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a Texas A&M Univ. System Agric. Research and Extension Center, 1509 Aggie Drive, Beaumont, TX 77713
b USDA-ARS, 1509 Aggie Drive, Beaumont, TX 77713
* Corresponding author (sosamonte{at}aesrg.tamu.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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Abbreviations: AMMI, additive main effects and multiplicative interactions • E, environment • G, genotype • GE, genotype x environment • GEI, genotype environment interaction • GGE, genotype and genotype x environment • IPCA, interaction principal component analysis • MET, multiple-environment trial • PCA, principal component analysis • SREG, sites regression • SVD, singular value decomposition
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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Zobel et al. (1988) compared the traditional statistical analyses (analysis of variance [ANOVA], principal component analysis [PCA], and linear regression) with AMMI analyses, and showed that the traditional analyses were not always effective in analyzing the MET data structure. The ANOVA is an additive model that describes main effects effectively and determines if GE interaction is a significant source of variation, but it does not provide insight into the patterns of genotypes or environments that give rise to the interaction. The PCA is a multiplicative model that contains no sources of variation for additive G or E main effects and does not analyze the interactions effectively. The linear regression method uses E means, which are frequently a poor estimate of environments, such that the fitted lines in most cases account for a small fraction of the total GE (Zobel et al., 1988). The AMMI model analysis combines the ANOVA (with additive parameters) and PCA (with multiplicative parameters) into a single analysis. The AMMI model analysis is useful in making cultivar recommendations, specifically by megaenvironment analysis, in which the best performing cultivar for each subregion of the crop's growing region is identified (Zobel et al., 1988; Gauch and Zobel, 1997). Gauch and Zobel (1997) demonstrated the usefulness of AMMI analysis in supporting breeding program decisions, such as in the selection of environments or test site locations. Although AMMI model analysis results are based only on yield data (not environmental data), Ebdon and Gauch (2002a) reported that AMMI environmental (interaction) statistics were correlated with environmental factors, such as precipitation, mean daily maximum and minimum temperature, altitude, latitude, N fertilization, irrigation, and clay content.
Biplot graphs, which show markers of both genotypes and environments, are used to present AMMI analysis results (Gauch and Zobel, 1997; Ebdon and Gauch, 2002b). Recently, biplots have also been used to interpret results of the SREG model analysis of MET data. Genotype and GE interaction, which are the two factors that are important in cultivar selection, are the sources of variation in the SREG model analysis of MET data. These factors are graphically shown through a GGE biplot, which is used in the visual evaluation of both genotypes and environments (Yan et al., 2000, 2001; Yan and Hunt, 2002).
Crop breeding programs should take GE interaction into consideration and have an estimate of its magnitude, relative to the magnitude of G and E effects, which affect grain yield. Furthermore, the identification of the cultivar that yields best at a specific growing environment would be useful to breeders and producers. Using data from a multienvironment (years and locations) experiment, this study demonstrated the utility of AMMI model analysis and GGE biplots obtained from SREG model analysis in evaluating the significance and magnitude of the GE interaction effect on grain yield and in determining the best performing cultivar for each environment.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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Replicated grain yield data (kg ha–1) were obtained during three main cropping seasons (2000, 2001, and 2002) from four locations in Texas (Bay City, Matagorda County, 28°58' N, 95°57' W; Eagle Lake, Colorado County, 29°35' N, 96°20' W; Ganado, Jackson County, 28°59' N, 96° 27' W; and Beaumont, Jefferson County, 29°57' N, 94°30' W). The randomized complete block design was used in all locations and years. At Bay City, the numbers of replicates were two, four, and three in 2000, 2001, and 2002, respectively. At Eagle Lake and Ganado, there were three replicates in 2000 and 2002, and four replicates in 2001. There were eight replicates at Beaumont in each of the 3 yr. Plot dimensions during the 2000, 2001, and 2002 field experiments were 1.9 x 4.9 m at Bay City, 1.2 x 6.1 m at Beaumont, and 1.9 x 4.9 m at Ganado. At Eagle Lake, they were 1.9 x 4.9 m in 2000 and 2001, and 1.5 x 6.1 m in 2002. Planting dates were 19 April 2000, 1 May 2001, and 17 April 2002 at Bay City; 20 April 2000, 27 April 2001, and 5 April 2002 at Beaumont; 27 March 2000, 9 April 2001, and 5 April 2002 at Eagle Lake; and 6 April 2000, 5 April 2001, and April 3 2002 at Ganado.
