Weikai Yan

GGE Biplot Analysis : A Graphical Tool for Breeders, Geneticists, and Agronomists

GENOTYPE-BY-ENVIRONMENT INTERACTION AND STABILITY ANALYSIS Genotype-by-Environment Interaction Heredity and Environment Genotype-by-Environment Interaction Implications of GEI in Crop Breeding Causes of Genotype-by-Environment Interaction Stability Analyses in Plant Breeding and Performance Trials Stability Analysis in Plant Breeding and Performance Trials Stability Concepts and Statistics Dealing with Genotype-by-Environment Interaction GGE Biplot: Genotype + GE Interaction GGE BIPLOT AND MULTI-ENVIRONMENTAL TRIAL ANALYSIS Theory of Biplot The Concept of Biplot The Inner-Product Property of a Biplot Visualizing the Biplot Relationships among Columns and among Rows Biplot Analysis of Two-Way Data Introduction to GGE Biplot The Concept of GGE and GGE Biplot The Basic Model for a GGE Biplot Methods of Singular Value Partitioning An Alternative Model for GGE Biplot Three Types of Data Transformation Generating a GGE Biplot Using Conventional Methods Biplot Analysis of Multi-Environment Trial Data Objectives of Multi-Environment Trial Data Analysis Simple Comparisons Using GGE Biplot Mega-Environment Investigation Cultivar Evaluation for a Given Mega-Environment Evaluation of Test Environments Comparison with the AMMI Biplot Interpreting Genotype-by-Environment Interaction GGE BIPLOT SOFTWARE AND APPLICATIONS TO OTHER TYPES OF TWO-WAY DATA GGE Biplot Software-The Solution for GGE Biplot Analyses The Need for GGE Biplot Software The Terminology of Entries and Testers Preparing Data File for GGE Biplot Organization of GGE Biplot Software Functions for a Genotype-by-Environment Dataset Function for a Genotype-by-Strain Dataset Application of GGE Biplot to Other Types of Two-way Data GGE Biplot Continues to Evolve Cultivar Evaluation Based on Multiple Traits Why Multiple Traits? Cultivar Evaluation Based on Multiple Traits Identifying Traits for Indirect Selection for Loaf Volume Identification of Redundant Traits Comparing Cultivars as Packages of Traits Investigation of Different Selection Strategies Systems Understanding of Crop Improvement Three-Mode Principal Component Analysis and Visualization QTL Identification Using GGE Biplot Why Biplot? Data Source and Model Grouping of Linked Markers Gene Mapping Using Biplot QTL Identification via GGE Biplot Interconnectedness among Traits and Pleiotropic Effects of a Given Locus Understanding DH Lines through the Biplot Pattern QTL and GE Interaction Biplot Analysis of Diallel Data Model for Biplot Analysis of Diallel Data General Combining Ability of Parents Specific Combining Ability of Parents Heterotic Groups The Best Testers for Assessing General Combining Ability of Parents The Best Crosses Hypothesis on the Genetic Constitution of Parents Targeting a Large Dataset Advantages and Disadvantages of the Biplot Approach Biplot Analysis of Host Genotype-by-Pathogen Strain Interactions Vertical vs. Horizontal Resistance Genotype-By-Strain Interaction for a Barley Net Blotch Genotype-by-Strain Interaction for Wheat Fusarium Head Blight Biplot Analysis to Detect Synergism between Genotypes of Different Species Genotype-by-Strain Interaction for Nitrogen-Fixation Wheat-Maize Interaction for Wheat Haploid Embryo Formation References Index

Biplot analysis of multi-environment trial data: Principles and applications

Biplot analysis has evolved into an important statistical tool in plant breeding and agricultural research. Here we review the basic principles of biplot analysis and recent developments in its application in analyzing multi-environment trail (MET) data, with the aim of providing a working guide for breeders, agronomists, and other agricultural scientists on biplot analysis and interpretation. The review is divided into four sections. The first section is a complete but succinct description of the principles of biplot analysis. The second section is a detailed treatment of biplot analysis of genotype by environment data. It addresses environment and genotype evaluation from all perspectives. The third section deals with biplot analysis of various two-way tables that can be generated from a three-way MET dataset, which is an integral and essential part to a fuller understanding and exploration of MET data. The final section discusses questions that are frequently asked about biplot analysis. Methods descri...

