Some vocabulary and grammar for the analysis of multi-environment trials, as applied to the analysis of FPB and PPB trials

For the improvement of genetic material suitable for on farm use under low-input conditions, participatory and formal plant breeding strategies are frequently presented as competing options. A common frame of reference to phrase mechanisms and purposes related to breeding strategies will facilitate clearer descriptions of similarities and differences between participatory plant breeding and formal plant breeding. In this paper an attempt is made to develop such a common framework by means of a statistically inspired language that acknowledges the importance of both on farm trials and research centre trials as sources of information for on farm genetic improvement. Key concepts are the genetic correlation between environments, and the heterogeneity of phenotypic and genetic variance over environments. Classic selection response theory is taken as the starting point for the comparison of selection trials (on farm and research centre) with respect to the expected genetic improvement in a target environment (low-input farms). The variance-covariance parameters that form the input for selection response comparisons traditionally come from a mixed model fit to multi-environment trial data. In this paper we propose a recently developed class of mixed models, namely multiplicative mixed models, also called factor-analytic models, for modelling genetic variances and covariances (correlations). Mixed multiplicative models allow genetic variances and covariances to be dependent on quantitative descriptors of the environment, and confer a high flexibility in the choice of variance-covariance structure, without requiring the estimation of a prohibitively high number of parameters. As a result detailed considerations regarding selection response comparisons are facilitated. ne statistical machinery involved is illustrated on an example data set consisting of barley trials from the International Center for Agricultural Research in the Dry Areas (ICARDA). Analysis of the example data showed that participatory plant breeding and formal plant breeding are better interpreted as providing complementary rather than competing information.

Mixed model formulations for multi-environment trials

When studying genotype X environment interaction in multi-environment trials, plant breeders and geneticists often consider one of the effects, environments or genotypes, to be fixed and the other to be random. However, there are two main formulations for variance component estimation for the mixed model situation, referred to as the unconstrained-parameters (UP) and constrained-parameters (CP) formulations. These formulations give different estimates of genetic correlation and heritability as well as different tests of significance for the random effects factor. The definition of main effects and interactions and the consequences of such definitions should be clearly understood, and the selected formulation should be consistent for both fixed and random effects. A discussion of the practical outcomes of using the two formulations in the analysis of balanced data from multi-environment trials is presented. It is recommended that the CP formulation be used because of the meaning of its parameters and the corresponding variance components. When managed (fixed) environments are considered, users will have more confidence in prediction for them but will not be overconfident in prediction in the target (random) environments. Genetic gain (predicted response to selection in the target environments from the managed environments) is independent of formulation.

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.

GGE biplot analysis of multi-environment yield trials of rice produced in a temperate climate

Low temperature is one of the main environmental constraints for rice ( Oryza sativa L.) grain production yield. It is known that multi-environment studies play a critical role in the sustainability of rice production across diverse environments. However, there are few studies based on multi-environment studies of rice in temperate climates. The aim was to study the performance of rice plants in cold environments. Four experimental lines and six cultivars were evaluated at three locations during three seasons. The grain yield data were analyzed with ANOVA, mixed models based on the best linear unbiased predictors (BLUPs), and genotype plus Genotype × Environment interaction (GGE) biplot. High genotype contribution (> 25%) was observed in grain yield and the interaction between genotype and locations was not very important. Results also showed that ‘Quila 241319’ was the best experimental line with the highest grain yield (11.3 t ha-1) and grain yield stability across the environments; commercial cultivars were classified as medium grain yield genotypes.

Milling quality and protein properties of autumn-sown Chinese wheats evaluated through multi-location trials

