation in the presence and strength of G × E requires explanation. Here I ask whether the explanation may lie in the grain of the Environment at which G × E is expressed. The grain (or grain size) of the Environment refers to the scale of Environmental heterogeneity relative to generation time – that is, relative to the window of operation of selection – with higher rates of heterogeneity occurring in finer-grained Environments. The hypothesis that the grain of the Environment explains variation in the expression of G × E encapsulates variation in the power of selection to shape reaction norms: selection should be able to erode G × E in fine-grained Environments but lose its power as the grain becomes coarser. I survey studies of G × E in sexual traits and demonstrate that the strength of G × E varies with the grain of the Environment across which it is expressed, with G × E being stronger in coarser-grained Environments. This result elucidates when G × E is most likely to be sustained in the reaction norms of fitness-related traits and when its evolutionary consequences will be most pronounced.
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Genotype × Environment Interaction in the allometry of body, genitalia and signal traits in Enchenopa treehoppers (Hemiptera: Membracidae)
Biological Journal of the Linnean Society, 2011Co-Authors: Rafael L. Rodríguez, Nooria Al-wathiquiAbstract:Developmental plasticity may promote divergence by exposing genetic variation to selection in novel ways in new Environments. We tested for this effect in the static allometry (i.e. scaling on body size) of traits in advertisement signals, body and genitalia. We used a member of the Enchenopa binotata species complex of treehoppers – a clade of plant-feeding insects in which speciation is associated with colonization of novel Environments involving marked divergence in signals, subtle divergence in body size and shape, and no apparent divergence in genitalia. We found no change in mean allometric slopes across Environments, but substantial genetic variation and Genotype × Environment Interaction (G × E) in allometry. The allometry of signal traits showed the most genetic variation and G × E, and that of genitalia showed the weakest G × E. Our findings suggest that colonizing novel Environments may have stronger diversifying consequences for signal allometry than for genitalia allometry. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105, 187–196.
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Genotype × Environment Interaction is weaker in genitalia than in mating signals and body traits in Enchenopa treehoppers (Hemiptera: Membracidae)
Genetica, 2011Co-Authors: Rafael L. Rodríguez, Nooria Al-wathiquiAbstract:Theory predicts that selection acting across Environments should erode genetic variation in reaction norms; i.e., selection should weaken Genotype × Environment Interaction (G × E). In spite of this expectation, G × E is often detected in fitness-related traits. It thus appears that G × E is at least sometimes sustained under selection, a possibility that highlights the need for theory that can account for variation in the presence and strength of G × E. We tested the hypothesis that trait differences in developmental architecture contribute to variation in the expression of G × E. Specifically, we assessed the influence of canalization (robustness to genetic or Environmental perturbations) and condition-dependence (association between trait expression and prior resource acquisition or vital cellular processes). We compared G × E across three trait types expected to differ in canalization and condition-dependence: mating signals, body size-related traits, and genitalia. Because genitalia are expected to show the least condition-dependence and the most canalization, they should express weaker G × E than the other trait types. Our study species was a member of the Enchenopa binotata species complex of treehoppers. We found significant G × E in most traits; G × E was strongest in signals and body traits, and weakest in genitalia. These results support the hypothesis that trait differences in developmental architecture (canalization and condition-dependence) contribute to variation in the expression of G × E. We discuss implications for the dynamics of sexual selection on different trait types.
Mateo Vargas - One of the best experts on this subject based on the ideXlab platform.
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Genotype Environment Interaction for zinc and iron concentration of wheat grain in eastern gangetic plains of india
Field Crops Research, 2010Co-Authors: José Crossa, Mateo Vargas, A K Joshi, B Arun, Ramesh Chand, Richard Trethowan, Ivan OrtizmonasterioAbstract:Abstract Zinc and iron are important micronutrients for human health for which widespread deficiency occurs in many regions of the world including South Asia. Breeding efforts for enriching wheat grains with more zinc and iron are in progress in India, Pakistan and CIMMYT (International Maize and Wheat Improvement Centre). Further knowledge on Genotype × Environment Interaction of these nutrients in the grain is expected to contribute to better understand the magnitude of this Interaction and the potential identification of more stable Genotypes for this trait. Elite lines from CIMMYT were evaluated in a multilocation trial in the eastern Gangetic plains (EGP) of India to determine Genotype × Environment (GE) Interactions for agronomic and nutrient traits. Agronomic (yield and days to heading) data were available for 14 Environments, while zinc and iron concentration of grains for 10 Environments. Soil and meteorological data of each of the locations were also used. GE was significant for all the four traits. Locations showed contrasting response to grain iron and zinc. Compared to iron, zinc showed greater variation across locations. Maximum temperature was the major determinant for the four traits. Zinc content in 30–60 cm soil depth was also a significant determinant for grain zinc as well as iron concentration. The results suggest that the GE was substantial for grain iron and zinc and established varieties of eastern Gangetic plains India are not inferior to the CIMMYT germplasm tested. Hence, greater efforts taking care of GE Interactions are needed to breed iron and zinc rich wheat lines.
