Graphical Analysis of Multi-Environment Trials for Barley Yield Using AMMI and GGE-Biplot Under Rain-Fed Conditions

Introduction

Multi-environment yield trials (MEYTs) are essential because of the presence of genotype × environment (GE) interactions. The GE interaction that results from the differential responses of genotypes across a range of environments reduces the correlation between phenotypic and genotypic values and complicates the selection of the best genotypes (Ebdon and Gauch 2002). Plant breeding programs should take GE interaction into consideration as well as the estimate of its magnitude, relative to the magnitude of genotype and environment effects, which affects grain yield. Furthermore, the identification of genotypes that yield best across a number of environments would be useful to breeders and producers. Therefore, experimental research needs to be carried out over multiple environments in order to identify and analyze the major factors that are responsible for genotype adaptation (De Lacy et al. 1996). For the accurate analysis of MEYTs, the additive main effects and multiplicative interaction (AMMI) model is a valuable tool due to the accuracy that it provides in GE interaction studies (Gauch 2006; Li et al. 2006). AMMI analysis combines the additive parameters of traditional ANOVA with multiplicative parameters of PCA (principal component analysis). It is very useful in visualizing multi-environment data and gaining accuracy (Gauch 2006). Another method that has gained importance in investigating the role of genotype, environment and GE interaction effects in MEYTs is the genotype main effects plus genotype × environment interaction (GGE) biplot. Using a site regression model (SREG), Yan (2001) combined  G and GE and provided to the agricultural research community an excellent scientific method of visual analysis, called ‘GGE biplot analysis’ and developed a sophisticated Windows-based software called ‘GGEbiplot’ to summarize the G and GE and to address the issue of cultivar recommendation in multi-environment trials. This methodology uses a biplot to show the factors (G and GE) that are important in genotype evaluation as well as sources of variation in GE interaction (Yan et al. 2000, 2001). The GGE biplot emphasizes two concepts. First, although the measured yield is the combined effect of G, E and GE interaction, only G and GE interaction are relevant to, and must be considered simultaneously in genotype evaluation, hence the term GGE. Second, the biplot technique is employed to approximate and display the GGE of a MEYT, hence the term GGE biplot. This GGE-biplot is constructed by the first two principal components (PC1 and PC2) derived from subjecting environment centered yield data to singular value decomposition. It clearly shows which genotype won in which environments, and thus facilitates mega-environments (MEs) identification (Yan et al. 2000). The AMMI and GGE biplot models are defined as powerful tools for effective analysis and interpretation of multi-environment data structure in breeding programs (Yan et al. 2000; Ebdon and Gauch 2002; Samonte et al. 2005). The AMMI and GGE biplot have frequently been used for explaining GE interaction and to identify high yielding and adapted cultivars. Also the effectiveness of this methods in analyzing MEYTs data have been well documented (Yan et al. 2000, 2001; Kaya et al. 2002; Yan and Kang 2002; Morris et al. 2004; Yan and Tinker 2005; Samonte et al. 2005; Kang et al. 2006; Dehghani et al. 2006; Gauch 2006; Fan et al. 2007; Setimela et al. 2007; Mohammadi et al. 2007; Yan et al. 2007; Sabaghnia et al. 2008).

Accordingly, the aim of this study was (i) to apply AMMI and GGE biplot models to evaluate the significance and magnitude of GE interaction effect on grain yield of 18 advanced lines of barely tested across 12 rain-fed environments and (ii) to identify the best performing lines for selection environments by using and comparing the AMMI and GGE biplot methods.

Material and Methods

This study was carried out to determine the yield performances of 18 advanced lines of barely across four rain-fed locations undertaken in Mogan, Gachsaran, Gorgan and Lorestan during the 2004, 2005 and 2006 cropping seasons under non-irrigated conditions. These multi-environment yield trials were conducted in four research stations of Dryland Agricultural Research Institute (DARI), located in the semi-warm regions of Iran. These sites widely differ in terms of geographic position, altitude and rainfall (Table 1). The code of 18 lines and their pedigrees are given in Table 2. The experimental layout was a randomized complete block design with four replications at each site and year. Sowing was done in 1.05 m × 7.03 m plots, consisting of 6 rows with 17.5 cm distance between the rows. The central four rows were harvested for grain yield measurement in order to exclude border effects. Following harvest, grain yield was determined for each line in each test environment, and mean yield averages were computed in accordance with the experimental design. Combinations of three years and four locations were treated as 12 environments. The SAS software was used to partition yield variation into E, G and GE interaction. The grain yield data were subjected to AMMI and GGE biplot analyses. The GGEbiplot software (Yan 2001) was used to generate graphs showing (i) “which-won-where” pattern, (ii) ranking of cultivars on the basis of yield and stability, (iii) ranking of environments on the basis of discriminating ability and representativeness, (iv) environment vectors, and (v) comparing relative genotype performance in different locations (Yan and Kang 2003).

