Analysis of yield and oil from a series of canola breeding trials. Part I. Fitting factor analytic mixed models with pedigree information

In this paper multiplicative mixed models have been used for the analysis of multi-environment trial (MET) data for canola oil and grain yield. Information on pedigrees has been included to allow for the modelling of additive and nonadditive genetic effects. The MET data set included a total of 19 trials (synonymous with sites or environments), which were sown across southern Australia in 2007 and 2008. Each trial was designed as a p-rep design using DiGGeR with the default prespecified spatial model. Lines in their first year of testing were unreplicated, whereas there were two or three replications of advanced lines or varieties. Pedigree information on a total of 578 entries was available, and there were 69 entries that had unknown pedigrees. The degree of inbreeding varied from 0 (55 entries) to nearly fully inbred (337 entries). Subsamples of 2 g harvested grain were taken from each plot for determination of seed oil percentage by near infrared reflectance spectroscopy. The MET analysis for both yield and oil modelled genetic effects in different trials using factor analytic models and the residual plot effects for each trial were modelled using spatial techniques. Models in which pedigree information was included provided significantly better fits to both yield and oil data.     

Optimization of multi-environment trials for genomic selection based on crop models

Key message

We propose a statistical criterion to optimize multi-environment trials to predict genotype × environment interactions more efficiently, by combining crop growth models and genomic selection models.

Abstract

Genotype × environment interactions (GEI) are common in plant multi-environment trials (METs). In this context, models developed for genomic selection (GS) that refers to the use of genome-wide information for predicting breeding values of selection candidates need to be adapted. One promising way to increase prediction accuracy in various environments is to combine ecophysiological and genetic modelling thanks to crop growth models (CGM) incorporating genetic parameters. The efficiency of this approach relies on the quality of the parameter estimates, which depends on the environments composing this MET used for calibration. The objective of this study was to determine a method to optimize the set of environments composing the MET for estimating genetic parameters in this context. A criterion called OptiMET was defined to this aim, and was evaluated on simulated and real data, with the example of wheat phenology. The MET defined with OptiMET allowed estimating the genetic parameters with lower error, leading to higher QTL detection power and higher prediction accuracies. MET defined with OptiMET was on average more efficient than random MET composed of twice as many environments, in terms of quality of the parameter estimates. OptiMET is thus a valuable tool to determine optimal experimental conditions to best exploit MET and the phenotyping tools that are currently developed.

     

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.     

Estimation in a multiplicative mixed model involving a genetic relationship matrix

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.     

Simple outlier detection for a multi-environmental field trial

The aim of plant breeding trials is often to identify crop variety that are well adapt to target environments. These varieties are identified through genomic prediction from the analysis of multi-environmental field trial (MET) using linear mixed models. The occurrence of outliers in MET is common and known to adversely impact the accuracy of genomic prediction yet the detection of outliers are often neglected. A number of reasons stand for this—first, complex data such as a MET give rise to distinct levels of residuals (eg, at a trial level or individual observation level). This complexity offers additional challenges for an outlier detection method. Second, many linear mixed model software packages that cater for complex variance structures needed in the analysis of MET are not well streamlined for diagnostics by practitioners. We demonstrate outlier detection methods that are simple to implement in any linear mixed model software packages and computationally fast. Although these methods are not optimal methods in outlier detection, they offer practical value for ease of application in the analysis pipeline of regularly collected data. These are demonstrated using simulation based on two real bread wheat yield METs. In particular, models that consider analysis of yield trials either independently or jointly (thus borrowing strength across trials) are considered. Case studies are presented to highlight benefit of joint analysis for outlier detection.     

