Crop Variety Trials -- Contents -- Preface -- Chapter 1 Theoretical Framework for Crop Variety Trials -- 1.1 Heritability under the genotype-location-year framework -- 1.2 Possible approaches to improve the variety trial efficiency -- 1.2.1 Increase the genotypic variance -- 1.2.2 Increase the number of years -- 1.2.3 Increase the number of test locations -- 1.2.4 Increase the number of replicates in each trial -- 1.2.5 Reduce the experimental error -- 1.2.6 Make use of any repeatable genotype-by-location interaction -- 1.3 Heritability under various scenarios and their interpretations -- 1.3.1 Unreplicated data from multiyear, multilocation variety trials -- 1.3.2 Multilocation trial data from a single year -- 1.3.3 Multiyear data at a single location -- 1.3.4 Data from a single trial -- 1.4 Heritability estimated in the genotype-environment framework -- 1.4.1 Replicated genotype-environment data -- 1.4.2 Genotype-environment two-way table of means -- 1.4.3 Genotype-environment two-way table of unreplicated trials -- 1.4.4 Genotype-location table of means across years and replications -- 1.5 Heritability and target region subdivision -- 1.5.1 Heritability and variance component analysis -- 1.5.2 Heritability and target region subdivision -- 1.5.3 How to divide the target region -- 1.5.4 The merging of different target regions -- 1.6 Genotype-specific heritability as a shrinkage factor -- 1.7 Estimation of variance components and heritability -- 1.7.1 Mean square, expected mean square, and variance components -- 1.7.2 An example of heritability estimation -- 1.8 Summary -- Chapter 2 An Overview of Variety Trial Data and Analyses -- 2.1 Levels of variety trial data -- 2.1.1 Three levels of variety trial data -- 2.1.2 Three types of traits -- 2.1.3 The hierarchy of variety trial data analyses -- 2.2 Single-trial data and analyses.

2.2.1 Single-trial data -- 2.2.2 Objectives of data analysis -- 2.2.3 Approaches and techniques -- 2.3 Single-year data and analyses -- 2.3.1 Multilocation data from a single year -- 2.3.2 Objectives of data analysis -- 2.3.2.1 Human error detection and correction -- 2.3.2.2 Elimination of inferior genotypes -- 2.3.2.3 Mega-environment analysis -- 2.3.2.4 Test location evaluation -- 2.3.2.5 Understanding the trait associations and trait profiles of the genotypes -- 2.3.3 Approaches and techniques -- 2.4 Multiyear data and analyses -- 2.4.1 Multiyear variety trial data -- 2.4.2 Objectives of data analysis -- 2.4.3 Approaches and techniques -- 2.5 Decision-making based on multiple traits -- 2.5.1 Objectives of data analysis -- 2.5.2 Approaches and techniques -- Chapter 3 Introduction to Biplot Analysis -- 3.1 Biplot and matrix multiplication -- 3.2 Visualizing a biplot based on the inner-product property -- 3.2.1 To visualize the sign and value of each element in matrix P -- 3.2.2 Rank the columns within a row -- 3.2.3 Rank the rows within a column -- 3.2.4 Compare two rows -- 3.2.5 Compare two columns -- 3.2.6 Find which row is the largest in a column -- 3.2.7 Find which column is the largest in a row -- 3.3 Constructing a biplot based on research data in the form of a two-way table -- 3.3.1 Singular value decomposition and principal component analysis -- 3.3.2 Singular value partition -- 3.3.3 Rescaling of the row and columns scores -- 3.3.4 Flipping the biplot vertically and/or horizontally -- 3.3.5 Biplot rotation -- 3.3.6 Row and column scores versus biplot patterns -- 3.4 Implementation of biplot analysis -- Chapter 4 Data Centering for Biplot Analysis -- 4.1 Five possible types of data centering -- 4.1.1 Uncentered -- 4.1.2 Grand mean-centered -- 4.1.3 Environment-centered -- 4.1.4 Double-centered -- 4.1.5 Genotype-centered.

4.2 Suitability of various biplots for genotype evaluation -- 4.2.1 Biplot based on uncentered data -- 4.2.2 Biplot based on grand mean-centered data -- 4.2.3 Biplot based on environment-centered data -- 4.2.4 Biplot based on double-centered data -- 4.2.5 Biplot based on genotype-centered data -- 4.2.6 The GGE biplot is the only suitable biplot for genotype evaluation -- 4.3 Suitability of various biplots for test environment evaluation -- 4.3.1 Biplot based on uncentered data -- 4.3.2 Biplot based on grand mean-centered data -- 4.3.3 Biplot based on environment-centered data -- 4.3.4 Biplot based on double-centered data -- 4.4 Unique properties of the GGE biplot -- 4.4.1 "G + GE" is a key concept in quantitative genetics -- 4.4.2 The GGE distance between genotypes equals the Euclidean distance between them -- 4.4.3 The vector length of the environments is proportional to their SD -- 4.4.4 The cosine of the angle between two environments approximates the correlation between them -- 4.5 Utilities of other types of biplots -- 4.5.1 Biplot based on uncentered data for studying QTL-by-environment interactions -- 4.5.2 The GE biplot for visualizing gene expression data -- 4.5.3 The EGE biplot for identifying suitable production regions -- 4.6 How to generate biplots based on different data centering -- 4.6.1 The ANOVA table -- 4.6.2 Generating biplots based on different data-centering methods -- 4.6.3 Generating an EGE biplot based on genotype-centered data -- 4.6.4 The which-won-where view of a biplot -- 4.6.5 The environmental vector view of a biplot -- 4.6.6 Correlation among testers -- 4.6.7 Remove less responsive genes from the biplot -- Chapter 5 Data Scaling and Weighting for GGE Biplot Analysis -- 5.1 The link between the theory of indirect selection in quantitative genetics and test environment evaluation in GGE biplot analysis.