Table 1. Site description and rainfall data of experimental sites in Iran where the

experiments were conducted

Table 2. Code and pedigree of 18 barely advanced lines used in the study

Results and Discussion

Analysis of variance

The analysis of variance and AMMI for grain yield of 18 advanced lines of barely tested across 12 environments is presented in Table 3. The ANOVA for grain yield showed that mean squares of environments, genotypes and genotype × environment interaction (GEI) were highly significant (p<0.01) which accounted for 70.4%, 6.8% and 22.8% of model sum of squares (SS), respectively (Table 3). This case, along with a highly significant GEI, indicated the need for the  stability analysis. The genotype and the environment means for each location and each genotype are given in Table 4. The environment was the main cause of variations in grain yield, explaining 70.4% of the model (G + E+ GEI) SS (Table 3). A large yield variation explained by environments indicated that the environments were diverse, because large differences among environmental means caused most of the variation in grain yield. The environment yield means (averaged across genotypes) varied from 3412 kgha^-1 at Gorgan in 2005 (Gor5) to 4866 kgha^-1 at Gachsaran in 2005 (Gac5) (Table 4). Only the small portion, 6.8% of the total SS, was attributed to genotypic effects. The yields of the lines (averaged across environments) varied from 3290 kgha^-1 for G6 to 4256 kgha^-1 for G1 (Table 4). GEI significantly explained 22.8% of model variation in grain yield. The magnitude of the GEI sum of squares was about 3.5 times larger than that for genotypes. It is very common for MEYTs data to embody a mixture of crossover and non-crossover types of GEI. Gauch and Zobel (1997) reported that E accounts for about 80% of the total variation, while G and GE each account for about 10% in normal MEYTs. More pronounced influence of environment on the grain yield compared to the genotype or the GEI effects has been documented in many crops (Akcura et al. 2005).  Similar results were found in our study since the E effect was about 2.5 times higher than G + GE effects. On the other hand, the differential rankings of genotypes observed across test environments revealed a plausible existence of crossover GEI.

Analysis of genotype by environment interaction is vital for breeders in order to design the dissemination strategies for new varieties. It is important to identify cultivars with specific and general adaptation. Precise recommendation of lines for general and specific adaptation requires clear understanding of the real pattern of genotype by environment interaction. Thus, GE sum of squares was partitioned into “noise” and “real structure” following the procedure by Gauch and Zobel (1997). This computation ignores irrelevant environmental effects and much interaction noise while focusing mainly on the relevant genotype and real interaction effects (Campbell and Jones 2005). The AMMI analysis partitioned the SS of GEI into four significant interaction principal components axes (IPCA) (Table 3). The first principal axis (AMMI1) captured 28% of the SS GEI, the second 20%, the third 17% and the fourth 11%. Accordingly, the GEI contained 71357.7 (pooled error mean square) × 187 (degree of freedom for GEI) = 13343889.9 noise SS (32.6%) and 40862400 - 13343889.9 = 27518510.1 pattern SS (67.3%). This contribution of pattern SS (67.3%) was larger than that retained by the first two multiplicative terms that together accounted for 48% of the GEI sum of squares. Moreover, the first two terms had SS greater than that of genotypes and were highly significant (p<0.01). This suggested that the AMMI model with the first and second multiplicative terms was adequate for cross-validation of the yield variation explained by GEI in the present data set since it excludes most of its actual noise. Admassu et al. (2008) proposed that two interactions PCA for AMMI model was sufficient for the predictive model. Other interaction PCA captured mostly non-predictive random variation (noise) and did not fit to predict validation observations. Therefore, the approximation of factual interaction pattern of the 18 barely advanced lines with 12 environments was best cross-validated with the first two multiplicative terms of genotypes and environments that easily was visualized with the aid of a biplot.

Table 3.  AMMI analysis of variance and partitioning of the sum of squares (SS) for

grain yield (kgha^-1) of 18 barely advanced lines evaluated across 12 environments

a: % of model sum of squares for genotypes, environments and GEI; % (underlined numbers) of GEI sum of squares for IPCAs.

**: Significant at the 0.01 probability level; ns: non-significant; df: degree of freedom; SS: sum of squares; MS: mean   squares.

Table 4. Mean grain yield (kgha^-1) of 18 barely advanced lines across 12 environments

(combination of four locations and three years) in Iran

Underlined values are the maximum yield at each test environment.

Environment is designated as locations first letters (Gorgan, Mogan, Lorestan and Gachsaran) followed by 4, 5 or 6 (i.e. 2004,

2005 and 2006) to indicate year.

AMMI biplot analysis

To visualize the lines’ performance in relation to stability, main effects (mean performance) was plotted against IPCA1 (Figure 1). Displacement along the vertical axis indicated interaction differences between lines and between environments, and displacement along the horizontal axis indicated difference in line and environment main effects. This biplot (Figure 1) based on AMMI1 model explained treatments SS, with 6.82% due to Genotype SS, 70.41% due to Environment SS, and 6.3% due to PC1 SS. