Full and reduced models for yield trials

Summary Empirical results routinely demonstrate that the reduced Additive Main effects and Multiplicative Interaction (AMMI) model achieves better predictive accuracy for yield trials than does the full treatment means model. It may seem mysterious that treatment means are not the most accurate estimates, but rather that the AMMI model is often more accurate than its data. The statistical explanation involves the Stein effect, whereby a small sacrifice in bias can produce a large gain in accuracy. The corresponding agricultural explanation is somewhat complex, beginning with a yield trial's design and ending with its research purposes and applications. In essence, AMMI selectively recovers pattern related to the treatment design in its model, while selectively relegating noise related to the experimental design in its discarded residual. For estimating the yield of a particular genotype in a particular environment, the AMMI model uses the entire yield trial, rather than only the several replications of this particular trial, as in the treatment means model. This use of more information is the source of AMMI's gain in accuracy.This research was supported by the Rhizobotany Project of the USDA-ARS     

AMMI adjustment for statistical analysis of an international wheat yield trial

Summary Multilocation trials are important for the CIMMYT Bread Wheat Program in producing high-yielding, adapted lines for a wide range of environments. This study investigated procedures for improving predictive success of a yield trial, grouping environments and genotypes into homogeneous subsets, and determining the yield stability of 18 CIMMYT bread wheats evaluated at 25 locations. Additive Main effects and Multiplicative Interaction (AMMI) analysis gave more precise estimates of genotypic yields within locations than means across replicates. This precision facilitated formation by cluster analysis of more cohesive groups of genotypes and locations for biological interpretation of interactions than occurred with unadjusted means. Locations were clustered into two subsets for which genotypes with positive interactions manifested in high, stable yields were identified. The analyses highlighted superior selections with both broad and specific adaptation.     

Accuracy and selection success in yield trial analyses

Summary Yield trials serve research purposes of estimation and selection. Order statistics are used here to quantify the successes or problems to be expected in selection tasks commonly encountered in breeding and agronomy. Greater accuracy of yield estimates implies greater selection success. A New York soybean yield trial serves as a specific example. The Additive Main effects and Multiplicative Interaction (AMMI) statistical model is used to increase the accuracy of these soybean yield estimates, thereby increasing the probability of successfully selecting, on the basis of the empirical yield data, that genotype which has the maximum true mean. The statistical strategy for increasing accuracy is extremely cost effective relative to the alternative strategy of increasing the number of replications. Better selections increase the speed and effectiveness of breeding programs, and increase the reliability of variety recommendations. Selection tasks are frequently more difficult than may be suspected.This research was supported by the Rhizobotany Project of the USDA-ARS     

Combining genotype, environment and attribute variables in regression models for predicting the cell-means of multi-environment cultivar trials

 The main objectives of this study were: (1) to develop models which combine variables of genotype, environment and attribute in regression models (GEAR) for increasing the accuracy of predicted cell-means of the genotype×environment two-way table, and (2) to compare GEAR models with the additive main effects and multiplicative interaction (AMMI) model. GEAR models were developed by regressing the observed values on principal components of genotypes (PCG) and environments (PCE). Genetic and environmental attributes were also added to the GEAR models. GEAR and AMMI models were applied to multi-environment trials of triticale (trial 1), maize (trial 2) and broad beans (trial 3). The random data-splitting and cross-validation procedure was used and the root mean square-predicted difference (RMSPD) was computed to validate each model. GEAR models increased the accuracy of predicted cell-means. Attribute variables, such as soil pH, rainfall, altitude and class of genotype, did not improve the best GEAR model of trial 1, but they increased the predictive value of other models. Two iterations of the computer program further refined the best GEAR model. Based on the RMSPD criterion, GEAR models were as good as, or better than, some AMMI truncated models for predicting cell-means. The approximate accuracy gain factors (GF) of the best GEAR model over the raw data were 2.08, 3.02 and 2.22, for trials 1, 2 and 3, respectively. The GF of the best AMMI model were 1.74, 2.28 and 2.32 for trials 1, 2 and 3, respectively. The analysis of variance of the predicted cell means showed that the genotype×environment interaction (GEI) variance was reduced by about 20% in trial 1 and 81% in trial 2. A bias associated with the predicted cell reduced the GEI variability. Advantages of using GEAR models in muti-environment cultivar trials are that they: (1) increase the precision of cell-mean estimates and (2) reduce the GEI variance and increase trait heritability. Received: 15 August 1997 / Accepted: 28 October 1997     