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     

Retrospective analysis of the relationships among the test environments of the Southern Queensland sugarcane breeding programme

Repeatability of aspects of genotype by environment (GxE) interactions is an important factor to be assessed in designing more efficient selection programmes. Sugar yield data from multi environment trials (METs) which were part of the sugarcane breeding programme in southern Queensland were analysed. Data were obtained from 71 environments consisting of trials planted from 1986 to 1989. Retrospective analysis on these data was conducted to assess the repeatability of the clone by environment (CxE) interactions over locations and years. This analysis focussed on identifying similarities among test environments in the way they discriminated among clones for sugar yield. Analyses of variance and pattern analyses on environments over years based on standardised data were conducted. The pattern analyses were done sequentially according to the accumulated data sets over years. Squared Euclidean distances among environments were averaged over data sets and years before pattern analyses across the data sets were conducted. A graphical methodology was developed to present the results of the cumulative historical analysis. CxE interactions of a magnitude which affected selection decisions were present in each data set studied. Pattern analyses on cumulative data sets identified environmental groupings that were based on geographical positions. Each location generated a different pattern of discrimination among the clones. These results emphasised the importance of clone by location (CxL) interactions in southern Queensland and the need to concentrate more on testing across locations than on ratooning ability within a location. The classifications identified similarities among ratoon crops within a location, differences among locations and differences between ratoon crops and their plant crop (PC). This suggested that some aspects of CxL and clone by crop-year (CxY) interactions were repeatable across years. The potential applications of these results to increase efficiency of the sugarcane breeding programme, such as the possibility of applying indirect selection among environments generating similar discrimination among clones, are discussed.Abbreviations GxE Genotype-by-environment interactions - METs multi-environment trials - CxE clone-by-en-vironment interactions - CxL clone-by-location interactions - PC plant crop - CxY clone-by-crop-year interactions - CxLxF clone-by-location-by-crop-year interactions - SYT substation yield trials - BSES Bureau of SugarExperiment Stations     

Fitting a regression model for genotype-by-environment data on heading dates in grasses by methods for nonlinear mixed models

The analysis of agricultural crop variety trials is usually complicated by the presence of genotype-by-environment interaction. A number of methods and models have been proposed to tackle this problem. One of the most common methods is the regression approach due to Yates and Cochran (1938, Journal of Agricultural Science 28, 556-580), in which performances of genotypes in the environments are regressed onto environmental means. The underlying regression model contains a multiplicative term with two unknown parameters (one for genotypes and one for environments). In the present paper, the model is modified by exchanging the role of genotypes and environments. Various diagnostic plots show that this modified model is adequate for a data set on heading dates in the grass species Dactylis glomerata. If environments are considered as a random factor while genotypes are taken as fixed, the model falls into the class of nonlinear mixed models. Recently, a number of procedures have been suggested for this class of models, which are based on first-order Taylor series expansion. Alternatively, the model can be estimated by maximum likelihood. This paper discusses the application of these methods for estimating parameters of the model.     

Advantage of single-trial models for response to selection in wheat breeding multi-environment trials

An investigation was conducted to evaluate the impact of experimental designs and spatial analyses (single-trial models) of the response to selection for grain yield in the northern grains region of Australia (Queensland and northern New South Wales). Two sets of multi-environment experiments were considered. One set, based on 33 trials conducted from 1994 to 1996, was used to represent the testing system of the wheat breeding program and is referred to as the multi-environment trial (MET). The second set, based on 47 trials conducted from 1986 to 1993, sampled a more diverse set of years and management regimes and was used to represent the target population of environments (TPE). There were 18 genotypes in common between the MET and TPE sets of trials. From indirect selection theory, the phenotypic correlation coefficient between the MET and TPE single-trial adjusted genotype means [r _p(MT)] was used to determine the effect of the single-trial model on the expected indirect response to selection for grain yield in the TPE based on selection in the MET. Five single-trial models were considered: randomised complete block (RCB), incomplete block (IB), spatial analysis (SS), spatial analysis with a measurement error (SSM) and a combination of spatial analysis and experimental design information to identify the preferred (PF) model. Bootstrap-resampling methodology was used to construct multiple MET data sets, ranging in size from 2 to 20 environments per MET sample. The size and environmental composition of the MET and the single-trial model influenced the r _p(MT). On average, the PF model resulted in a higher r _p(MT) than the IB, SS and SSM models, which were in turn superior to the RCB model for MET sizes based on fewer than ten environments. For METs based on ten or more environments, the r _p(MT) was similar for all single-trial models.Communicated by H.C. Becker     

