GGE Biplots and Traditional Stability Measures for Interpreting Genotype by Environment Interactions

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GGE Biplots and Traditional StabilityMeasures for Interpreting Genotype byEnvironment InteractionsSterling Brooks Blanche a , Gerald O. Myers b & Manjit S. Kang ba Rice Research Station, Louisiana State University AgriculturalCenter , 1373 Caffey Road, Rayne, LA, 70578, USAb Department of Agronomy and Environmental Management ,Louisiana State University Agricultural Center , 104 Sturgis Hall,Baton Rouge, LA, 70803-2110, USAPublished online: 22 Sep 2008.

To cite this article: Sterling Brooks Blanche , Gerald O. Myers & Manjit S. Kang (2007) GGE Biplotsand Traditional Stability Measures for Interpreting Genotype by Environment Interactions, Journal ofCrop Improvement, 20:1-2, 123-135, DOI: 10.1300/J411v20n01_07

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GGE Biplots and Traditional StabilityMeasures for Interpreting Genotype

by Environment Interactions

Sterling Brooks BlancheGerald O. MyersManjit S. Kang

ABSTRACT. Cotton (Gossypium hirsutum L.) breeders conduct multi-environment trials to determine the performance of genotypes in relationto environmental changes and to determine their area of adaptation. Theobjective of this study was to compare within-model and within-scalingGGE Biplot stability values (GE distance) with those generated by someof the “traditional” stability analytical methods. Correlation coefficientsof GE distance of GGE Biplot (stability evaluation) with Cultivar Supe-riority Measure, Shukla’s Stability Variance, Eberhart-Russell regres-sion model, Kang’s yield stability statistic, and AMMI were 0.54, 0.91,0.86, 0.63, and 0.55, respectively. Correlation coefficients between

Sterling Brooks Blanche is affiliated with Rice Research Station, Louisiana StateUniversity Agricultural Center, 1373 Caffey Road, Rayne, LA 70578.

Gerald O. Myers is affiliated with the Department of Agronomy and EnvironmentalManagement, Louisiana State University Agricultural Center, 104 Sturgis Hall, BatonRouge, LA 70803-2110.

Manjit S. Kang was affiliated with the Department of Agronomy and Environmen-tal Management, Louisiana State University Agricultural Center, 104 Sturgis Hall, Ba-ton Rouge, LA 70803-2110 at the time of the study.

Address correspondence to: Sterling Brooks Blanche at the above address (E-mail:[email protected]).

The authors thank Cotton Incorporated and the Cotton Incorporated FellowshipProgram for financial assistance during this project.

Approved for publication by the Director of the Louisiana Agricultural ExperimentStation as manuscript number 06-61-0368.

Journal of Crop Improvement, Vol. 20(1/2) (#39/40) 2007Available online at http://jcrip.haworthpress.com

© 2007 by The Haworth Press, Inc. All rights reserved.doi:10.1300/J411v20n01_07 123

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GGE distance of GGE Biplot (mean performance + stability evaluation)and the Cultivar Superiority Measure, the Eberhart-Russell regressionmodel, Kang’s yield stability statistic, and AMMI were 0.95, 0.60, 0.85,and �33, respectively. Some of the “traditional” methods focus heavilyon yield, while others focus on stability; GGE Biplot allows for a moreversatile and easily comprehensible presentation of the data and varietyselection based on both yield and stability. Based on the results of thisstudy and our experience using GGE Biplot, Model 3 (uses replicatedand standard error-standardized data) with an entry-focused scaling isthe most valuable analysis for breeders to select widely adapted geno-types. doi:10.1300/J411v20n01_07 [Article copies available for a fee from TheHaworth Document Delivery Service: 1-800-HAWORTH. E-mail address:<[email protected]> Website: <http://www.HaworthPress.com>© 2007 by The Haworth Press, Inc. All rights reserved.]

