Predictive and postdictive success of statistical analyses of yield trials

Summary The accuracy of a yield trial can be increased by improved experimental techniques, more replicates, or more efficient statistical analyses. The third option involves nominal fixed costs, and is therefore very attractive. The statistical analysis recommended here combines the Additive main effects and multiplicative interaction (AMMI) model with a predictive assessment of accuracy. AMMI begins with the usual analysis of variance (ANOVA) to compute genotype and environment additive effects. It then applies principal components analysis (PCA) to analyze non-additive interaction effects. Tests with a New York soybean yield trial show that the predictive accuracy of AMMI with only two replicates is equal to the predictive accuracy of means based on five replicates. The effectiveness of AMMI increases with the size of the yield trial and with the noisiness of the data. Statistical analysis of yield trials with the AMMI model has a number of promising implications for agronomy and plant breeding research programs.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     

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     

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     

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.     

Genotype × environment interaction analysis of North American shrub willow yield trials confirms superior performance of triploid hybrids

Development of dedicated bioenergy crop production systems will require accurate yield estimates, which will be important for determining many of the associated environmental and economic impacts of their production. Shrub willow (Salix spp) is being promoted in areas of the USA and Canada due to its adaption to cool climates and wide genetic diversity available for breeding improvement. Willow breeding in North America is in an early stage, and selection of elite genotypes for commercialization will require testing across broad geographic regions to gain an understanding of how shrub willow interacts with the environment. We analyzed a dataset of first‐rotation shrub willow yields of 16 genotypes across 10 trial environments in the USA and Canada for genotype‐by‐environment interactions using the additive main effects and multiplicative interactions (AMMI) model. Mean genotype yields ranged from 5.22 to 8.58 oven‐dry Mg ha^?1 yr^?1. Analysis of the main effect of genotype showed that one round of breeding improved yields by as much as 20% over check cultivars and that triploid hybrids, most notably Salix viminalis × S. miyabeana, exhibited superior yields. We also found important variability in genotypic response to environments, which suggests specific adaptability could be exploited among 16 genotypes for yield gains. Strong positive correlations were found between environment main effects and AMMI parameters and growing environment temperatures. These findings demonstrate yield improvements are possible in one generation and will be important for developing cultivar recommendations and for future breeding efforts.     

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.     

Evaluation of a bracken (Pteridium aquilinum (L.) Kuhn) growth model in predicting the effects of control strategies across a range of climatic zones in Great Britain

A nationwide bracken control experiment provided data over a three-year period for testing the accuracy of a bracken growth model (BRACON). Objective assessments of model validity identified the model as a reasonably accurate predictor of bracken stand dynamics given the range of environmental conditions currently prevailing in Great Britain, in relation to (1) cutting regimes and (2) spraying asulam. Ranking of treatment efficacy at individual sites was closely reflected in model predictions. Predicted response of the rhizome system to cutting treatments underestimated bracken resilience. Failure to consider the consequences of frond regrowth in the latter portion of the growing season as a means to offsetting energy loss was identified as a potential explanation for this discrepancy. The role of the model as a practical management tool is discussed with particular reference to relating model predictions, based upon generalised environmental data (40 km plusmn; 40 km grid cells), to bracken management at individual sites.     

Seventy-five percent accuracy in protein secondary structure prediction

In this study we present an accurate secondary structure prediction procedure by using a query and related sequences. The most novel aspect of our approach is its reliance on local pairwise alignment of the sequence to be predicted with each related sequence rather than utilization of a multiple alignment. The residue-by-residue accuracy of the method is 75% in three structural states after jack-knife tests. The gain in prediction accuracy compared with the existing techniques, which are at best 72%, is achieved by secondary structure propensities based on both local and long-range effects, utilization of similar sequence information in the form of carefully selected pairwise alignment fragments, and reliance on a large collection of known protein primary structures. The method is especially appropriate for large-scale sequence analysis efforts such as genome characterization, where precise and significant multiple sequence alignments are not available or achievable. Proteins 27:329–335, 1997. © 1997 Wiley-Liss, Inc.     

Overview of drugs in arterial thrombosis

The recent history of randomized controlled trails in the prevention of ischaemic heart disease (i.h.d.) is considered. In 1970, it seemed that little could be done to prevent recurrent of the disease and there was almost no information on the potential for preventing its onset. Over the past decade, this rather pessimistic view has changed to one of guarded optimism. Yet there are still no drug régimes that command general support. One reason for the inconclusive results of recent trails may have been the assumption that myocardial infraction and sudden death share the same pathology. Another reason is the diversity of pathogenetic mechanisms and prognoses in i.h.d. Many patients probably stand little chance of benefiting from a particular drug either because it affects mechanisms other than those responsible for their disease or because their prognosis, excellent or hopeless, is unlikely to be influenced whatever treatment they receive. It is consequently difficult to ensure reasonable chances of demonstrating benefits in those who may really stand to gain. A tendency of pharmacological information to become available during or after a large trial, rather than beforehand, has added to the difficulties. Despite all their problems, randomized controlled trials remained the only way of testing drugs for the prevention of arterial disease. Suggestions are made for increasing the chances of clear results in future trails and of reaching the stage of benefit demonstrated sufficiently convincingly to form a basis for clinical practice. These suggestions include the use of factorial designs enabling the evaluation of more than one drug in a particular trial and the development of methods for selecting homogeneous groups of patients.     