Singular-value partitioning in biplot analysis of multienvironment trial data

GGE biplot, is an ideal tool for MET data analysis (Yan, 2001; Yan et al., 2000, 2001). A GGE biplot that Multienvironment trials (MET) are conducted every year for all sufficiently approximates the GGE of a MET data set major crops throughout the world, and best use of the information allows, among other things, visualization of three imporcontained in MET data for cultivar evaluation and recommendation tant aspects: (i) the genotype environment relations has been an important issue in plant breeding and agricultural reas represented by the which-won-where pattern, which search. A genotype main effect plus genotype environment interaction (GGE) biplot based on MET data allows visualizing (i) the whichfacilitate megaenvironment investigation (Gauch and won-where pattern of the MET, (ii) the interrelationship among test Zobel, 1997); (ii) the interrelationships among test envienvironments, and (iii) the ranking of genotypes based on both mean ronments, which facilitate identification of better enviperformance and stability. Correct visualization of these aspects, howronments for cultivar evaluation (Cooper et al., 1997) ever, requires appropriate singular-value (SV) partitioning between and of redundant environments that can be dismissed the genotype and environment eigenvectors. This paper compares (Yan and Rajcan, 2002); and (iii) the interrelationships four SV scaling methods. Genotype-focused scaling partitions the among genotypes, which facilitate comparison among entire SV to the genotype eigenvectors; environment-focused scaling genotypes and genotype ranking on both mean yield and partitions the entire SV to the environment eigenvectors; symmetrical stability (Yan et al., 2001). In all previous publications, it scaling splits the SV symmetrically between the genotype and the has been implicatively claimed that a single GGE biplot environment eigenvectors; and equal-space scaling splits the SV such is sufficient for all these purposes (Yan, 2001; Yan et that genotype markers and environment markers take equal biplot al., 2000, 2001). The purpose of this paper is to demonspace. It is recommended that the genotype-focused scaling be used strate that different GGE biplots are required to propin visualizing the interrelationship and comparison among genotypes erly address different aspects. and the environment-focused scaling be used in visualizing the interrelationship and comparison among environments. All scaling methods are equally valid in visualizing the which-won-where pattern of the THEORY MET data, but the symmetric scaling is preferred because it has all properties intermediate between the genotypeand the environmentThe Model for a GGE Biplot focused scaling methods. A GGE biplot is constructed by first subjecting the GGE matrix, i.e., the environment-centered data, to singular-value (SV) decomposition. The GGE matrix is decomposed into R performance trials are conducted every three component matrices—the SV matrix (array), the genoyear for all major crops throughout the world with type eigenvector matrix, and the environment eigenvector mathe purpose of identifying superior cultivars for the tartrix—so that each element in the GGE matrix is recovered get region. The measured yield of each cultivar in each through test environment is a mixture of environment main effect (E), genotype main effect (G), and genotype Yij j k l 1 l il lj εij [1] environment interaction (GE). Typically, E explains most (up to 80% or higher) of the total yield variation, where and G and GE are usually small. However, it is G and Yij the measured mean yield of genotype i ( 1, 2,...n) GE that are relevant to cultivar evaluation. Moreover, in environment j ( 1, 2,...m) G and GE must be considered simultaneously when the grand mean making cultivar selection decisions. For this reason, inj the main effect of environment j, ( j ) being the stead of trying to separate G and GE, Yan et al. (2000) mean yield in environment j deliberately put the two together and referred to the l the SV of lth principal component (PC), the square mixture as GGE. Yield data from regional performance of which is the sum of squares explained by PCl (l trials, or more generally, multienvironment trials (MET), 1, 2,...k, with k min(m, n) and k 2 for a twoare usually quite large, and it is difficult to grasp the dimensional biplot) general pattern of the data without some kind of graphiil the eigenvector of genotype i for PC l cal presentation. The biplot technique (Gabriel, 1971) lj the eigenvector of environment j for PC l provides a powerful solution to this problem. A biplot εij the residual associated with genotype i in environthat displays the GGE of a MET data, referred to as a ment j Abbreviations: AEC, average environment coordinates; G, genotype Cereal Breeding and Biometrics, Univ. of Guelph, Guelph, ON, Canmain effects; GE, genotype environment interaction; GGE, genoada N1G 2W1. Received 16 Nov. 2001. *Corresponding author (wyan@ type main effects plus genotype environment interaction effects; uoguelph.ca; wyan@ggebiplot.com). MET, multienvironment trials; PC, principal component; SV, singular value. Published in Agron. J. 94:990–996 (2002).