KEYWORDS. Cultivar stability, genotype by environment interaction,GGE Biplot, multi-environment trial

ABBREVIATIONS. (G) genotype; (E) environment; (MET) multi-en-vironment trial; (σi

2) Shukla’s stability variance; (si2) Shukla’s stability

variance with a location covariate; (ER) Eberhart and Russell; (bi) geno-type slopes; (sdi

2) deviations from regression; (CSM) cultivar superior-ity measure; (AMMI) additive main effect and multiplicativeinteraction; (AM1) AMMI axis 1; (YSi) Kang’s yield stability statistic;(SVD) singular value decomposition; (M1GE) Model 1, GE; (M2GE)Model 2, GE; (M3GE) Model 3, GE; (M1GGE) Model 1, GGE;(M2GGE) Model 2, GGE; (M3GGE) Model 3, GGE

INTRODUCTION

Plant breeders have recently been introduced to GGE Biplot, a stabil-ity analysis and variety selection tool, and have begun to incorporate itinto their breeding programs (Yan, 2001; Blanche et al., 2002; Myers,2002; Lubbers, 2003; Kang et al., 2005). Research focusing on stability,or genotype (G) � environment (E) interactions, is necessary for plantbreeders to develop cultivars that respond optimally and consistentlyacross environments. GE interactions exist when the responses of twogenotypes to different levels of environmental stress are not parallel(Allard and Bradshaw, 1964). Numerous tools have been developed tomeasure the response of genotypes to changes in environment (Wricke,

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1962; Eberhart and Russell, 1966; Shukla, 1972; Gauch, 1988; Lin andBinns, 1988). However, GGE Biplot offers breeders a more completeand visual evaluation of all aspects of the data by creating a biplot thatsimultaneously represents both mean performance and stability (Yan,2001). Widespread acceptance of GGE Biplot for its ability to evaluatemean performance and stability and to identify mega-environments hascreated a need for research to compare GGE Biplot to other “tradi-tional” stability analysis tools.

The measured performance of a genotype is the result of its geneticmake-up, the environment in which the genotype is grown, and the in-teraction between the genotype and environments. Studies have shownthat the environment in which the genotype is grown is the largestsource of variation based on the contribution to total sum of squares(Verhalen and Murray, 1970; Kerby et al., 2000; Blanche et al., 2002).In many cases, the obscuring effect of environmental variation makes itdifficult to focus on G and GE interactions. While some classical stabil-ity analysis tools, such as ecovalence (Wricke, 1962) and Shukla’sstability variance statistic (Shukla, 1972) effectively quantify GE inter-action, they do not provide the evaluator with a statistic that includesboth mean performance and stability. Shukla’s stability variance statis-tic (σi

2) generates values that represent estimates of the ith genotype’svariance across environments (Shukla, 1972). Shukla (1972) proposeda model that uses an environmental covariate, e.g., difference betweenthe mean of all genotypes at a location (X.j) and overall (grand) mean(X..), to remove its linear effect so that the remaining GE interactionvariance can be attributed to cultivars as si

2. Kang proposed methods tointegrate yield and yield stability using Shukla’s σi

2 (Kang, 1988; Kang1993).

Others have used a regression model of genotype means on environ-mental means to model the GE interaction by estimating a set of straightlines (Yates and Cochran, 1938; Finlay and Wilkinson, 1963; Eberhartand Russell, 1966; Tai, 1971). The regression model proposed byEberhart and Russell (1966) allows for the computation of a completeanalysis of variance with individual stability estimates and departurefrom linearity (sdi

2) of a regression line. In this model, cultivars with ahigh sdi

2 deviate significantly from linearity and have a less predictableresponse for the given set of environments. Differences in genotypeslopes (bi), along with sdi

2, account for GE interactions; however, thevalidity of these methods has been questioned (Freeman and Perkins,1971; Shukla, 1972; Freeman, 1973; Vargas et al., 2001).

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The cultivar superiority measure (CSM) involves calculations (acrossenvironments) of the mean square difference between the performanceof a variety and the best variety within a given environment, measuringmean performance and stability simultaneously (Lin and Binns, 1988).An additive main effect and multiplicative interaction (AMMI) model(Gauch, 1988; Zobel et al., 1988) has been frequently used to analyzemulti-environment trial (MET) data. The AMMI model presents abiplot similar to GGE Biplot but does not allow for many of the func-tions that GGE Biplot provides and can be misleading for identifyingwhich genotypes won in which environment (Yan and Kang, 2003).Kang’s yield stability statistic (YSi) (Kang, 1993), an example of simul-taneous selection for mean performance and stability, involves cultivarrankings based on σi

2 (Shukla, 1972) and mean performance rankingsafter a protected LSD adjustment. Another effective tool for analyzingGE interactions is GGE Biplot, which uses singular value decomposi-tion (SVD) to decompose GGE into two or more principal components.Each principal component consists of a set of genotype scores multi-plied by a set of environment scores, and a two-dimensional biplot canbe generated. Another significant characteristic of GGE Biplot is itsability to remove the impact of E, allowing the evaluator to focus on thetwo components of performance that are meaningful to a breeder or pro-duction agronomist, G and GE (Yan and Kang, 2003).