5.2 Statistical parameters charactering a variety trial -- 5.3 Data scaling methods in GGE biplot analysis -- 5.3.1 Unscaled GGE biplot -- 5.3.2 SD-scaled GGE biplot -- 5.3.3 SE-scaled GGE biplot -- 5.3.4 SD-scaled and h-weighted GGE biplot -- 5.3.5 h-Weighted GGE biplot -- 5.3.6 Environmental mean-scaled and h-weighted GGE biplot -- 5.3.7 Environmental max-scaled and h-weighted GGE biplot -- 5.4 Factor analytic-based GGE biplot -- 5.5 Preferred data scaling in GGE biplot analysis -- 5.5.1 Suitability for test environment evaluation -- 5.5.2 Suitability for genotype evaluation -- 5.6 How to implement data scaling in biplot analysis -- Chapter 6 Frequently Asked Questions About Biplot Analysis -- 6.1 Frequently asked questions -- 6.1.1 What do PC1 and PC2 represent? -- 6.1.2 What are the units of PC1 and PC2? -- 6.1.3 What do I need to do before conducting biplot analysis? -- 6.1.4 Is the biplot adequate in displaying the patterns of the two-way table? -- 6.1.5 What if only the first PC is needed? -- 6.1.6 What if the biplot does not adequately display the data? -- 6.1.7 What if my dataset has missing values? -- 6.1.7.1 Fill missing cells with the environmental means -- 6.1.7.2 Find the complete subset -- 6.1.7.3 Fill missing cells with estimated values -- 6.1.8 Is the difference between two genotypes observed in the biplot statistically significant? -- 6.1.9 Is the observed correlation between two environments statistically significant? -- 6.1.10 Is the observed interaction pattern in the biplot statistically significant? -- 6.1.11 GGE biplots versus AMMI "biplots": which is better? -- 6.1.12 Is the FA biplot superior to the GGE biplot? -- 6.2 Frequently seen mistakes in biplot interpretation -- 6.2.1 "PC1 scores represent the genotypic main effects" -- 6.2.2 "The GGE biplot displays the correlations between genotypes".

6.2.3 "The GGE biplot displays the correlation between the genotypes and the environments" -- 6.2.4 Biplots without indication of the data centering and scaling methods -- 6.2.5 Biplots not drawn to scale -- 6.2.6 GGL biplot based on a genotype-by-location two-way table averaged across years -- 6.2.7 Biplots based on PCs other than PC1 and PC2 -- 6.2.8 "GE biplot can be interpreted similarly as the GGE biplot" -- Chapter 7 Single-Trial Data Analysis -- 7.1 Objectives and steps in single-trial data analysis -- 7.2 The discrimination and precision of a variety trial -- 7.3 Detecting and correcting any human errors -- 7.3.1 Use of simply inherited traits to detect human errors -- 7.3.2 Genotype-by-replication biplot to detect typos in the data -- 7.3.3 Genotype-by-replicate biplot to detect other human errors -- 7.4 Spatial analysis to correct any field trend and variation -- 7.4.1 Control of field variation through experimental design and spatial analysis -- 7.4.2 Spatial analysis models -- 7.4.2.1 Model 1 -- 7.4.2.2 Model 2 -- 7.4.2.3 Model 3 -- 7.4.2.4 Model 4 -- 7.4.3 Case study 1: an oat variety trial conducted at Princeville, Quebec, 2008 -- 7.4.3.1 Trial description -- 7.4.3.2 Analysis and results -- 7.4.4 Case study 2: an oat variety trial conducted at Ottawa, Ontario, in 2011 -- 7.4.4.1 Trial description -- 7.4.4.2 Analysis and results -- 7.4.5 Case study 3: a dataset that does not need spatial adjustment -- 7.4.6 Case study 4: a dataset that cannot be improved by spatial adjustment -- 7.5 A road map for single-trial analysis -- 7.6 How to implement single-trial data analysis -- 7.6.1 GGEbiplot modules for single-trial data analysis -- 7.6.2 How to generate a genotype-by-replicate biplot -- 7.6.3 The GGEbiplot module for ANOVA/spatial analysis -- 7.6.4 How to conduct design-based analysis -- 7.6.5 How to conduct spatial variation adjustment.

7.6.6 How to generate a scatter plot of two variables.