Multi-environment Trials Data Research Articles

Application of factor analytic and spatial mixed models for the analysis of multi-environment trials in common bean (Phaseolus vulgaris L.) in Ethiopia.

Common bean (Phaseolus vulgaris L.) is one of the most important grain legumes consumed globally, especially in Ethiopia, for its edible seeds, cash crops, and supply of protein for farmers. Efficient statistical methods must be employed for the evaluation of common bean varieties to accurately select superior varieties that contribute to agricultural productivity. The objective of this study was to identify promising large mottled bean varieties through analysis of multi-environment trials (MET) data using multiplicative spatial mixed models. In this study, 16-18 large mottled common bean varieties, including one check, were sown across nine growing environments in Ethiopia using lattice and alpha lattice designs, with three replications laid out in a square or rectangular (row by column) array of plots, respectively during the main cropping season from 2015 to 2018. We present a linear mixed model analysis that integrates spatial and factor analytic (FA) models, and the heritability measure was used to evaluate the efficiency of these models with the conventional analysis. The analysis of the spatial model, and more significantly, the spatial+FA model, revealed a notable enhancement in heritability. With the exception of a trial conducted at Kobo, a genotype DAP 292, found to be good performing for days to flowering and maturity, but for yield only across four clusters of trials, C2, C3, C5 and C7, formed with trials of relatively high genetic variance. Across these clusters, the yield advantage of this variety over the check ranged from 10-32%. This genotype also has a yield that is somewhat comparable to the check across the remaining clusters. Overall, both the spatial and factor analytic models proved to be effective approaches for analyzing the data in this study. The analysis of multi-environment trial data through the use of more efficient statistical models can provide a more robust platform for evaluating common bean varieties with greater confidence in selecting superior varieties across a range of environments. Hence, scaling up the use of this efficient analysis method is indispensable for enhancing the selection of superior varieties.

Incorporating the pedigree information in multi-environment trial analyses for improving common vetch.

Common vetch is one of the most profitable forage legumes due to its versatility in end-use which includes grain, hay, green manure, and silage. Furthermore, common vetch is one of the best crops to rotate with cereals as it can increase soil fertility which results in higher yield in cereal crops. The National Vetch Breeding Program located in South Australia is focused on developing new vetch varieties with higher grain and dry matter yields, better resistance to major diseases, and wider adaptability to Australian cropping environments. As part of this program, a study was conducted with 35 field trials from 2015 to 2021 in South Australia, Western Australia, Victoria, and New South Wales with the objective of determining the best parents for future crosses and the vetch lines with highest commercial value in terms of grain yield production. A total of 392 varieties were evaluated. The individual field trials were combined in a multi-environment trial data, where each trial is identified as an environment. Multiplicative mixed models were used to analyze the data and a factor analytic approach to model the genetic by environment interaction effects. The pedigree of the lines was then assembled and incorporated into the analysis. This approach allowed to partition the total effects into additive and non-additive components. The total and additive genetic effects were inspected across and within environments for broad and specific selections of the lines with the best commercial value and the best parents. Summary measures of overall performance and stability were used to aid with selection of parents. To the best of our knowledge, this is the first study which used the pedigree information to breed common vetch. In this paper, the application of this statistical methodology has been successfully implemented with the inclusion of the pedigree improving the fit of the models to the data with most of the total genetic variation explained by the additive heritable component. The results of this study have shown the importance of including the pedigree information for common vetch breeding programs and have improved the ability of breeders to select superior commercial lines and parents.

Multi-environment analysis enhances genomic prediction accuracy of agronomic traits in sesame.

Introduction: Sesame is an ancient oilseed crop containing many valuable nutritional components. The demand for sesame seeds and their products has recently increased worldwide, making it necessary to enhance the development of high-yielding cultivars. One approach to enhance genetic gain in breeding programs is genomic selection. However, studies on genomic selection and genomic prediction in sesame have yet to be conducted. Methods: In this study, we performed genomic prediction for agronomic traits using the phenotypes and genotypes of a sesame diversity panel grown under Mediterranean climatic conditions over two growing seasons. We aimed to assess prediction accuracy for nine important agronomic traits in sesame using single- and multi-environment analyses. Results: In single-environment analysis, genomic best linear unbiased prediction, BayesB, BayesC, and reproducing kernel Hilbert spaces models showed no substantial differences. The average prediction accuracy of the nine traits across these models ranged from 0.39 to 0.79 for both growing seasons. In the multi-environment analysis, the marker-by-environment interaction model, which decomposed the marker effects into components shared across environments and environment-specific deviations, improved the prediction accuracies for all traits by 15%-58% compared to the single-environment model, particularly when borrowing information from other environments was made possible. Discussion: Our results showed that single-environment analysis produced moderate-to-high genomic prediction accuracy for agronomic traits in sesame. The multi-environment analysis further enhanced this accuracy by exploiting marker-by-environment interaction. We concluded that genomic prediction using multi-environmental trial data could improve efforts for breeding cultivars adapted to the semi-arid Mediterranean climate.