Nitrogen, P, and K were added as fertilizer in the amounts of 177–43–43, 199–43–43, and 244–43–43 kg ha–1 at Bay City in 2000, 2001, and 2002, respectively. At Beaumont, 224 kg ha–1 of N was added as fertilizer in 2000, 2001, and 2002, respectively, while 56 kg ha–1 P was added in 2002. The amounts of N, P, and K added as fertilizer at Eagle Lake in 2000, 2001, and 2002 were 224–43–43, 231–43–43, and 155–43–43 kg ha–1, respectively. At Ganado, fertilizer N, P, and K were added in the amounts of 222–43–43, 231–43–43, and 222–43–43 kg ha–1 in 2000, 2001, and 2002, respectively. Insect pest, disease, and weed management practices were applied as outbreak preventive measures.
Additive Main Effects and Multiplicative Interaction Model Analysis
The AMMI model analysis of grain yield was performed by a SAS (SAS Institute Inc., 1999) program written by Hernandez and Crossa (2000). Although the number of replications varied across locations and years (from two to eight replications), only two randomly selected replications were used because of the requirement of equal replications by the SAS program. In the analysis, each combination between the four locations and 3 yr was considered as an environment, making a total of 12 environments. The ANOVA model is
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g are genotype mean deviations (mean minus the grand mean), ße are the environment mean deviations, N is the number of SVD (singular value decomposition) axes retained in the model, 
n is the singular value for SVD axis n, 
gn are the genotype singular vector values for SVD axis n, 
en are the environment singular vector values for SVD axis n, 
ge are the interaction residuals, 
ge are the AMMI residuals, and 
ger is the error term.
Correlation Analyses
Correlation analyses were conducted to determine if any linear relationship existed between AMMI environment interaction principal components analysis (IPCA) axis scores and environmental variables. The 29 variables were amounts of N, P, and K applied during fertilization, soil pH, latitude, longitude, dates of growth stages (seedling emergence date, heading, and harvest), and climatic data (temperature [maximum, minimum, and daily mean], heat units [sum of degree days > 10°C and average daily degree days > 10°C)], daily mean relative humidity, heat index [maximum, minimum, daily mean], and precipitation). Climatic data for the entire growing season (emergence to maturity) and for the period from heading to maturity were tested for their correlation with environment IPCA scores. The weather data of each location and year was obtained from a weather station at or near the experimental site.
AMMI Biplot Analyses
The results of the AMMI model analysis were interpreted on the basis of two AMMI biplots—a biplot that showed the main and first interaction principal components analysis (IPCA 1) axis effects of both G and E and a biplot that showed the nominal yield (expected yield from the AMMI model equation without environmental deviations) of genotypes across IPCA 1 scores (Gauch and Zobel, 1997). The nominal grain yield of each genotype was estimated as the G mean plus the product of G and E IPCA 1 scores.
Sites Regression Model Analysis
The SREG model analysis of grain yield was performed by a SAS (SAS Institute Inc., 1999) program written by Burgueño et al. (2001). The SREG linear-bilinear model is represented by
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ij. is the mean of the ith cultivar in the jth environment for g genotypes and e environments (i = 1, 2, ..., g and j = 1, 2, ..., e); µ is the overall mean; 
j is the site effect; k (1 
2 ... t) are scaling constants (singular values) that allow the imposition of orthonormality constraints on the singular vectors for cultivars, k = (1k,...,gk) and sites, 
k = (1k,...,ek); ik and jk for k = 1, 2, 3, ... are called "primary," "secondary," "tertiary," ... etc. effects of the ith cultivar and jth site, respectively; 
ij. is the residual error assumed to be normally and independently distributed (0, 
2/r) (where 2 is the pooled error variance and r is the number of replicates). In the SREG model, the main effects of cultivars (G) plus the GE interaction were absorbed into the bilinear terms (Burgueño et al., 2001; Crossa et al., 2002).