油用向日葵主要农艺性状的遗传效应及相关性研究

根据加性-显性与环境互作的遗传模型,对6个油用向日葵自交系及其配制的9个杂交组合在2个环境下的7个农艺性状表现进行遗传分析,揭示油用向日葵主要农艺性状遗传性质、规律以及主要农艺性状对含油率的贡献率。结果表明:株高、茎粗、盘径、百粒重、籽仁率和单盘粒重等6个遗传性状主要受加性和显性共同控制,结实率的遗传以加性、显性×环境互作效应为主,籽仁率、单盘粒重以加性、显性、显性×环境互作效应为主;性状间的各项遗传相关性多以加性遗传相关为主。百粒重的净效应对籽实含油率的加性遗传方差贡献率最高,结实率的净效应对籽实含油率的显性遗传方差贡献率最高,单盘粒重对籽实含油率的加性×环境互作遗传方差的贡献率最高。     

Environmental stress alters genetic regulation of novelty seeking in vervet monkeys

Considerable attention has been paid to identifying genetic influences and gene-environment interactions that increase vulnerability to environmental stressors, with promising but inconsistent results. A nonhuman primate model is presented here that allows assessment of genetic influences in response to a stressful life event for a behavioural trait with relevance for psychopathology. Genetic and environmental influences on free-choice novelty seeking behaviour were assessed in a pedigreed colony of vervet monkeys before and after relocation from a low stress to a higher stress environment. Heritability of novelty seeking scores, and genetic correlations within and between environments were conducted using variance components analysis. The results showed that novelty seeking was markedly inhibited in the higher stress environment, with effects persisting across a 2-year period for adults but not for juveniles. There were significant genetic contributions to novelty seeking scores in each year (h(2) = 0.35-0.43), with high genetic correlations within each environment (rhoG > 0.80) and a lower genetic correlation (rhoG = 0.35, non-significant) between environments. There were also significant genetic contributions to individual change scores from before to after the move (h(2) = 0.48). These results indicate that genetic regulation of novelty seeking was modified by the level of environmental stress, and they support a role for gene-environment interactions in a behavioural trait with relevance for mental health.     

烤烟主要农艺性状的遗传与相关分析

利用包括基因型与环境互作的加性-显性遗传模型,对14个烤烟品种(系)及其配制的41个杂交组合在4个环境下的7个农艺性状表现进行遗传分析。结果表明,株高、节距、腰叶宽主要受加性效应控制,叶数、腰叶长受显性×环境互作效应影响最大,茎围以加性×环境互作效应、显性×环境互作效应为主,产量以加性效应、显性×环境互作效应为主。适应当地生态条件的品种（系）具有较高的正向加性效应。许多组合的显性主效应及在各试验点的显性×环境互作效应在方向上不尽一致,杂交组合的选配宜针对特定的生态环境进行。性状相关分析表明,大多数成对性状的各项相关系数为正值,且多以加性遗传相关为主,可利用株高对产量进行间接选择。
     

A multiplicative-epistatic model for analyzing interspecific differences in outcrossing species

Epistasis may play an important role in evolution and speciation. Under multiplicative interactions between different loci, an analytical model is proposed to estimate genetic parameters at the individual locus level that contribute to interspecific differences in outcrossing species. The multiplicative epistasis model, inferred from a number of animal and plant experiments, suggests that genotypes at a pair of loci have genotypic values equal to the product of genotypic values at the two different loci. By considering the genetic property of outcrossing species (i.e., high polymorphisms) in the multilevel family structure analysis for an intra- and interspecific factorial mating design, a method is developed to provide estimates for allele frequencies and additive and dominant effects at individual loci in each of the two parental populations, the genotypic values of newly formed heterozygotes through species combination each with one allele from a parental population and the second from the other parental population, and the numbers of genetic factors that lead to species differentiation. Use of clones offers a tremendous power to test the adequacy of the model. However, the utilization of the model with species that cannot be cloned is also discussed. An example with interspecific hybrids of two forest tree species is used to demonstrate the model.     