Nested association mapping-based GWAS for grain yield and related traits in wheat grown under diverse Australian environments.

Utilising a nested association mapping (NAM) population-based GWAS, 98 stable marker-trait associations with 127 alleles unique to the exotic parents were detected for grain yield and related traits in wheat. Grain yield, thousand-grain weight, screenings and hectolitre weight are important wheat yield traits. An understanding of their genetic basis is crucial for improving grain yield in breeding programmes. Nested association mapping (NAM) populations are useful resources for the dissection of the genetic basis of complex traits such as grain yield and related traits in wheat. Coupled with phenotypic data collected from multiple environments, NAM populations have the power to detect quantitative trait loci and their multiple alleles, providing germplasm that can be incorporated into breeding programmes. In this study, we evaluated a large-scale wheat NAM population with two recurrent parents in unbalanced trials in nine diverse Australian field environments over three years. By applying a single-stage factor analytical linear mixed model (FALMM) to the NAM multi-environment trials (MET) data and conducting a genome-wide association study (GWAS), we detected 98 stable marker-trait associations (MTAs) with their multiple alleles. 74 MTAs had 127 alleles that were derived from the exotic parents and were absent in either of the two recurrent parents. The exotic alleles had favourable effects on 46 MTAs of the 74 MTAs, for grain yield, thousand-grain weight, screenings and hectolitre weight. Two NAM RILs with consistently high yield in multiple environments were also identified, highlighting the potential of the NAM population in supporting plant breeding through provision of germplasm that can be readily incorporated into breeding programmes. The identified beneficial exotic alleles introgressed into the NAM population provide potential target alleles for the genetic improvement of wheat and further studies aimed at pinpointing the underlying genes.

LearnMET: an R package to apply machine learning methods for genomic prediction using multi-environment trial data.

We introduce the R-package learnMET, developed as a flexible framework to enable a collection of analyses on multi-environment trial breeding data with machine learning-based models. learnMET allows the combination of genomic information with environmental data such as climate and/or soil characteristics. Notably, the package offers the possibility of incorporating weather data from field weather stations, or to retrieve global meteorological datasets from a NASA database. Daily weather data can be aggregated over specific periods of time based on naive (for instance, nonoverlapping 10-day windows) or phenological approaches. Different machine learning methods for genomic prediction are implemented, including gradient-boosted decision trees, random forests, stacked ensemble models, and multilayer perceptrons. These prediction models can be evaluated via a collection of cross-validation schemes that mimic typical scenarios encountered by plant breeders working with multi-environment trial experimental data in a user-friendly way. The package is published under an MIT license and accessible on GitHub.

Handling outliers in multi-environment trial data analysis: in the direction of robust SREG model

ABSTRACT Site regression model (SREG) is utilized by plant breeders for the analysis of multi-environment trials (MET) to examine the relationships among test environments and genotypes (G) and genotype-by-environment interaction (GE). In its regular form, singular-value decomposition (SVD) is applied on residual matrix from one-way analysis of variance (ANOVA) to partition G plus GE effects. However, ANOVA and SVD are sensitive to atypical observations, which are common in MET. To overcome this problem, three robust models are proposed to obtain valid results even in the presence of outliers. Their efficacy was evaluated by simulation and compared with standard SREG. Different scenarios were considered to identify the appropriate strategies to deal with outliers in real situations. Two real datasets are also presented to highlight the usefulness of the proposed methods in agricultural data. Our results indicate that the use of the proposed alternatives enables to effectively analyze MET data in the presence of outliers and maintain good performance without them as well.