SNP Discovery and Chromosome Anchoring Provide the First Physically-Anchored Hexaploid Oat Map and Reveal Synteny with Model Species

A physically anchored consensus map is foundational to modern genomics research; however, construction of such a map in oat (Avena sativa L., 2n = 6x = 42) has been hindered by the size and complexity of the genome, the scarcity of robust molecular markers, and the lack of aneuploid stocks. Resources developed in this study include a modified SNP discovery method for complex genomes, a diverse set of oat SNP markers, and a novel chromosome-deficient SNP anchoring strategy. These resources were applied to build the first complete, physically-anchored consensus map of hexaploid oat. Approximately 11,000 high-confidence in silico SNPs were discovered based on nine million inter-varietal sequence reads of genomic and cDNA origin. GoldenGate genotyping of 3,072 SNP assays yielded 1,311 robust markers, of which 985 were mapped in 390 recombinant-inbred lines from six bi-parental mapping populations ranging in size from 49 to 97 progeny. The consensus map included 985 SNPs and 68 previously-published markers, resolving 21 linkage groups with a total map distance of 1,838.8 cM. Consensus linkage groups were assigned to 21 chromosomes using SNP deletion analysis of chromosome-deficient monosomic hybrid stocks. Alignments with sequenced genomes of rice and Brachypodium provide evidence for extensive conservation of genomic regions, and renewed encouragement for orthology-based genomic discovery in this important hexaploid species. These results also provide a framework for high-resolution genetic analysis in oat, and a model for marker development and map construction in other species with complex genomes and limited resources.

Prediction of cultivar performance based on single- versus multiple-year tests in soybean