Use of AMMI and linear regression models to analyze genotype-environment interaction in durum wheat

Summary The joint durum wheat (Triticum turgidum L var durum) breeding program of the International Maize and Wheat Improvement Center (CIMMYT) and the International Center for Agricultural Research in the Dry Areas (ICARDA) for the Mediterranean region employs extensive multilocation testing. Multilocation testing produces significant genotype-environment (GE) interaction that reduces the accuracy for estimating yield and selecting appropriate germ plasm. The sum of squares (SS) of GE interaction was partitioned by linear regression techniques into joint, genotypic, and environmental regressions, and by Additive Main effects and the Multiplicative Interactions (AMMI) model into five significant Interaction Principal Component Axes (IPCA). The AMMI model was more effective in partitioning the interaction SS than the linear regression technique. The SS contained in the AMMI model was 6 times higher than the SS for all three regressions. Postdictive assessment recommended the use of the first five IPCA axes, while predictive assessment AMMI1 (main effects plus IPCA1). After elimination of random variation, AMMI1 estimates for genotypic yields within sites were more precise than unadjusted means. This increased precision was equivalent to increasing the number of replications by a factor of 3.7.     

Integration of statistical and physiological analyses of adaptation of near-isogenic barley lines

Seven near-isogenic barley lines, differing for three independent mutant genes, were grown in 15 environments in Spain. Genotype x environment interaction (G x E) for grain yield was examined with the Additive Main Effects and Multiplicative interaction (AMMI) model. The results of this statistical analysis of multilocation yield-data were compared with a morpho-physiological characterization of the lines at two sites (Molina-Cano et al. 1990). The first two principal component axes from the AMMI analysis were strongly associated with the morpho-physiological characters. The independent but parallel discrimination among genotypes reflects genetic differences and highlights the power of the AMMI analysis as a tool to investigate G x E. Characters which appear to be positively associated with yield in the germplasm under study could be identified for some environments.     

甘蔗品种主要性状的基因型与环境及其互作效应分析

用AMMI模型双标图对国家第六轮甘蔗品种区域试验5个试点的12个甘蔗品种试验数据进行分析,研究甘蔗区试中不同品种的产量稳定性问题。结果表明,参试品种的6个产量性状在品种间和地点间差异显著,品种与地点的互作效应差异显著;FN30、YG16蔗茎产量和含糖量高,稳定性强,属于高产、稳产性较好的品种。AMMI模型很好地解释了甘蔗品种产量性状的基因型效应、环境效应和GE互作效应。     

对应用几种统计模型评价甘蔗品种稳定性的初步比较

利用广东省2009年甘蔗品种区域试验产量数据,对线性回归模型、AMMI模型和LR-PCA模型在评价甘蔗品种稳定性方面的应用进行了初步比较,结果发现,回归法计算简便、直观,AMMI模型和LR-PCA模型的分析结果则更全面、深入,而这两种模型之间仍存在着一定差异.实际操作中,在根据不同的数据资料选择相适宜的分析方法的同时,也可以采用不同的方法进行分析,通过比较选择较为合理的结果.     

Empirical best linear unbiased prediction in cultivar trials using factor-analytic variance-covariance structures

 Results of multi-environment trials to evaluate new plant cultivars may be displayed in a two-way table of genotypes by environments. Different estimators are available to fill the cells of such tables. It has been shown previously that the predictive accuracy of the simple genotype by environment mean is often lower than that of other estimators, e.g. least-squares estimators based on multiplicative models, such as the additive main effects multiplicative interaction (AMMI) model, or empirical best-linear unbiased predictors (BLUPs) based on a two-way analysis-of-variance (ANOVA) model. This paper proposes a method to obtain BLUPs based on models with multiplicative terms. It is shown by cross-validation using five real data sets (oilseed rape, Brassica napus L.) that the predictive accuracy of BLUPs based on models with multiplicative terms may be better than that of least-squares estimators based on the same models and also better than BLUPs based on ANOVA models. Received: 18 October 1997 / Accepted: 31 March 1998     