Genotype selection based on multiple traits in cotton crops: The application of genotype by yield*trait biplot

In cotton crops, the cotton seed yield significantly contributes with the success of any cultivar. However, other traits are considered when an ideotype is pointed out in the selection, such as the fiber quality traits. The aim of this study was to applied genotype by yield*trait (GYT) biplot to a multi-environment trial data of cotton genotypes and selected the best genotypes. For this end, thirteen genotypes from nineteen trials were assessed. Seven traits were evaluated [cotton seed yield (SY), fiber percentage (FP), fiber length (FL), fiber uniformity (FU), short fiber index (SFI), fiber strength (FS), and elongation (EL)] and residual error variances structures [identity variance (IDV) and diagonal (Diag)] were tested by bayesian information criterion. After, the REML/BLUP approach was applied to predict the genetic values of each trait and the selective accuracy were measured from the prediction. Then, the GYT-biplot were applied to the data. For SP and SFI traits, the model with Diag residual variance was indicated, whereas for SY FL, FU, FS, and EL traits the model with IDV residual variance demonstrated the best fit to the data. Values of accuracy were higher than 0.9 for all traits analyzed. In the GYT-biplot acute angles were find for all traits relations, which means high correlation between the yield*traits combination. Besides that, the correlation still can be seen in the GYT-biplot, as shown by the magnitudes of the angles between the pairs Yield*FU-Yield*FS and Yield*FS-Yield*EL. Also, the GYT-biplot indicates the genotype G4 with the best performance for Yield*FS, Yield*SFI, Yield*FU, Yield*FL, and Yield*FP combined. The genotypes G4, G1, G13, G8, and G9 represent those genotypes with yield advantage over the other cultivars. Then, the genotype G4 combines all desirable characteristics and demonstrate have large potential in the cotton breeding. The GYT approach were valuable and were highly recommended in cotton breeding programs for selection purpose in a multivariate scenario.

Genotype plus genotype by-environment interaction biplot and genetic diversity analyses on multi-environment trials data of yield and technological traits of cotton cultivars

ABSTRACT: Understanding the genetic diversity and overcoming genotype-by-environment interaction issues is an essential step in breeding programs that aims to improve the performance of desirable traits. This study estimated genetic diversity and applied genotype + genotype-by-environment (GGE) biplot analyses in cotton genotypes. Twelve genotypes were evaluated for fiber yield, fiber length, fiber strength, and micronaire. Estimation of variance components and genetic parameters was made through restricted maximum likelihood and the prediction of genotypic values was made through best linear unbiased prediction. The modified Tocher and principal component analysis (PCA) methods, were used to quantify genetic diversity among genotypes. GGE biplot was performed to find the best genotypes regarding adaptability and stability. The Tocher technique and PCA allowed for the formation of clusters of similar genotypes based on a multivariate framework. The GGE biplot indicated that the genotypes IMACV 690 and IMA08 WS were highly adaptable and stable for the main traits in cotton. The cross between the genotype IMACV 690 and IMA08 WS is the most recommended to increase the performance of the main traits in cotton crops.

"Spatial Field Trend Analysis and Factor Analytic Model Under Linear Mixed Model in MultiEnvironment Trial Data: The Case of Durum Wheat in Ethiopia"

"Spatial Field Trend Analysis and Factor Analytic Model Under Linear Mixed Model in MultiEnvironment Trial Data: The Case of Durum Wheat in Ethiopia"

Comparing a Mixed Model Approach to Traditional Stability Estimators for Mapping Genotype by Environment Interactions and Yield Stability in Soybean [Glycine max (L.) Merr.

Identifying genetic loci associated with yield stability has helped plant breeders and geneticists begin to understand the role and influence of genotype by environment (GxE) interactions in soybean [Glycine max (L.) Merr.] productivity, as well as other crops. Quantifying a genotype’s range of performance across testing locations has been developed over decades with dozens of methodologies available. This includes directly modeling GxE interactions as part of an overall model for yield, as well as methods which generate overall yield “stability” values from multi-environment trial data. Correspondence between these methods as it pertains to the outcomes of genome wide association studies (GWAS) has not been well defined. In this study, the GWAS results for yield and yield stability were compared in 213 soybean lines across 11 environments to determine their utility and potential intersection. Both univariate and multivariate conventional stability estimates were considered alongside a mixed model for yield that fit marker by environment interactions as a random effect. One-hundred and six total QTL were discovered across all mapping results, however, genetic loci that were significant in the mixed model for grain yield that fit marker by environment interactions were completely distinct from those that were significant when mapping using traditional stability measures as a phenotype. Furthermore, 73.21% of QTL discovered in the mixed model were determined to cause a crossover interaction effect which cause genotype rank changes between environments. Overall, the QTL discovered via explicitly mapping GxE interactions also explained more yield variance that those QTL associated with differences in traditional stability estimates making their theoretical impact on selection greater. A lack of intersecting results between mapping approaches highlights the importance of examining stability in multiple contexts when attempting to manipulate GxE interactions in soybean.