based on multiple-location trials across multiple years. Surprisingly, the hypothesis that multiple-year data give Because of the omnipresent genotype year or genotype better prediction of the next year’s performance has location year interactions in crop performance trials, it is commonly been tested by only a few researchers (Cross and Helm, believed that multiple-year data should be used in selecting cultivars for the next year. An implicated but rarely tested hypothesis is that 1986; Gellner, 1989; Bowman, 1998). On the other hand, multiple-year data are more predictive than single-year data of cultivar it is not feasible for researchers to make decisions on performance in the next year. Yield data of the 1991 to 2000 Ontario the basis of many years of testing because few genotypes Soybean Variety Trials in the 2800 Crop Heat Unit (CHU) area were (except the checks) are tested in many years and many used to study the power of single-year, multiple-location trials in genotypes are withdrawn from the trials if they do not predicting cultivar performances in the following year, and to see if perform well in the first year. data from multiple-year trials are more predictive. Mixed models were This project was set up to address the following quesused to estimate best linear unbiased predictions (BLUP) of tested tions: (i) what is the predictive power of single-year genotypes on the basis of singleor multiple-year trials, and the t-stamultiple-location trials in cultivar selection; (ii) are data tistic of BLUP (tBLUP) was used as a measure of cultivar perforfrom multiple-year trials more predictive than those mance. Results indicated that a single-year, multiple-location trial had sufficient power for identifying genotypes that would perform well from a single-year trial; and (iii) what is the merit of or poorly in the next year. Two to four years’ data gave only slightly using multiple-year data? better predictions of next-year performances than single-year data but allowed more genotypes to be evaluated conclusively. The tBLUP MATERIALS AND METHODS of genotype effects based on 2 yr of multiple-location trials should be used as a basis for soybean cultivar selection and recommendation Data Source in the 2800 CHU area of Ontario. Yield data from the 1991 to 2000 Ontario Soybean Variety Test (OSVT) in the 2800 crop heat unit (CHU) (OMAFRA, 1993) area of Ontario, Canada, were used in this study. The R performance trials are conducted annuOSVT is an official annual test conducted by the Ontario Oil ally for all major crops throughout the world to and Protein Seed Crop Committee (OOPSCC) and supported help growers select cultivars for the next year. Such a by Ontario Ministry of Agriculture and Food and the Ontario Soybean Growers. The OSVT assumes the functions of both decision would be straightforward were there no soybean [Glycine max (L.) Merr.] registration trials and pergenotype environment (GE) interaction (Gauch and formance trials and is conducted across Ontario covering cultiZobel, 1996). GE interaction is, however, almost omnivars from 2300 to 3400 CHU. The cultivars in the 2800 CHU present, which complicates the decision making. test belong approximately to relative maturity groups from GE interaction in multiple-location and multiple-year 0.4 to 1.5. The 2800 CHU trials included four test locations, trials can be dissected into genotype location interacnamely, Exeter, St. Pauls, Woodstock, and Winchester. tion (GL), genotype year interaction (GY), and genoGeographically, the first three locations are in southwestern type location year three-way interaction (GLY) Ontario, whereas Winchester is in eastern Ontario. Although (Comstock and Moll, 1963; Annicchiarico and Perenzin, there were strong crossover GL interactions each year, the 1994). Presence of GL within a single year necessitates interaction pattern varied considerably across years (Yan and Rajcan, 2002). Each year, 60 to 113 adapted cultivars or breedmultiple-location trials; presence of GY warrants multiing lines from public and/or private breeding programs were ple-year trials; and presence of GLY requires both multested. Many more entries were tested in recent years, as tiple-year and multiple-location trials. Since GE intercompared with the earlier years (Table 1). Although the same action is almost omnipresent, and as yearly variation sets of genotypes were tested at all locations within a single is typically the largest source of yield variation, it is year, the genotypes varied greatly with the year. In general, commonly believed that the greater the number of years about 50% or more of the entries were removed each year; a genotype is tested, the more reliable its evaluation and only one cultivar was tested in all 10 yr (Table 1). A total will be. An extended belief is that results based on of 526 genotypes were tested during the 10-yr period. Except more years of performance trials are more predictive for the check cultivars, which were determined by the of cultivar performance in the next year, which becomes OOPSCC, cultivar sponsors were solely responsible for the entering of their cultivars into the tests. Also, in some years, a dogma for cultivar recommendation. Thus, it is recomas a result of poor germination, data from only three locations mended in regional performance trial reports, almost without exception, that cultivar selection should be Abbreviations: BLUP, best linear unbiased prediction; CHU, crop heat units; E, environment main effect; G, genotype main effect; GE, genotype environment interaction; GL, genotype location Dep. of Plant Agriculture, Crop Sci. Bldg., Univ. of Guelph, Guelph, interaction; GLY, genotype location year interaction; GY, ON, N1G 2W1, Canada. Received 25 Feb. 2002. *Corresponding author genotype year interaction; L, location main effect; tBLUP, t-statis(irajcan@uoguelph.ca). tics of BLUP; Y, year main effect; OOPSCC, Ontario Oil and Protein Seed Crop Committee; OSVT, Ontario Soybean Variety Test. Published in Crop Sci. 43:549–555 (2003).

Biplot Analysis of Host-by-Pathogen Data

Effective breeding for disease resistance relies on a thorough understanding of host-by-pathogen relations. Achieving such understanding can be difficult and challenging, particularly for large data sets with complex host genotype-by-pathogen strain interactions. This paper presents a biplot approach that facilitates visual analysis of host-by-pathogen data. A biplot displays both host genotypes and pathogen isolates in a single scatter plot; each genotype or isolate is displayed as a point defined by its scores on the first two principal components derived from subjecting genotype- or strain-centered data to singular value decomposition. From a biplot, clusters of host genotypes and clusters of pathogen strains can be simultaneously visualized. Moreover, the basis for genotype and strain classifications, i.e., interactions between individual genotypes and strains, can be visualized at the same time. A biplot based on genotype-centered data and that based on strain-centered data are appropriate for visual evaluation of susceptibility/resistance of genotypes and virulence/avirulence of strains, respectively. Biplot analysis of genotype-by-strain is illustrated with published response scores of 13 barley line groups to 8 net blotch isolate groups.