Eight milling quality and protein properties of autumn-sown Chinese wheats were investigated using 59 cultivars and advanced lines grown in 14 locations in China from 1995 to 1998. Wide ranges of variability for all traits were observed across genotypes and locations. Genotype, location, year, and their interactions all significantly influenced most of the quality parameters. Kernel hardness, Zeleny sedimentation value, and mixograph development time were predominantly influenced by the effects of genotype. Genotype, location and genotype x location interaction were all important sources of variation for thousand kernel weight, test weight, protein content, and falling number, whereas genotype x location interaction had the largest effect on flour yield. Most of the genotypes were characterized by weak gluten strength with Zeleny sedimentation values less than 40 ml and mixograph development time shorter than 3 min. Eight groups of genotypes were recognized based on the average quality performance, grain hardness and gluten strength were the two parameters that determined the grouping, with contributions from protein content. Genotypes such as Zhongyou 16 and Annong 8903 displayed good milling quality, high grain hardness, protein content and strong gluten strength with high sedimentation value and long mixograph development time. Genotypes such as Lumai 15 and Yumai 18 were characterized by low grain hardness, protein content and weak gluten strength. Genotypes such as Yannong 15 and Chuanmai 24 were characterized by strong gluten strength with high sedimentation value and long mixograph development time, but low grain hardness and protein content lower than 12.3%. Genotypes such as Jingdong 6 and Xi'an 8 had weak gluten strength, but with high grain hardness and protein content higher than 12.2%. Five groups of locations were identified, and protein content and gluten strength were the two parameters that determined the grouping. Beijing, Shijiazhuang, Nanyang, Zhumadian and Nanjing produced wheats with medium to strong gluten strength and medium protein content, although there was still a large variation for most of the traits investigated between the locations. Wheat produced in Yantai was characterized by strong gluten strength, but with low protein content. Jinan, Anyang and Linfen locations produced wheats with medium to weak gluten strength and medium to high protein content. Wheats produced in Yangling, Zhenzhou, and Chengdu were characterized by weak gluten strength with medium to low protein content, whereas wheats produced in Xuzhou and Wuhan were characterized by weak gluten strength with low protein content. Industrial grain quality could be substantially improved through integrating knowledge of geographic genotype distribution with key location variables that affected end-use quality.

Using crop simulation to generate genotype by environment interaction effects for sorghum in water-limited environments

Multi-environment trials (METs) used to evaluate breeding lines vary in the number of years that they sample. We used a cropping systems model to simulate the target population of environments (TPE) for 6 locations over 108 years for 54 'near-isolines' of sorghum in north-eastern Australia. For a single reference genotype, each of 547 trials was clustered into 1 of 3 'drought environment types' (DETs) based on a seasonal water stress index. Within sequential METs of 2 years duration, the frequencies of these drought patterns often differed substantially from those derived for the entire TPE. This was reflected in variation in the mean yield of the reference genotype. For the TPE and for 2-year METs, restricted maximum likelihood methods were used to estimate components of genotypic and genotype by environment variance. These also varied substantially, although not in direct correlation with frequency of occurrence of different DETs over a 2-year period. Combined analysis over different numbers of seasons demonstrated the expected improvement in the correlation between MET estimates of genotype performance and the overall genotype averages as the number of seasons in the MET was increased.

New strategies to detect and understand genotype-by-environment interactions and QTL-by-environment interactions

Dissertação para obtenção do Grau de Doutor em Estatística e Gestão do Risco, especialidade em Estatística

STATISTICAL TEST FOR GENOTYPE AND ENVIRONMENT CONTRIBUTION IN THE GENOTYPES x ENVIRONMENTS INTERACTION MATRIX

The objective of the present work was to propose a method for testing the contribution of each level of the factors in a genotypes x environments (GxE) interaction using multi-environment trials analyses by means of an F test. The study evaluated a data set, with twenty genotypes and thirty-four environments, in a block design with four replications. The sum of squares within rows (genotypes) and columns (environments) of the GxE matrix was simulated, generating 10000 experiments to verify the empirical distribution. Results indicate a noncentral chi-square distribution for rows and columns of the GxE interaction matrix, which was also verified by the Kolmogorov-Smirnov test and Q-Q plot. Application of the F test identified the genotypes and environments that contributed the most to the GxE interaction. In this way, geneticists can select good genotypes in their studies.

Multi-Environment Model Estimation for Motility Analysis of Caernorhabditis elegans

The nematode Caenorhabditis elegans is a well-known model organism used to investigate fundamental questions in biology. Motility assays of this small roundworm are designed to study the relationships between genes and behavior. Commonly, motility analysis is used to classify nematode movements and characterize them quantitatively. Over the past years, C. elegans' motility has been studied across a wide range of environments, including crawling on substrates, swimming in fluids, and locomoting through microfluidic substrates. However, each environment often requires customized image processing tools relying on heuristic parameter tuning. In the present study, we propose a novel Multi-Environment Model Estimation (MEME) framework for automated image segmentation that is versatile across various environments. The MEME platform is constructed around the concept of Mixture of Gaussian (MOG) models, where statistical models for both the background environment and the nematode appearance are explicitly learned and used to accurately segment a target nematode. Our method is designed to simplify the burden often imposed on users; here, only a single image which includes a nematode in its environment must be provided for model learning. In addition, our platform enables the extraction of nematode ‘skeletons’ for straightforward motility quantification. We test our algorithm on various locomotive environments and compare performances with an intensity-based thresholding method. Overall, MEME outperforms the threshold-based approach for the overwhelming majority of cases examined. Ultimately, MEME provides researchers with an attractive platform for C. elegans' segmentation and ‘skeletonizing’ across a wide range of motility assays.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.