Genetic Divergence and GGE Bi-plot Analysis of Multi-environment Trial Data of Barley (Hordeum vulgare L.) to Identify “Ideal” Genotype

The present research revealed the study of genetic divergence and genotype (G) main effect and genotype by the environment (GE) interaction (G × GE) bi-plot analysis for multi-environmental trial data using yield data of three years. Since, genotypes were planted in 2017 in two dates like early and lates own condition hence, there was very slight differences in their yield so both the environments come together as compared to third environment (2018) which for from the two locations of year 2017. The objective of this study was to determine the effects of genotype, environment and their interaction on grain yield and to identify stable barley genotypes. The field experiment comprising of 69 barley genotypes laid out in a Randomized Block Design with three replications during Rabi 2016-2017. The extent of genetic variability, association between yield and yield components, frequency distribution of 25 top best genotypes in response to yield in three different environments, yield stability analysis and genetic diversity was studied. For stability analysis yield data of current year for one location and yield data of two locations/environments of previous year have been used. Field observations were recorded on six important characters days to 50% flowering, days to maturity, effective tillers per plant, plant height with awn, plant height without awn and 1000 grain weight (g). The result of bi-plot analysis using yield data of three years revealed that AXIS1 explained 57.6 per cent variation while AXIS2 was explained 31.07 per cent variation. Since, genotypes were planted in 2017 in two dates like early and late sown condition hence, there was very slight differences in their yield so both the environments come together (Figure1) as compared to third environment (2018) which for from the two locations of year 2017. Our result indicate that line G69 recommended as most stable genotype for yield potential and stability whereas lines G9, G55, G67 and G68 were consider as superior genotypes.

Use of Contemporary Groups in the Construction of Multi-Environment Trial Datasets for Selection in Plant Breeding Programs.

Plant breeding programs use multi-environment trial (MET) data to select superior lines, with the ultimate aim of increasing genetic gain. Selection accuracy can be improved with the use of advanced statistical analysis methods that employ informative models for genotype by environment interaction, include information on genetic relatedness and appropriately accommodate within-trial error variation. The gains will only be achieved, however, if the methods are applied to suitable MET datasets. In this paper we present an approach for constructing MET datasets that optimizes the information available for selection decisions. This is based on two new concepts that characterize the structure of a breeding program. The first is that of “contemporary groups,” which are defined to be groups of lines that enter the initial testing stage of the breeding program in the same year. The second is that of “data bands,” which are sequences of trials that correspond to the progression through stages of testing from year to year. MET datasets are then formed by combining bands of data in such a way as to trace the selection histories of lines within contemporary groups. Given a specified dataset, we use the A-optimality criterion from the model-based design literature to quantify the information for any given selection decision. We demonstrate the methods using two motivating examples from a durum and chickpea breeding program. Datasets constructed using contemporary groups and data bands are shown to be superior to other forms, in particular those that relate to a single year alone.

Parametric and Non-parametric Procedures for Identifying Stable and Adapted Tropical Maize Genotypes in NLB Disease Infested Environments

Multi-locational trials are critical for establishing stable and adaptable genotypes across different geographic areas prior to considering commercial release. The stability and adaptation of 20 tropical maize hybrids in environments infected with Northern leaf blight disease were assessed using 12 parametric and 14 nonparametric parameters across five environments. The purpose of this research is to estimate the genotype-environment interaction (GEI) for grain yield in selected maize genotypes and to identify associated stability factors to aid in the rationalization of stability analysis in Multi-Environment Trial (MET) data used in breeding programs. Except for De Kroon and Van der Laan (1981), both the combined ANOVA and nonparametric tests of GEI showed significant differences across hybrids, as well as significant crossover and non-crossover interactions. This suggests differential genotypes responses to the test environments. Spearman correlation analysis revealed significant differences between many nonparametric and parametric parameters, indicating that the two may be utilized interchangeably. Additionally, the correlation matrix and principal component analysis results from parametric and nonparametric parameters demonstrated their potential to assess the responses of maize genotypes to changing environments. G13 and G20 appeared most phenotypically stable with associated high mean yield based on the high values expressed by most parametric and nonparametric parameters.

Spatial analysis in multi-environment trials of malt barley in Ethiopia

Selection of superior genotypes and measuring heritability are some of the basic objectives of plant breeding. For this purpose, plant breeders grow crops across environments. Understanding the pattern of response across environments is an integral component of selection of superior and stable genotypes. The objective of this study was to improve selection strategies in barley breeding of Ethiopia through modeling spatial field trend. A set of multi-environment trials (MET) data from the national variety trial series conducted over four years, was taken from the Ethiopian Barley Breeding Programme, spanning stages from early generation to national variety trial testing for yield, was used in this study. The trials were analysed in a linear mixed model framework. Then, fitting a one-stage model for MET data, including a correlated spatial process for field trend within each trial, and combining a factor analytic (FA) model for genotype by environment interaction was conducted. The genetic correlations from this MET analysis were then used to cluster the environments based on their similarity. Performance of genotypes across these environmental clusters indicate broad (Bekoji-2005 and Bekoji-2004) and specific adaptation (Sgonder-2007 and Sgonder-2006) of genotype to certain types of environments. In addition, analysis of this historical MET data shed light on how breeding programme design can be improved to capture responses across the target population of environments, as it can inform the adequacy of the current number of barley grown areas in Ethiopia and the improvement in measuring heritability. Key words: Barley MET, heritability, linear mixed model

Testing multiplicative terms in AMMI and GGE models for multienvironment trials with replicates.

For analysing multienvironment trials with replicates, a resampling-based method is proposed for testing significance of multiplicative interaction terms in AMMI and GGE models, which is superior compared to contending methods in robustness to heterogeneity of variance. The additive main effects and multiplicative interaction model and genotype main effects and genotype-by-environment interaction model are commonly used for the analysis of multienvironment trial data. Agronomists and plant breeders are frequently using these models for cultivar trials repeated across different environments and/or years. In these models, it is crucial to decide how many significant multiplicative interaction terms to retain. Several tests have been proposed for this purpose when replicate data are available; however, all of them assume that errors are normally distributed with a homogeneous variance. Here, we propose resampling-based methods for multienvironment trial data with replicates, which are free from these distributional assumptions. The methods are compared with competing parametric tests. In an extensive simulation study based on two multienvironment trials, it was found that the proposed methods performed well in terms of Type-I error rates regardless of the distribution of errors. The proposed method even outperforms the robust [Formula: see text] test when the assumptions of normality and homogeneity of variance are violated.

Estimation of Factor Analytic Mixed Models for the Analysis of Multi-treatment Multi-environment Trial Data

An efficient and widely used method of analysis for multi-environment trial (MET) data in plant improvement programs involves a linear mixed model with a factor analytic (FA) model for the variety by environment effects. The variance structure is generally constructed as the kronecker product of two matrices that relate to the variety and environment dimensions, respectively. In many applications, the FA variance structure is assumed for the environment dimension and either an identity matrix or a known matrix, such as the numerator relationship matrix, is used for the variety dimension. The factor analytic linear mixed model can be fitted to large and complex MET datasets using the sparse formulation of the average information algorithm of Thompson et al. (Aust N Z J Stat 45:445–459, 2003) or the extension provided by Kelly et al. (Genet Sel Evo, 41:1186–1297, 2009) for the case of a known non-identity matrix for the variety dimension. In this paper, we present a sparse formulation of the average information algorithm for a more general separable variance structure where all components are parametric and one component has an FA structure. The approach is illustrated using a large and highly unbalanced MET dataset where there is a factorial treatment structure. Supplementary materials accompanying this paper appear online.

Yield Stability of Soybean Genotypes in Tropical Environments based on Genotype and Genotype-by-Environment Biplot

Genotype × environment interaction is universal phenomenon when different genotypes are tested in a number of environments. The objective of this experiment was to determine the seed yield stability of soybean genotypes. Seven soybean genotypes and two check cultivars were evaluated at eight soybean production centers during the dry season 2015. Stability analysis on seed yield was based on the GGE biplot method. The combined analysis showed that yield and yield components were significantly affected by genotype (G), environments (E), and genotype × environment interaction (GEI), except for number of filled pods. The highest yield was G6 (3.07 ton ha-1), followed by G7 (2.93 ton ha-1). The “which-won-where” polygon mapping resulted two mega-environments. The best genotype for the first mega-environment was G1 (G511H/Anjasmoro//Anjasmoro-2-8) at E5 (Pasuruan2); and the second one was G6 (G511 H/Anj//Anj///Anj////Anjs-6-7) at E1 (Nganjuk), E2 (Mojokerto), E3 (Blitar), E4 (Pasuruan1), E6 (Jembrana), E7 (Tabanan), and E8 (Central Lombok). The G7 (G511 H/Anjasmoro-1-4-2) was closest to ideal genotype as indicated by relatively stable and produced high yield across environments. The analysis of multi-environment trials data using GGE is useful for determining mega-environment analysis and stability of genotype which focusing on overall performance to identify superior genotypes.Keywords: GE interaction, GGE biplot, Glycine max, seed yield

AMMI and GGE Biplot for genotype × environment interaction: a medoid–based hierarchical cluster analysis approach for high–dimensional data

Summary The presence of genotype-environment interaction (GEI) influences production making the selection of cultivars in a complex process. The two most used methods to analyze GEI and evaluate genotypes are AMMI and GGE Biplot, being used for the analysis of multi environment trials data (MET). Despite their different approaches, both models complement each other in order to strengthen decision making. However, both models are based on biplots, consequently, biplot-based interpretation doesn’t scale well beyond two-dimensional plots, which happens whenever the first two components don’t capture enough variation. This paper proposes an approach to such cases based on cluster analysis combined with the concept of medoids. It also applies AMMI and GGE Biplot to the adjusted data in order to compare both models. The data is provided by the International Maize and Wheat Improvement Center (CIMMYT) and comes from the 14th Semi-Arid Wheat Yield Trial (SAWYT), an experiment concerning 50 genotypes of spring bread wheat (Triticum aestivum) germplasm adapted to low rainfall. It was performed in 36 environments across 14 countries. The analysis provided 25 genotypes clusters and 6 environments clusters. Both models were equivalent for the data’s evaluation, permitting increased reliability in the selection of superior cultivars and test environments.

Methodological approach for predicting and mapping the phenological adaptation of tropical maize (Zea mays L.) using multi-environment trials

BackgroundThe phenological development of the maize crop from emergence through flowering to maturity, usually expressed as a rate (i.e. 1/duration), is largely controlled by temperature in the tropics. Maize plant phenological responses vary between varieties and quantifying these responses can help in predicting the timing and duration of critical periods for crop growth that affect the quality and quantity of seed. We used routine multi-environment trials data of diverse tropical maize varieties to: (1) fit 82 temperature dependent phenology models and select the best model for an individual variety, (2) develop a spatial framework that uses the phenology model to predict at landscape level the length of the vegetative and reproductive phases of diverse varieties of maize in different agro-ecologies. Multi-environment trial data of 22 maize varieties from 16 trials in Kenya, Ethiopia, and Sudan was analyzed and the Levenberg–Marquardt algorithm combined with statistical criteria was applied to determine the best temperature-dependent model.ResultsThe Briere model, which is not often used in plant phenology, provided the best fit, with observed and predicted days to flowering showing good agreement. Linking the model with temperature and scaling out through mapping gave the duration from emergence to maturity of different maize varieties in areas where maize could potentially be grown.ConclusionThe methodology and framework used in the study provides an opportunity to develop tools that enhance farmers’ ability to predict stages of maize development for efficient crop management decisions and assessment of climate change impacts. This methodology could contribute to increase maize production if used to identify varieties with desired maturity for a specific agro-ecology in in the targeted regions.

Plant breeding selection tools built on factor analytic mixed models for multi-environment trial data

An advanced and widely used method of analysis for multi-environment trial data involves a linear mixed model with factor analytic (FA) variance structures for the variety by environment effects. This model can accommodate unbalanced data, that is, not all varieties in all environments, it allows the use of pedigree information and appropriate accommodation of individual trial experimental designs, and most importantly the FA structure for the variety by environment effects is parsimonious and regularly results in a good fit to the data. The model provides accurate predictions of the variety effects for every environment in the data-set but this constitutes a large and unwieldly amount of information to process for the purpose of variety selection. We address this issue in the current paper by proposing factor analytic selection tools to summarise the predictions in a concise yet informative manner. The tools, which are natural derivatives of the FA structure, result in measures of overall performance and stability across the environments in the data-set. All measures are expressed on the same scale as the trait under consideration and can easily be combined to form an index for selection.