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。     

Improving accuracy of breeding values by incorporating genomic information in spatial-competition mixed models

Climate change and the increasing demand for sustainable energy resources require urgent strategies to increase the accuracy of selection in tree breeding (associated with higher gain). We investigated the combined pedigree and genomic-based relationship approach and its impact on the accuracy of predicted breeding values using data from 5-year-old Eucalyptus grandis progeny trial. The number of trees that can be genotyped in a tree breeding population is limited; therefore, the combined approach can be a feasible and efficient strategy to increase the genetic gain and provide more accurate predicted breeding values. We calculated the accuracy of predicted breeding values for two growth traits, diameter at breast height and total height, using two evaluation approaches: the combined approach and the classical pedigree-based approach. We also investigated the influence of two different trait heritabilities as well as the inclusion of competition genetic effects or environmental heterogeneity in an individual-tree mixed model on the estimated variance components and accuracy of breeding values. The genomic information of genotyped trees is automatically propagated to all trees with the combined approach, including the non-genotyped mothers. This increased the accuracy of overall breeding values, except for the non-genotyped trees from the competition model. The increase in the accuracy was higher for the total height, the trait with low heritability. The combined approach is a simple, fast, and accurate genomic selection method for genetic evaluation of growth traits in E. grandis and tree species in general. It is simple to implement in a traditional individual-tree mixed model and provides an easy extension to individual-tree mixed models with competition effects and/or environmental heterogeneity.     

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.     

A systematic error in tests of ideal free theory

Classical ideal free theory predicts that the distribution of consumers within a patchy environment should correspond to the distribution of resources. Tests of this prediction have inappropriately compared ratios of mean resource levels and mean consumer densities, rather than means of ratios. We show that this error, which has propagated through hundreds of studies, leads to a systematic bias: the theory will appear to underestimate the number of consumers occupying poor patches. We explain the correct way to test ideal free theory and apply it to published data; the classical model is then seen to yield far more accurate predictions than previously thought.     

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.     

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.     

Selection system efficiencies for computer simulated progeny test field designs in loblolly pine

Summary Six simulated progeny test field designs in combination with three within-family selection systems were tested on three loblolly pine (Pinus taeda L.) progeny test sites in southeastern Oklahoma and southwestern Arkansas, to compare genetic gains for the single trait, height. Residual deviations obtained by subtraction of family and plantation mean effects for each plantation were combined with simulated genetic effects with known family variance structure. The simulated genetic populations, arranged in the following progeny test field designs — large square or almost square plots, five- and ten-tree row plots, five-tree noncontiguous plots, two tree row plots, and single-tree plots — were superimposed on the residual data for each plantation. Within-family selection methods based on deviations from block means, deviations from neighborhood means and deviations from plot means were built into the model. Realized genetic gain attained by each design — selection system combination was compared with the genetic gain theoretically possible if selection accuracy were perfect, and with expected gain estimated using the general linear model. In general, average realized genetic gain compared well with expected gain. Differences between designs with large versus small plots were generally lower than expected, although the single-tree plot design always yielded highest realized gain. Realized gain was generally higher than expected when within-family selection was based on deviations from block or neighborhood means, but equal to or lower than expected when selection was based on deviations from plot means.     

Experimental Evaluation of the Impact of Intrinsic Process Parameters on the Performance of a Continuous Chromatographic Polishing Unit (MCSGP)

The semicontinuous twin‐column multicolumn countercurrent solvent gradient purification (MCSGP) process improves the trade‐off between purity and yield encountered in traditional batch chromatography, while its complexity, in terms of hardware requirements and process design, is reduced in comparison to process variants using more columns. In this study, the MCSGP process is experimentally characterized, specifically with respect to its unique degrees of freedom, i.e., the four switching times, which alternate the columns between interconnected and batch states. By means of isolation of the main charge isoform of an antibody, it is shown that purity is determined by the selection of the product collection window with negligible influence from the recycle phases. In addition, the amount of weak and strong impurities can be specifically attributed to the start and end of the collection, respectively. Due to higher abundance of weakly adsorbing impurities, the start of product collection influences productivity and yield more than the other switching times. Furthermore, most of the encountered tendencies scale between different loadings. The found trends can be rationalized from the corresponding batch chromatogram and therefore used during process design to obtain desirable process performances without extensive trial‐and‐error experimentation or complete model development and calibration.     

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.