Environment characterization as an aid to wheat improvement: interpreting genotype-environment interactions by modelling water-deficit patterns in North-Eastern Australia

Genotype-environment interactions (GEI) limit genetic gain for complex traits such as tolerance to drought. Characterization of the crop environment is an important step in understanding GEI. A modelling approach is proposed here to characterize broadly (large geographic area, long-term period) and locally (field experiment) drought-related environmental stresses, which enables breeders to analyse their experimental trials with regard to the broad population of environments that they target. Water-deficit patterns experienced by wheat crops were determined for drought-prone north-eastern Australia, using the APSIM crop model to account for the interactions of crops with their environment (e.g. feedback of plant growth on water depletion). Simulations based on more than 100 years of historical climate data were conducted for representative locations, soils, and management systems, for a check cultivar, Hartog. The three main environment types identified differed in their patterns of simulated water stress around flowering and during grain-filling. Over the entire region, the terminal drought-stress pattern was most common (50% of production environments) followed by a flowering stress (24%), although the frequencies of occurrence of the three types varied greatly across regions, years, and management. This environment classification was applied to 16 trials relevant to late stages testing of a breeding programme. The incorporation of the independently-determined environment types in a statistical analysis assisted interpretation of the GEI for yield among the 18 representative genotypes by reducing the relative effect of GEI compared with genotypic variance, and helped to identify opportunities to improve breeding and germplasm-testing strategies for this region.     

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.     

Analyzing multi-environment variety trials using randomization-derived mixed models

Of interest is the analysis of results of a series of experiments repeated at several environments with the same set of plant varieties. Suppose that the experiments, multi-environment variety trials, are all conducted in resolvable incomplete block (IB) designs. Following the randomization approach adopted in Caliński and Kageyama (2000, Lecture Notes in Statistics, 150), two models for analyzing such trial data can be considered. One is derived under a complete additivity assumption, the other takes into account possible different responses of the varieties to variable environmental conditions. The analysis under the first, the standard model, does not provide answers to questions related to the performance of the individual varieties at different environments. These can be considered when using the more general second model. The purpose of this article is to devise interesting parameter estimation and hypothesis testing procedures under that more realistic model. Its application is illustrated by a thorough analysis of a set of data from a winter wheat series of trials.     

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。     

二棱大麦茎杆特性的ADAA模型的遗传研究

以二棱大麦(Hordeum,distichum L.)甘木二条等7个品种进行半双列杂交,对1992年和1997年的亲本、F     

A statistical simulation model for field testing of non‐target organisms in environmental risk assessment of genetically modified plants

Genetic modification of plants may result in unintended effects causing potentially adverse effects on the environment. A comparative safety assessment is therefore required by authorities, such as the European Food Safety Authority, in which the genetically modified plant is compared with its conventional counterpart. Part of the environmental risk assessment is a comparative field experiment in which the effect on non‐target organisms is compared. Statistical analysis of such trials come in two flavors: difference testing and equivalence testing. It is important to know the statistical properties of these, for example, the power to detect environmental change of a given magnitude, before the start of an experiment. Such prospective power analysis can best be studied by means of a statistical simulation model. This paper describes a general framework for simulating data typically encountered in environmental risk assessment of genetically modified plants. The simulation model, available as Supplementary Material, can be used to generate count data having different statistical distributions possibly with excess‐zeros. In addition the model employs completely randomized or randomized block experiments, can be used to simulate single or multiple trials across environments, enables genotype by environment interaction by adding random variety effects, and finally includes repeated measures in time following a constant, linear or quadratic pattern in time possibly with some form of autocorrelation. The model also allows to add a set of reference varieties to the GM plants and its comparator to assess the natural variation which can then be used to set limits of concern for equivalence testing. The different count distributions are described in some detail and some examples of how to use the simulation model to study various aspects, including a prospective power analysis, are provided.