GGE Biplot Analyses
The GGE biplot methodology, which is composed of two concepts, the biplot concept (Gabriel, 1971) and GGE concept (Gauch and Zobel 1996; Yan et al., 2000), was used to visually analyze the results of SREG analysis of MET data. This methodology uses a biplot to show the two factors (G plus GE) that are important in cultivar evaluation and that are also the sources of variation in SREG model analysis of MET data (Yan et al., 2000, 2001). The GGE biplot shows the first two principal components (PC1 and PC2, also referred to as primary and secondary effects, respectively) derived from subjecting environment-centered yield data (the yield variation due to GGE) to singular value decomposition (Yan et al., 2000). In this study, GGE biplots were used to compare the performance of different genotypes at an environment, compare the performance of a genotype at different environments, compare the performance of two genotypes at all environments, identify the highest yielding genotypes at the different megaenvironments, and identify ideal cultivars and test locations.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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AMMI Biplot Analysis
The main and IPCA 1 effects of both G and E on grain yield were shown in Fig. 2
. The AMMI biplot illustrates 84.2% of treatment SS (118.702), with 17.8% due to G SS (21.174), 55.4% due to E SS (65.795), and 10.9% due to IPCA 1 SS (12.980). Since IPCA 1 SS is 61.3% that of the G SS, this emphasizes the importance of taking GE interaction into consideration when estimating cultivar yield at different locations or when targeting rice cultivars onto specific locations.
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Rice cultivars that had IPCA 1 scores >0 responded positively (adaptable) to environments that had IPCA 1 scores >0 (i.e., their interaction is positive) but responded negatively to environments that had IPCA 1 scores <0. The reverse applies for rice cultivars that had IPCA 1 scores <0. Hence, Cocodrie, Saber, and Wells were adapted to Bay City (2002), Ganado (2001 and 2002), and Beaumont (2000, 2001, and 2002). In contrast, Cypress, Jefferson and Lemont were adapted to Bay City (2000 and 2001), Ganado (2000) and Eagle Lake (2000, 2001, and 2002).
The differences among cultivars in terms of direction and magnitude along the x axis (yield) and y axis (IPCA 1 scores) were also important. The best cultivar should be high-yielding and stable across environments. For example, the two highest yielding cultivars, Cocodrie (8.88 Mg ha–1) and Wells (8.82 Mg ha–1), can be differentiated on the basis of their stability. The cultivar with a lower absolute IPCA 1 score (Cocodrie) would produce a lower absolute GE interaction effect than the cultivar with a higher absolute IPCA 1 score (Wells) and have a less variable (more stable) yield across environments. The cultivar stability ranking based on lower absolute IPCA 1 scores was Cocodrie (0.28), Lemont (0.307), Saber (0.437), Cypress (0.536), Jefferson (0.787), and Wells (1.164). Hence, Cocodrie was identified as the best cultivar (highest yield and stability).
Ganado had the highest variability in interaction (IPCA 1 scores) from year to year, while Eagle Lake had the least. This indicated that relative rankings of cultivars were more stable at Eagle Lake than at Ganado, making it difficult to recommend a specific cultivar for Ganado.