GGE Biplot is equipped with a variety of models, scalings, and datatransformations to provide the user with a customized biplot of an METdataset. A total of nine different model-by-scaling combinations can beused, each affecting the visual outcome of the biplot and stability-re-lated values that are placed in the GGE log output file. Three models canbe used to generate a biplot: (1) Model 1 (M1) generates biplots basedon SVD of tester-centered data, commonly used for datasets in whichall testers use the same unit, such as a genotype by environment table ofa single trait; (2) Model 2 (M2) generates biplots based on SVD ofwithin-tester standard deviation-standardized data and is used fordatasets in which different units are used for different testers or when alltesters are assumed to be equally important; and (3) Model 3 (M3) gen-erates biplots based on SVD of within-tester standard error-standard-ized data and is used only when replicated data are input and to removeany heterogeneity among the testers. A biplot can be scaled in threeways: (1) entry-focused scaling, when the singular values are parti-tioned entirely into the genotype eigenvectors, is used when the investi-gator is primarily interested in genotypes; (2) tester-focused scaling,

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when the singular values are partitioned entirely into the environmentscores, is to be used when testers are the primary focus; and (3) symmet-rical scaling, which is appropriate when the user wishes to focus equallyon testers and entries but is not ideal for either. The three scaling meth-ods of singular value partitioning do not alter the GE interaction patternand yield an identical “which-won-where” pattern (Yan and Kang,2003). The multiple combinations of features that are available increasethe potential application of the GGE Biplot analysis, but there has beenconcern over which model-by-scaling combination is most appropriatefor variety selection procedures of interest to breeders and producers.Thus, the objectives of this study were to compare the nine model-by-scaling combinations available within GGE Biplot with other stabilitymeasures to determine how closely correlated each model-by-scalingcombination is with the selected “traditional” stability measures.

MATERIALS AND METHODS

Yield data for medium maturity cotton from the Louisiana OfficialVariety Trials conducted from 2000 to 2002 were analyzed. Data werebalanced to obtain an equal number of genotypes in all environments.Genotypes included Delta and Pine Land (DP) ‘DeltaPearl’,‘NuCotn33B’, ‘DP458BR’, ‘DP565’, FiberMax (FM) ‘FM832’,Phytogen (PSC) ‘PSC355’, and Stoneville ‘STV580’. These seven ge-notypes were planted in 2000 to 2002 at the Dean Lee Research Stationnear Alexandria (ALEX00-02), the Red River Research Station nearBossier City (BC00-02), the Northeast Louisiana Experiment Stationnear St. Joseph, and the Macon Ridge Research Station near Winnsboro,Louisiana, yielding a total of 18 environments. In each year, two trialswere conducted at the Northeast Louisiana Experiment Station, one ona commerce silt loam (Commerce silt loam; fine-silty, mixed, nonacid,thermic, Aeric, Fluvaquent) (SJL00-02) and the other on a sharkey clayloam (Sharkey clay; very-fine, montmorillonitic, non-acid, thermicVertic Haplaquept) (SJC00-02) soil type, and at the Macon Ridge Re-search Station, one under irrigation (WI00-02) and the other non-irri-gated (WNI00-02). All experiments were conducted in randomizedcomplete-block designs at each location, following standard culturalpractices.

GGE Biplot generates statistics for G, GE, and G + GE, allowing theevaluator to assess cultivars for mean performance only, stability only,and desirability based on performance and stability, respectively. For

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the purpose of this study, the stability statistics evaluating only stabilitygenerated by models 1, 2, and 3 will be referred to as M1GE, M2GE, andM3GE, respectively. The GGE distance resulting from models 1, 2, and3 assessing both mean performance and stability (G + GE) and based onthe distance of a cultivar from an “ideal” cultivar will be referred to asM1GGE, M2GGE, and M3GGE, respectively. Comparisons were madebetween GGE Biplot and six commonly used stability measures: CSM(Lin and Binns, 1988), σi

2 (Shukla, 1972), si2 following removal of het-

erogeneity due to environmental index (Shukla, 1972), sdi2 (Eberhart

and Russell, 1966), YSi (Kang, 1993; Kang and Magari, 1995), andAM1 (Gauch, 1988). An analysis of variance indicated that the GE inter-action was significant (P < 0.001). Correlation coefficients were calcu-lated using ‘proc corr’ of SAS version 9 (SAS, 2002) between thestatistics generated by GGE Biplot and the traditional measures. Thenine model-by-scaling combinations within GGE Biplot were com-pared with each other and the traditional measures to determine degreeof similarity between them and to identify one that is most useful foraiding a breeder in genotype selection.