Improving efficiency of breeding for higher crop yield

Summary Exclusive selection for yield raises, the harvest index of self-pollinated crops with little or no gain in total bipmass. In addition to selection for yield, it is suggested that efficient breeding for higher yield requires simultaneous selection for yield's three major, genetically controlled physiological components. The following are needed: (1) a superior rate of biomass accumulation. (2) a superior rate of actual yield accumulation in order to acquire a high harvest index, and (3) a time to harvest maturity that is neither shorter nor longer than the duration of the growing season. That duration is provided by the environment, which is the fourth major determinant of yield. Simultaneous selection is required because genetically established interconnections among the three major physiological components cause: (a) a correlation between the harvest index and days to maturity that is usually negative; (b) a correlation between the harvest index and total biomass that is often negative, and (c) a correlation between biomass and days to maturity that is usually positive. All three physiological components and the correlations among them can be quantified by yield system analysis (YSA) of yield trials. An additive main effects and multiplicative interaction (AMMI) statistical analysis can separate and quantify the genotype × environment interaction (G × E) effect on yield and on each physiological component that is caused by each genotype and by the different environment of each yield trial. The use of yield trials to select parents which have the highest rates of accumulation of both biomass and yield, in addition to selecting for the G × E that is specifically adapted to the site can accelerate advance toward the highest potential yield at each geographical site. Higher yield for many sites will raise average regional yield. Higher yield for multiple regions and continents will raise average yield on a world-wide basis. Genetic and physiological bases for lack of indirect selection for biomass from exclusive selection for yield are explained.     

Use of trial clustering to study QTL × environment effects for grain yield and related traits in maize

A population of 300 F_3:4 lines derived from the cross between maize inbred lines F2 and F252 was evaluated for testcross value in a large range of environmental conditions (11 different locations in 2 years: 1995 and 1996) in order to study (1) the magnitude of genotype × environment and (2) the stability of quantitative trait loci (QTL) effects. Several agronomic traits were measured: dry grain yield (DGY), kernel weight, average number of kernels per plant, silking date (SD) and grain moisture at harvest. A large genotype × environment interaction was found, particularly for DGY. A hierarchical classification of trials and an additive main effects and multiplicative interaction (AMMI) model were carried out. Both methods led to the conclusion that trials could be partitioned into three groups consistent with (1) the year of experiment and (2) the water availability (irrigated vs non-irrigated) for the trials sown in 1995. QTL detection was carried out for all the traits in the different groups of trials. Between 9 and 15 QTL were detected for each trait. QTL × group and QTL × trial effects were tested and proved significant for a large proportion of QTL. QTL detection was also performed on coordinates on the first two principal components (PC) of the AMMI model. PC QTL were generally detected in areas where QTL × group and QTL × trial interactions were significant. A region located on chromosome 8 near an SD QTL seemed to play a key role in DGY stability. Our results confirm the key role of water availability and flowering earliness on grain yield stability in maize.     

Assessment of yield stability in sorghum using univariate and multivariate statistical approaches

The experiment was carried out to estimate GEI in sorghum for grain yield using univariate and multivariate statistical approaches based on two sets of performance trials (T1 and T2). While T1 consisted of 15 genotypes and tested in 8 environments, T2 that consisted of 13 genotypes was carried out in 13 environments. Because the combined ANOVA of each trial revealed significant differences among the genotypes, among the environments and GEI, the five univariate stability estimates: CV(i), S(i)(2), W(i)(2), sigma(i)(2), b(i) and Sd(i)(2) were evaluated for ranking the genotypes. There was positive rank-correlation between CVi and S(i)(2) and among W(i)(2), sigma(i)(2), b(i). Sd(i)(2) had significant positive rank-correlation with sigma(i)(2) and bi in T1 but weak rank-correlation with the remaining parameters in both trials. The three types of univariate stability estimates and the only multivariate stability estimate, the AMMI analysis declared genotypes 2 and 5 to be the most stable in T1, but they gave quite unrelated ranking in T2. Because of the lack of correspondence among the tested stability estimates in the two trials, it was difficult to reach a conclusion on producing genotype recommendation based on the univariate statistical approach. However, as GEI has multivariate nature, the multivariate approach is believed to give more robust inference. Hence, some stable genotypes were suggested using the AMMI model for sorghum growing dry lowlands of the country.     