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using partial least squares regression factorial regression and ammi models for interpreting Genotype Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, F A Van Eeuwijk, Martha E Ramirez, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
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using partial least squares regression factorial regression and ammi models for interpreting Genotype Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, Martha E Ramirez, F.a. Van Eeuwijk, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
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Using Partial Least Squares Regression, Factorial Regression, and AMMI Models for Interpreting Genotype × Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, Martha E Ramirez, F.a. Van Eeuwijk, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
Nooria Al-wathiqui - One of the best experts on this subject based on the ideXlab platform.
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Genotype × Environment Interaction in the allometry of body, genitalia and signal traits in Enchenopa treehoppers (Hemiptera: Membracidae)
Biological Journal of the Linnean Society, 2011Co-Authors: Rafael L. Rodríguez, Nooria Al-wathiquiAbstract:Developmental plasticity may promote divergence by exposing genetic variation to selection in novel ways in new Environments. We tested for this effect in the static allometry (i.e. scaling on body size) of traits in advertisement signals, body and genitalia. We used a member of the Enchenopa binotata species complex of treehoppers – a clade of plant-feeding insects in which speciation is associated with colonization of novel Environments involving marked divergence in signals, subtle divergence in body size and shape, and no apparent divergence in genitalia. We found no change in mean allometric slopes across Environments, but substantial genetic variation and Genotype × Environment Interaction (G × E) in allometry. The allometry of signal traits showed the most genetic variation and G × E, and that of genitalia showed the weakest G × E. Our findings suggest that colonizing novel Environments may have stronger diversifying consequences for signal allometry than for genitalia allometry. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105, 187–196.
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Genotype × Environment Interaction is weaker in genitalia than in mating signals and body traits in Enchenopa treehoppers (Hemiptera: Membracidae)
Genetica, 2011Co-Authors: Rafael L. Rodríguez, Nooria Al-wathiquiAbstract:Theory predicts that selection acting across Environments should erode genetic variation in reaction norms; i.e., selection should weaken Genotype × Environment Interaction (G × E). In spite of this expectation, G × E is often detected in fitness-related traits. It thus appears that G × E is at least sometimes sustained under selection, a possibility that highlights the need for theory that can account for variation in the presence and strength of G × E. We tested the hypothesis that trait differences in developmental architecture contribute to variation in the expression of G × E. Specifically, we assessed the influence of canalization (robustness to genetic or Environmental perturbations) and condition-dependence (association between trait expression and prior resource acquisition or vital cellular processes). We compared G × E across three trait types expected to differ in canalization and condition-dependence: mating signals, body size-related traits, and genitalia. Because genitalia are expected to show the least condition-dependence and the most canalization, they should express weaker G × E than the other trait types. Our study species was a member of the Enchenopa binotata species complex of treehoppers. We found significant G × E in most traits; G × E was strongest in signals and body traits, and weakest in genitalia. These results support the hypothesis that trait differences in developmental architecture (canalization and condition-dependence) contribute to variation in the expression of G × E. We discuss implications for the dynamics of sexual selection on different trait types.
Ken D Sayre - One of the best experts on this subject based on the ideXlab platform.
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using partial least squares regression factorial regression and ammi models for interpreting Genotype Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, F A Van Eeuwijk, Martha E Ramirez, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
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using partial least squares regression factorial regression and ammi models for interpreting Genotype Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, Martha E Ramirez, F.a. Van Eeuwijk, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL
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Using Partial Least Squares Regression, Factorial Regression, and AMMI Models for Interpreting Genotype × Environment Interaction
Crop Science, 1999Co-Authors: Mateo Vargas, José Crossa, Martha E Ramirez, F.a. Van Eeuwijk, Ken D SayreAbstract:Partial least squares (PLS) and factorial regression (FR) are statistical models that incorporate external Environmental and/or cultivar variables for studying and interpreting Genotype × Environment Interaction (GEl). The Additive Main effect and Multiplicative Interaction (AMMI) model uses only the phenotypic response variable of interest; however, if information on external Environmental (or genotypic) variables is available, this can be regressed on the Environmental (or genotypic) scores estimated from AMMI and superimposed on the AMMI biplot. The objectives of this study with two wheat [Triticum turgidum (L.) var. durum] field trials were (i) to compare the results of PLS, FR, and AMMI on the basis of external Environmental (and cultivar) variables, (ii) to examine whether procedures based PLS, FR, and AMMI identify the same or a different subset of cultivar and/or Environmental covariables that influence GEI for grain yield, and (iii) to find multiple FR models that include Environmental and cultivar covariables and their cross products that explain a large proportion of GEI with relatively few degrees of freedom. Results for the first trial showed that AMMI, PLS, and FR identified similar cultivar and Environmental variables that explained a large proportion of the cultivar × year Interaction. Results for the second wheat trial showed good correspondence between PLS and FR for 23 Environmental covariables. For both trials, PLS and FR complement each other and the AMMI and PLS biplots offered similar interpretations of the GEl. The FR analysis can be used to confirm these results and to obtain even more parsimonious descriptions of the GEL