RESULTS AND DISCUSSION

This study was conducted to compare various model-scaling combi-nations within GGE Biplot to several traditional stability measures togain perspective of the various combinations and determine which ismost appropriate for breeding purposes. A total of nine GGE model-scaling combinations were considered and are discussed below.

Within-Model Scaling Correlation

Differences in stability values between entry-focused, tester-focused,and symmetrical scaling options were minimal and primarily aided thevisual interpretation of the biplot (Figures not shown). All within-model scaling combinations were perfectly correlated as predicted bytheory, indicating that different scaling options would be suitable andshould depend solely on the focus of the evaluator (Table 1). Due to theidentical patterns generated by each scaling option, we chose only tocompare the entry-focused scaling method for each model with otherstability measures. Using the entry-focused scaling method, all of thesingular values were partitioned into the genotype scores, making them

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much greater than the environment scores, and causing environments tobe crowded on the biplot relative to genotypes, thus, allowing for bettercharacterization of genotypes, the primary focus of plant breeders.

Correlation Between GE Distancesfrom Different GGE Biplot Models

Correlation coefficients for GE distance from Models 1, 2, and 3ranged from 0.79 to 0.97, with the strongest one being between M2 andM3 (0.97) (Table 2). M1GE, which had correlations of 0.79 and 0.82with M2GE and M3GE, respectively, is referred to as an environ-ment-centered model because the environmental means are subtractedfrom each of the observed mean values (Table 2). This model is re-stricted to analyzing MET data in which: (1) all environments are as-sumed to be homogeneous, (2) a single trait is analyzed, and (3) traitsare measured in the same unit for all environments. Breeders, to repre-sent the range of growing regions, commonly use heterogeneous envi-ronments; therefore, M1 might not be appropriate for most MET datacollected by cotton breeders. The objective of M2, to circumvent thelimitations associated with M1, is to scale the environment-centereddata with the within-environment standard deviation. This procedureeliminates the possibility of detecting any differences among environ-ments in their discriminating ability by assuming that all environmentsare equally important. M2GE was correlated with M3GE (r = 0.97) dueto the similar methods for scaling the environment-centered data (Table2). M3, which requires replicated data, scales the environment-centereddata with the within-environment standard error accounting for theheterogeneity among environments (Yan, 2001).

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TABLE 1. Correlation coefficients for GGE Biplot within-model scaling options.

† 1, 2, 3=GGE Biplot Model 1, 2, 3; E=Entry-focused scaling; T=Tester-focused scaling;S=Symmetrical scaling.

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It is interesting that si2 and sdi

2 were perfectly correlated with eachother (Table 2). This is consistent with the discussion of the two statis-tics in Kang and Pham (1991). The authors explained that when envi-ronmental index is used as a covariate to generate si

2, these two statisticsare equivalent (Kang and Pham, 1991).

Correlation Between GE Distance of the GGE Biplotand Other Stability Measures

Since M2GE and M3GE were highly correlated (r = 0.97); future dis-cussion will focus only on M3GE. Correlation coefficients betweenM3GE and σi

2, sdi2, CSM, AM1, YSi, and M3GGE were 0.91, 0.86,

0.54, �0.55, 0.63, and 0.59, respectively (Table 2). M3GE, unlike esti-mates given by CSM, AM1, YSi, and M3GGE, approximates only thelevel of stability of each cultivar, not the desirability of each cultivarbased on G + GE. Hence, the high correlations between M3GE and thetraditional stability analyses focus solely on GE interaction, σi

2, andsdi

2. This indicates that the biplot and stability statistics generated by

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TABLE 2. Correlation coefficients between GGE Biplot models and “traditional”stability measures.

