A Weighted AMMI Algorithm to Study Genotype‐by‐Environment Interaction and QTL‐by‐Environment Interaction

Rodrigues, Paulo Canas; Malosetti, Marcos; Gauch, Hugh G.; Eeuwijk, F.A. van

doi:10.2135/cropsci2013.07.0462

Cited by 53 publications

(69 citation statements)

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“…For GBLUP M : y N´1 is the vector of mean yield for each genotype in the set of environments (i.e., the BLUEs from a model accounting for field design and environment) of length N (N = population size or number of genotypes in the set), 1 N´1 is a vector of ones of length N; m is the overall mean; g N´1 is a random vector of genotypic predictors with g ~ N(0, A N´N s g 2 ), where A is the realized additive relationship matrix; Z N´N is the corresponding incidence matrix; and  is the residual errors vector with  ~ N(0,R N´N ) where R is a diagonal matrix with elements as the reciprocals of the variances of the adjusted means for each genotype from the phenotypic analysis stage to account for heterogeneity in mean estimate precision following Rodrigues et al (2014).…”

Section: Genomic Predictions and Prediction Accuracymentioning

confidence: 99%

“…The genetic correlation matrix between environments was estimated using the spectral decomposition method described by Rebonato and Jäckel (1999) and subsequently used as the variance-covariance matrix. The mixed model for genomic prediction was fit with number of environments; Z n´n is the corresponding incidence matrix; and  is the residual errors vector with  ~ N(0,R n´n ), where R is a diagonal matrix with elements as the reciprocals of the variances of the adjusted means for each genotype from the phenotypic analysis stage to account for heterogeneity in mean estimate precision following Rodrigues et al (2014).…”

Section: Characterization Of Genotype ´ Environment Interactionmentioning

confidence: 99%

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Modeling Genotype × Environment Interaction for Genomic Selection with Unbalanced Data from a Wheat Breeding Program

et al. 2016

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Genomic selection (GS) has successfully been used in plant breeding to improve selection efficiency and reduce breeding time and cost. However, there is not a clear strategy on how to incorporate genotype × environment interaction (GEI) to GS models. Increased prediction accuracy could be achieved using mixed models to exploit GEI by borrowing information from other environments. The objective of this work was to compare strategies to exploit GEI in GS using mixed models. Specifically, we compared strategies to predict new genotypes by borrowing information from other environments modeling the correlation matrix across environments and to design sets of environments aiming for low GEI to predict genomic performance in new environments. We evaluated 1477 advanced wheat (Triticum aestivum L.) lines for yield in 35 location–year combinations genotyped with genotyping‐by‐sequencing (GBS). Mixed models were used to obtain either overall or by‐environment predictions for different sets of environments. Overall accuracy was high (0.5). Borrowing information from relatives evaluated in multiple environments and modeling the correlation matrix across environments was the best strategy to predict new genotypes. On the other hand, the best strategy for predicting the performance of genotypes in new environments was either to predict across locations for single years or to predict within defined mega‐environments (MEs) for any year or location. In summary, higher predictive ability was obtained by characterizing and by modeling GEI in the GS context.

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Section: Genomic Predictions and Prediction Accuracymentioning

confidence: 99%

Section: Characterization Of Genotype ´ Environment Interactionmentioning

confidence: 99%

Modeling Genotype × Environment Interaction for Genomic Selection with Unbalanced Data from a Wheat Breeding Program

et al. 2016

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“…A differential response of genotypes across environments (often locationby-year combinations) is frequent in multiple-environment trials (METs) and is known as GEI (Rodrigues et al, 2014). MET data are often summarized in two-way tables, which have rows with the means of genotypes and columns with the environments.…”

Section: Introductionmentioning

confidence: 99%

“…In has the most extreme form it consists of crossover interactions. An example may be a genotype which is superior under wet conditions but may yield poorly under dry conditions (Rodrigues et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

“…It can be used to understand and structure interactions between genotypes and environments. In its essence, the AMMI model applies the singular value decomposition (SVD) to the residuals of an additive two-way analysis of variance (ANOVA) model as applied to the GEI table of means (Gauch, 2013;Rodrigues et al, 2014). The two main purposes of AMMI analysis of a yield trial's treatment design are: (i) understanding complex GEI, which includes delineating mega-environments and selecting genotypes to exploit narrow adaptations; and (ii) increasing accuracy to improve recommendations, repeatability, selections, and genetic gains.…”

Section: Introductionmentioning

confidence: 99%

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Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

Hongyu

García-Peña

Araújo

et al. 2014

Biometrical Letters

100

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SummaryThe genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.Key words: genotype environment interaction (GEI), adaptability and stability, additive main effects and multiplicative interaction model, multienvironment trials

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An analysis of simulated yield data for pepper shows how genotype × environment interaction in yield can be understood in terms of yield components and their QTLs

et al. 2021

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Complex traits like yield are those in which phenotypic variation can be modeled as a linear function of a set of quantitative trait loci (QTLs) with environment dependency. This environment dependency can be observed at a phenotypic level as genotype × environment interaction (GEI) for yield itself and at an underlying genetic level as QTL × environment interaction (QEI). We show how GEI in yield may follow from pleiotropic QTLs for yield components that themselves are not environment dependent. We generated synthetic yield data via a crop growth model and analyzed these data by common statistical models for GEI and QEI. The QTLs for yield were pleiotropic with those for yield components. Such pleiotropy offers a path for improvement of yield under GEI. As a model system we used sweet pepper (Capsicum annuum L.) and developed an eco‐physiological model for yield with seven genotype‐specific inputs or yield components. Synthetic yields were simulated for a back cross population of 500 lines across a factorial combination of four major environmental drivers. The yield components were given a simple QTL basis and produced credible amounts and patterns of GEI for yield. The QEI for yield could be interpreted from the expression of QTLs for yield components and the interaction of these components with the environmental drivers. We see the generation of synthetic yield data via crop growth models followed by an analysis with statistical models for GEI and QEI to quantify the contribution of yield components to GEI as a helpful step in the development of yield prediction models for complex traits across environments that can also serve as a basis for decisions on selection strategies of complex traits.

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A Weighted AMMI Algorithm to Study Genotype‐by‐Environment Interaction and QTL‐by‐Environment Interaction

Cited by 53 publications

References 55 publications

Modeling Genotype × Environment Interaction for Genomic Selection with Unbalanced Data from a Wheat Breeding Program

Modeling Genotype × Environment Interaction for Genomic Selection with Unbalanced Data from a Wheat Breeding Program

Statistical analysis of yield trials by AMMI analysis of genotype × environment interaction

An analysis of simulated yield data for pepper shows how genotype × environment interaction in yield can be understood in terms of yield components and their QTLs

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