Identification of QTL for growth- and grain yield-related traits in rice across nine locations of Asia

Rice double-haploid (DH) lines of an indica and japonica cross were grown at nine different locations across four countries in Asia. Genotype-by-environment (G x E) interaction analysis for 11 growth- and grain yield-related traits in nine locations was estimated by AMMI analysis. Maximum G x E interaction was exhibited for fertility percentage number of spikelets and grain yield. Plant height was least affected by environment, and the AMMI model explained a total of 76.2% of the interaction effect. Mean environment was computed by averaging the nine environments and subsequently analyzed with other environments to map quantitative trait loci (QTL). QTL controlling the 11 traits were detected by interval analysis using mapmaker/qtl. A threshold LOD of >/=3.20 was used to identify significant QTL. A total of 126 QTL were identified for the 11 traits across nine locations. Thirty-four QTL common in more than one environment were identified on ten chromosomes. A maximum of 44 QTL were detected for panicle length, and the maximum number of common QTL were detected for days to heading detected. A single locus for plant height (RZ730-RG810) had QTL common in all ten environments, confirming AMMI results that QTL for plant height were affected the least by environment, indicating the stability of the trait. Two QTL were detected for grain yield and 19 for thousand-grain weight in all DH lines. The number of QTL per trait per location ranged from zero to four. Clustering of the QTL for different traits at the same marker intervals was observed for plant height, panicle number, panicle length and spikelet number suggesting that pleiotropism and or tight linkage of different traits could be the possible reason for the congruence of several QTL. The many QTL detected by the same marker interval across environments indicate that QTL for most traits are stable and not essentially affected by environmental factors.     

SAS applications for Tai's stability analysis and AMMI model in genotype x environmental interaction (GEI) effects

A user-friendly graphical data analysis to perform stability analysis of genotype x environmental interactions, using Tai's stability model and additive main effects and multiplicative interaction (AMMI) biplots, are presented here. This practical approach integrates statistical and graphical analysis tools available in SAS systems and provides user-friendly applications to perform complete stability analyses without writing SAS program statements or using pull-down menu interfaces by running the SAS macros in the background. By using this macro approach, the agronomists and plant breeders can effectively perform stability analysis and spend more time in data exploration, interpretation of graphs, and output, rather than debugging their program errors. The necessary MACRO-CALL files can be downloaded from the author's home page at http://www.ag.unr.edu/gf. The nature and the distinctive features of the graphics produced by these applications are illustrated by using published data.     

Sensitivity of Resistance to Net Blotch in Barley

The aim of this study was to demonstrate various methods of analysing terminal net blotch, Pyrenophora teres Drechs. f. teres Smedeg., severity data from 15 spring barleys, Hordeum vulgare L., grown in Finnish official variety trials in five environments. The analyses have been developed and used principally by plant breeders for assessing crop yield, but lend themselves to use by plant pathologists. Pyrenophora teres is the major barley phytopathogen in Finland and improved resistance to it is sought. Joint regression analysis (JRA) and an additive main effects and multiplicative interaction (AMMI) model were used to investigate the data. Statistically significant genotype by environment (GE) interaction for resistance was indicated, and this included qualitative (crossover) interactions among genotypes over environments. A stable, non-sensitive, response to net blotch over environments, combined with a low mean score for terminal severity of the disease characterized the six-row barley 'Thule' which showed statistically significant crossover interaction only with 'Tyra'. 'Kustaa' exhibited the lowest mean terminal net blotch severity, but was relatively sensitive to net blotch. 'Arve' exhibited severe terminal net blotch in all environments, was relatively sensitive to environment and exhibited no crossover interaction with other genotypes. AMMI analysis appeared to represent a useful method for analysing these disease severity data, facilitating the selection of useful sources of resistance. Plots of AMMI-adjusted mean net blotch severities against first principal component axis (PCA) scores were informative for differentiating genotype response over environments, and are therefore potentially useful to plant pathologists and barley breeders seeking to gauge and subsequently improve the resistance status of barley to net blotch.     

Best Linear Unbiased Prediction (BLUP) for regional yield trials: a comparison to additive main effects and multiplicative interaction (AMMI) analysis

Multilocation trials are often used to analyse the adaptability of genotypes in different environments and to find for each environment the genotype that is best adapted; i.e. that is highest yielding in that environment. For this purpose, it is of interest to obtain a reliable estimate of the mean yield of a cultivar in a given environment. This article compares two different statistical estimation procedures for this task: the Additive Main Effects and Multiplicative Interaction (AMMI) analysis and Best Linear Unbiased Prediction (BLUP). A modification of a cross validation procedure commonly used with AMMI is suggested for trials that are laid out as a randomized complete block design. The use of these procedure is exemplified using five faba bean datasets from German registration trails. BLUP was found to outperform AMMI in four of five faba bean datasets.     