Crop variety trials : data management and analysis

Preface vi Chapter 1 Theoretical Framework for Crop Variety Trials 1 Chapter 2 An Overview of Variety Trial Data and Analyses 23 Chapter 3 Introduction to Biplot Analysis 31 Chapter 4 Data Centering for Biplot Analysis 51 Chapter 5 Data Scaling and Weighting for GGE Biplot Analysis 75 Chapter 6 Frequently Asked Questions About Biplot Analysis 91 Chapter 7 Single-Trial Data Analysis 107 Chapter 8 Genotype-by-Location Two-Way Data Analysis 133 Chapter 9 Genotype-by-Trait Data Analysis and Decision-Making 163 Chapter 10 Trait Association-by-Environment Two-Way Table Analysis 187 Chapter 11 Location-by-Trait Two-Way Data Analysis 199 Chapter 12 Mega-environment Analysis Based on Multiyear Data 207 Chapter 13 Test Location Evaluation Based on Multiyear Data 231 Chapter 14 Genotype Evaluation Based on Multiyear Data 255 Chapter 15 Building and Utilizing a Relational Database for Crop Variety Trial Data 279 Chapter 16 Experimental Design for Variety Trials and Breeding Nurseries 295 Chapter 17 Modules and Functions in GGEbiplot 315 Chapter 18 Conclusions 341 References 345 Index 349

Associations Among Oat Traits and Their Responses to the Environment

Abstract Desirable qualities of milling oat varieties include low hull content (high groat content), high beta-glucan content, high groat protein, low oil concentration, low kernel breakage, high grain yield, and superior yield stability. The objective of this study was to develop a graphical method for understanding the influence of environment on genetic relationships among traits. Associations among agronomic and quality traits in 67 oat (Avena sativa L.) performance trials conducted during 1996-2003 across Canada and some northern US states were studied using a trait-association by environment biplot, which allows visual study of pair-wise trait associations in multiple environments (year-location combinations). Based on the differential association of yield with days to heading and plant height, the North American spring oat growing regions can be divided into Northern mega-environment (Canadian Prairies plus North Dakota and Idaho) and Southern megaenvironment (Minnesota, South Dakota, and Ontario). We also found that the following trait associations were relatively stable across environments: (1) negative association of protein content vs. oat yield, (2) positive association of beta-glucan vs. groat oil, (3) positive association of beta-glucan vs. protein content, and (4) negative association of beta-glucan vs. breakage. All trait-associations were of moderate magnitude and were responsive to the environment. This suggests that breeding for superior oat varieties with desired trait combinations is possible, but it must be achieved through direct selection for multiple traits in representative environments.

Population Genomics Related to Adaptation in Elite Oat Germplasm

An oat association‐mapping panel contributed by active breeding programs worldwide. Characterized population structure and found subdivisions related to adaptation Characterized genome‐wide and chromosome‐specific linkage disequilibrium Performed association‐mapping and post hoc modeling of heading date Found several consistently associated QTL

A biplot approach for investigating QTL-by-environment patterns

Due to the universal presence of genotype by environment interactions, understanding the pattern of quantitative trait loci (QTL)-by-environment interactions is a prerequisite for effective marker-assisted selection. In this report, we describe a biplot approach for investigating QTL-by-environment patterns. This approach involves two steps. It starts with a two-way table containing effects of individual QTLs in individual environments for the trait under investigation. This table is decomposed into principal components via singular value decomposition, and the first two principal components are plotted for both QTLs and environments to form a biplot. The resulting ‘QQE biplot’ contains information on QTL main effects (Q) and QTL-by-environment interactions (QE). A QQE biplot displays the QTL-by-environment patterns and allows visualization of: (1) the magnitude of the effect of a QTL, (2) the average effect of a QTL and its stability across environments, (3) the effects of a QTL in individual environments, (4) the similarity/dissimilarity among QTLs in effect and response to the environments, (5) the similarity/dissimilarity among environments in modulating QTL effects, (6) any differentiation of mega-environments, and (7) the combination of QTL alleles for maximum/minimum expression of the trait for each environment or mega-environment. A case study is provided using the QTL-by-environment two-way table for barley yield.