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GGE Biplot allow for an effective evaluation of genotype stability. Fig-ure 1 represents the mean vs. stability coordination biplot, which wasgenerated by M3 in GGE Biplot. A solid line with a single arrow, calledthe average tester axis (ATA), passes through the biplot origin and theaverage environmental coordinate (AEC). Ten dotted lines intersect theATA and are used for categorizing cultivar mean performance such thatcultivars further along the line, away from the biplot origin and in the di-rection of the arrow, exhibit a higher level of mean performance. In thismanner, G can be assessed with the biplot. GE interaction can be deter-mined as cultivar distance, in either direction, from the ATA such thatcultivars closer to the ATA are more stable than cultivars with a greater

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FIGURE 1. Biplot† showing mean lint yield‡ and yield stability# of seven geno-types.

† Biplot generated using model 3 with entry-focused scaling.‡ Cultivars further to the right in the direction of the single arrow yield more.# Cultivars further from the biplot origin, in either direction of the arrows on the vertical line, areless stable.

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distance from the ATA. A line bisecting the biplot origin and perpendic-ular to the ATA with arrows at each end, called the stability line, aids inthe interpretation such that longer projections onto the stability line in-dicate greater cultivar instability. The projections can be determined asthe point where a perpendicular line from the cultivar marker to the sta-bility line intersects. Using the biplot to make stability determinations,the most stable cultivars were DP565 and STV580 and the least stablecultivar was FM832 (Figure 1). The correlation coefficient betweenM3GE and σi

2 was 0.91 (Table 2), a fact easily validated by a visual as-sessment of the biplot (Figure 1) and cultivar rankings (Table 3). Al-though M1GE was significantly correlated with σi

2 and sdi2, correlation

coefficients were lower compared with M2 or M3 (Table 2). M1GE wascorrelated with CSM (r = 0.75), although correlations were not signifi-cant between CSM and M2GE or M3GE. A stronger correlation betweenCSM and M1GE is probably due to the fact that both assume homogene-ity of environments and use replicate means subtracted from abenchmark but do not standardize environments as in M2GE or M3GE.

Simultaneous selection for G and GE was accomplished using theconcentric-circle biplot (Figure 2) and distances from an “ideal” geno-

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TABLE 3. Stability values† and rankings‡ generated by GGE Biplot and otherstability models.

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type (Table 3). In the concentric-circle biplot, an “ideal” genotype, de-noted by the smallest circle on the ATA, is created and concentriccircles are drawn such that cultivars closer to the center are more desir-able relative to mean performance and stability. This property of thebiplot greatly simplifies the process of identifying stable, high-yieldingcultivars in MET datasets. Distances between cultivar markers and the“ideal” genotype, referred to as GGE distances, are printed to a log filesimilar to that for the GE stability statistics. Cultivar GE and G + GEstatistics and rankings generated by GGE Biplot and other stabilitymeasures are listed in Table 3.

We believe that between Models 2 and 3, the latter is more appropri-ate for replicated MET datasets; thus, comparisons will only be made

Blanche, Myers, and Kang 133

FIGURE 2. Biplot† of concentric circles ranking genotypes for yield‡ and yieldstability‡.

† Biplot generated using model 3 with entry-focused scaling.‡ Cultivars closer to the ideal genotype, denoted by the small circle on the single-arrow line,are more desirable considering yield and yield stability.D

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with M3GGE. Correlation coefficients between M3GGE and CSM,AM1, and YSi were 0.95, �0.33, and 0.85, respectively (Table 2). A vi-sual inspection of Figure 2 clearly indicates that Deltapearl was themost desirable and FM832 was the least desirable cultivar based on G +GE. This is validated by the strong correlation coefficients (Table 2)and similar cultivar rankings (Table 3) between M3GGE, CSM, AM1,and YSi.

The results of this study indicate that GGE Biplot can be used to ana-lyze MET datasets for G, GE, or G + GE and can provide results similarto other popular stability analysis tools. However, the multiple optionsand ease of visual interpretation clearly make GGE Biplot the preferredtool for breeders interested in cultivar stability evaluation. In addition tothe analyses performed in this study, GGE Biplot can be used to identifydiscriminating environments, partition multiple environments intomega-environments, and identify winning genotypes for each mega-en-vironment. An exhaustive list of GGE Biplot properties and functions,many of which are not available in other stability models, has beenpreviously published (Yan et al., 2000; Yan and Kang, 2003).

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