Additive main effect and multiplicative interaction model for a diallel-cross analysis

Diallel mating designs have proved informative in determining the inheritance of quantitative traits of interest to plant breeders. Apart from the well-established analyses of a complete diallel, the two-way factorial data structure of this design lends itself to analysis by the additive-main-effects-and-multiplicative-interaction (AMMI) model. This research article describes the joint application of the AMMI model and Griffing’s method 1, model I, to gain insight into the breeding value of inbred lines in a self-pollinated crop such as disomic, hexaploid bread wheat. Data from a multi-environment trial of a complete diallel cross between eight lines adapted to the East African highlands were analyzed to provide an example of this joint analysis. This combined approach identified not only the direction of a cross, i.e. which parent should be male or female, but also which crosses produce offspring showing F₁ heterosis. Received: 10 June 2000 / Accepted: 31 July 2000     

Stability of Sweet Potato Cultivars to Alternaria Leaf and Stem Blight Disease

Alternaria leaf petiole and stem blight is an economically important disease of sweet potato ( Ipomoea batatus L.) in tropical and sub-tropical environments. Published research on cultivar resistance to the sweet potato disease is limited. To evaluate cultivar reaction and stability to the disease, multi-location and replicated experiments were established in 12 environments in Uganda. Disease severity (area under disease progress curves – AUDPC), and cultivar root yield were also assessed. Significant differences (P < 0.001) in AUDPC were detected among cultivars. Mean AUDPC ranged from 46.3 (Araka Red) to 78.4 (New Kawogo) across locations and seasons and the genotypes Araka Red and Tanzania had the lowest disease values. The location and season effects accounted for 67.1% and 7.5% of the total variance of AUDPC recorded among cultivars. The ranking of cultivars based on predicted AUDPC from Additive Main Effect and Multiplicative Interactive model (AMMI) showed that the NASPOT 1, the susceptible check, and New Kawogo were most susceptible to the disease in 11 of the 12 environments. Low and stable disease was consistently recorded and predicted on NASPOT 3 and the landrace cultivars Tanzania, Dimbuca, and Araka Red across environments. These results suggest that landrace cultivars had relative stability to the disease and wide adaptation across environments. These results suggest that AMMI statistical model and other multivariate techniques can be utilized for prediction of Alternaria disease stability in these locations.     

Stability Performance of Inductively Coupled Plasma Mass Spectrometry-Phenotyped Kernel Minerals Concentration and Grain Yield in Maize in Different Agro-Climatic Zones

Deficiency of iron and zinc causes micronutrient malnutrition or hidden hunger, which severely affects ~25% of global population. Genetic biofortification of maize has emerged as cost effective and sustainable approach in addressing malnourishment of iron and zinc deficiency. Therefore, understanding the genetic variation and stability of kernel micronutrients and grain yield of the maize inbreds is a prerequisite in breeding micronutrient-rich high yielding hybrids to alleviate micronutrient malnutrition. We report here, the genetic variability and stability of the kernel micronutrients concentration and grain yield in a set of 50 maize inbred panel selected from the national and the international centres that were raised at six different maize growing regions of India. Phenotyping of kernels using inductively coupled plasma mass spectrometry (ICP-MS) revealed considerable variability for kernel minerals concentration (iron: 18.88 to 47.65 mg kg^–1; zinc: 5.41 to 30.85 mg kg^–1; manganese: 3.30 to17.73 mg kg^–1; copper: 0.53 to 5.48 mg kg^–1) and grain yield (826.6 to 5413 kg ha^–1). Significant positive correlation was observed between kernel iron and zinc within (r = 0.37 to r = 0.52, p < 0.05) and across locations (r = 0.44, p < 0.01). Variance components of the additive main effects and multiplicative interactions (AMMI) model showed significant genotype and genotype × environment interaction for kernel minerals concentration and grain yield. Most of the variation was contributed by genotype main effect for kernel iron (39.6%), manganese (41.34%) and copper (41.12%), and environment main effects for both kernel zinc (40.5%) and grain yield (37.0%). Genotype main effect plus genotype-by-environment interaction (GGE) biplot identified several mega environments for kernel minerals and grain yield. Comparison of stability parameters revealed AMMI stability value (ASV) as the better representative of the AMMI stability parameters. Dynamic stability parameter GGE distance (GGED) showed strong and positive correlation with both mean kernel concentrations and grain yield. Inbreds (CM-501, SKV-775, HUZM-185) identified from the present investigation will be useful in developing micronutrient-rich as well as stable maize hybrids without compromising grain yield.