Measurement and management of genotype-environment interaction (GxE) for the improvement of rainfed lowland rice yield in Cambodia

The magnitude and nature of genotype-by-environment interactions (G×E) for grain yield (GY) and days to flower (DTF) in Cambodia were examined using a random population of 34 genotypes taken from the Cambodian rice improvement program. These genotypes were evaluated in multi-environment trials (MET) conducted across three years (2000 to 2002) and eight locations in the rainfed lowlands. The G×E interaction was partitioned into components attributed to genotype-by-location (G×L), genotype-by-year (G×Y) and genotype-by-location-by-year (G×L×Y) interactions. The G×L×Y interaction was the largest component of variance for GY. The G×L interaction was also significant and comparable in size to the genotypic component (G). The G×Y interaction was small and non significant. A major factor contributing to the large G×L×Y interactions for GY was the genotypic variation for DTF in combination with environmental variation for the timing and intensity of drought. Some of the interactions for GY associated with timing of plant development and exposure to drought were repeatable across the environments enabling the identification of three-target populations of environments (TPE) for consideration in the breeding program. Four genotypes were selected for wide adaptation in the rainfed lowlands in Cambodia.

Genotype-by-management interactions for grain yield and grain protein concentration of wheat

The magnitude of genotype-by-management (G x M) interactions for grain yield and grain protein concentration was examined in a multi-environment trial (MET) involving a diverse set of 272 advanced breeding lines from the Queensland wheat breeding program. The MET was structured as a series of management-regimes imposed at 3 sites for 2 years. The management-regimes were generated at each site-year as separate trials in which planting time, N fertiliser application rate, cropping history, and irrigation were manipulated. irrigation was used to simulate different rainfall regimes. From the combined analysis of variance, the G x M interaction variance components were found to be the largest source of G x E interaction variation for both grain yield (0.117 +/- 0.005 t(2) ha(-2); 49% of total G x E 0.238 +/- 0.028 t(2) ha(-2)) and grain protein concentration (0.445 +/- 0.020%(2); 82% of total G x E 0.546 +/- 0.057%(2)), and in both cases this source of variation was larger than the genotypic variance component (grain yield 0.068 +/- 0.014 t(2) ha(-2) and grain protein 0.203 +/- 0.026%(2)). The genotypic correlation between the traits varied considerably with management-regime, ranging from -0.98 to -0.31, with an estimate of 0.0 for one trial. Pattern analysis identified advanced breeding lines with improved grain yield and grain protein concentration relative to the cultivars Hartog, Sunco and Meteor. It is likely that a large component of the previously documented G x E interactions for grain yield of wheat in the northern grains region are in part a result of G x M interactions. The implications of the strong influence of G x M interactions for the conduct of wheat breeding METs in the northern region are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

Identification of research to improve the efficiency of breeding strategies for white clover in Australia - a review

A major challenge faced by today's white clover breeder is how to manage resources within a breeding program. It is essential to utilise these resources with sufficient flexibility to build on past progress from conventional breeding strategies, but also take advantage of emerging opportunities from molecular breeding tools such as molecular markers and transformation. It is timely to review white clover breeding strategies. This background can then be used as a foundation for considering how to continue conventional plant improvement activities and complement them with molecular breeding opportunities. In this review, conventional white clover breeding strategies relevant to the Australian dryland target population environments are considered. Attention is given to: (i) availability of genetic variation, (ii) characterisation of germplasm collections, (iii) quantitative models for estimation of heritability, (iv) the role of multi-environment trials to accommodate genotype-by-environment interactions, (v) interdisciplinary research to understand adaptation to dryland environments, (vi) breeding and selection strategies, and (vii) cultivar structure. Current achievements in biotechnology with specific reference to white clover breeding in Australia are considered, and computer modelling of breeding programs is discussed as a useful integrative tool for the joint evaluation of conventional and molecular breeding strategies and optimisation of resource use in breeding programs. Four areas are identified as future research priorities: (i) capturing the potential genetic diversity among introduced accessions and ecotypes that are adapted to key constraints such as summer moisture stress and the use of molecular markers to assess the genetic diversity, (ii) understanding the underlying physiological/morphological root and shoot mechanisms involved in water use efficiency of white clover, with the objective of identifying appropriate selection criteria, (iii) estimation of quantitative genetic parameters of important morphological/physiological attributes to enable prediction of response to selection in target environments, and (iv) modelling white clover breeding strategies to evaluate the opportunities for integration of molecular breeding strategies with conventional breeding programs.