Targeting Rice Genotypes based on Nominal Yield
Estimates of cultivar nominal grain yields, on the basis of the AMMI model equation without the environmental deviation ße (i.e., based on G and GE IPCA 1 effects only), across E ICPA 1 scores indicated the adaptability of each cultivar and aided in the identification of the cultivar that yielded the highest at specific E IPCA 1 ranges (Fig. 3)
. The biplot represents the combined SS of G (21.17) and IPCA 1 (12.98) or 64.6% of the G + GE SS (52.90). Cocodrie had the highest nominal grain yield at E IPCA 1 <0.049. Environments within this IPCA 1 score range were Bay (2000 and 2001), Eagle Lake (2000, 2001, and 2002), and Ganado (2000). Wells had the highest nominal grain yield at environments that had IPCA 1 scores >0.049. Environments within this IPCA 1 score range were Bay City (2002), Beaumont (2000, 2001, and 2002), and Ganado (2001 and 2002). On the basis of the frequency that a cultivar was expected to yield highest in a location, Wells should be recommended for both Ganado and Beaumont, while Cocodrie should be recommended for Eagle Lake and Bay City.
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In addition to adaptability, the AMMI biplot (Fig. 3) showed the stability of a cultivar's nominal yield across environments. Cocodrie's nominal yield ranged from 8.86 to 8.90 Mg ha–1 across 12 environments. Because of its high and stable nominal yield across environments, Cocodrie was identified as the best cultivar among the six cultivars tested. Lemont also showed stability, with its nominal yield ranging from 7.85 to 8.28 Mg ha–1 across 12 environments. Lemont's moderately high yield and stable performance is one of the reasons why it was the most popular cultivar during the 1990s. Saber, which is a relatively new cultivar, had only moderate yield and stability.
The AMMI biplot can be used to identify the appropriate check cultivar for all locations (general check) or for specific locations (specific check). Rice breeders would then compare their promising lines against either the general or specific check cultivar in selecting for the next high yielding cultivar. For example, results from this study suggest that Cocodrie should be the general check cultivar for all environments because of its high and stable nominal yield across environments. In addition, Wells should be included in the MET and serve as an additional check cultivar at the Beaumont and Ganado test locations, since it had the highest nominal yield at these locations during three and 2 yr, respectively.
The AMMI biplot also sets the standard for nominal yield and stability levels that any upcoming rice cultivar should surpass. Rice breeders should aim for a cultivar with a stable yield performance (similar to that of Cocodrie), yet capable of out-yielding Wells and Cocodrie at the positive and negative ends of the E IPCA 1 scores, respectively.
SREG GGE Biplot Analysis
Performance of Different Genotypes at a Specific Environment
The GGE biplot of the SREG analysis results was used to show the relative performance of all cultivars at a specific environment. As an example, the 2002 Beaumont environment was used since it produced the highest yield among the 12 environments. A line was drawn that passed through the biplot's origin and the Bea02 (Beaumont, 2002) marker to make a Bea02 axis, and then a broken line was perpendicularly drawn from each cultivar toward the Bea02 axis (Fig. 4)
. The cultivars were ranked on the basis of their projections onto the Bea02 axis, with rank increasing in the direction toward the positive end (Yan et al., 2000; Yan and Hunt, 2002). In this example, the cultivar yield ranking at Beaumont in 2002 was as follows: Wells, Cocodrie, Jefferson, Saber, Lemont, and Cypress. The broken line, which passed through the plot's origin and was perpendicular to the 2002 Beaumont environment vector, separated the cultivars (Wells and Cocodrie) that had higher than average yield from cultivars (Jefferson, Saber, Lemont, and Cypress) that had lower than average yield.
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Results from both AMMI and SREG GGE biplot analyses indicated that Cocodrie was the best cultivar in terms of better yield mostly at Bay City and Eagle Lake, while Wells was the best cultivar mostly at Beaumont and Ganado. Both analyses also indicate that Wells qualifies as a check cultivar in multilocation trials of promising lines conducted at Beaumont and Ganado.
Identification of Ideal Cultivar
The requirement for the use of SREG-based GGE biplots in the identification of superior cultivars and ideal test environments that facilitate the identification of such cultivars is a high correlation (r > 0.95) between G PC1 scores and G yields (averaged across locations) (Yan et al., 2000; Yan et al., 2001; Yan and Rajcan, 2002; Crossa et al., 2002). Ideal cultivars are those that should have large PC1 scores (high mean yield) and small (absolute) PC2 scores (high stability) (Yan et al., 2000; Yan and Rajcan, 2002). Yan and Hunt (2002) further suggested that a mean-environment coordinates system be created by drawing a mean-environment axis line that passes through the biplot origin and the mean environment marker. In addition, a broken line that is perpendicular to the mean-environment axis and that passes through the biplot origin is drawn.
In this study, the correlation between cultivar PC1 scores and cultivar yields was high (r = 0.983). Hence, the G main effects can be represented by the cultivars PC1 scores. The yield ranking of cultivars relative to the positive end of the mean-environment axis was Wells, Cocodrie, Jefferson, Lemont, Saber, and then Cypress (Fig. 8) . The stability ranking of cultivars based on increasing absolute difference between the genotype markers and the mean-environment axis was Cypress, Lemont, Cocodrie, Saber, Wells, and then Jefferson. Although Wells was the highest yielding cultivar, it was undesirably the fifth in stability, and although Cypress was first in stability, it was last in yielding ability. When both yield and stability rankings were considered, it was Cocodrie that had the second highest yield and third highest stability that qualified as the best among these six cultivars. The PC1 and PC2 scores obtained from SREG analysis that respectively represent the G yield and stability are respectively comparable to the G effect (yield) and adaptability parameter (regression coefficient, b) of Finlay and Wilkinson (1963).
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Identification of Ideal Test Locations
Ideal test environments should have small (absolute) PC2 scores (more representative of the overall environment) and large PC1 scores (more power to discriminate genotypes in terms of the genotypic main effect) (Yan et al., 2000; Yan and Rajcan, 2002). The ranking of environments in terms of being the most representative environment (based on the absolute difference between environment markers and the mean-environment axis) was Bay City (2002), followed by Eagle Lake (2000, 2001), Beaumont (2002), Ganado (2000), and Beaumont (2000), Ganado (2001), Eagle Lake (2002), Bay City (2001), Ganado (2002), Bay City (2000), then Beaumont (2001). Eagle Lake had an average rank of 4.7, both Bay City and Beaumont had an average rank of 7, while Ganado had an average rank of 7.3. Selection during segregating generations or during trials that do not require testing across several locations are usually performed at one location that best represents the region where the newly developed cultivar is going to be recommended for production. Eagle Lake was the location identified as the most representative among the four locations tested.
The ranking of environments in terms of their ability to discriminate cultivars (based on the relative position of each environment's marker to the positive end of the mean-environment axis) was Bay City (2002 and 2000), Beaumont (2002), Ganado (2002), Beaumont (2001), Eagle Lake (2001), Beaumont (2000), Eagle Lake (2000 and 2002), Ganado (2000 and 2001), and Bay City (2001). Both Bay City and Beaumont had an average rank of 5.0, Eagle Lake had an average rank of 7.7, and Ganado had an average rank of 8.3. Selection trials that require testing across several locations, such as the advanced yield trials require locations that can discriminate and determine the differences in the performance of the rice genotypes being tested. This is required in order that the best cultivar for the whole region or for specific sub-regions can be identified and recommended. Both Bay City and Beaumont were identified as the locations that had better genotype-discriminating abilities than the other locations.
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SUMMARY |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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The GGE biplots of SREG analysis results were used to determine the relative performance of genotypes at a specific environment, compare the performance of a genotype at different environments, compare the performance of two genotypes at different environments, identify the highest yielding genotypes at the different megaenvironments, and identify ideal cultivars and test locations.
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ACKNOWLEDGMENTS |
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Received for publication October 25, 2004.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYREFERENCES |
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analysis of variance for the significance of the effects of genotype, environment, genotype x environment interaction (GEI) on grain yield, and the partitioning of GEI into AMMI axes.
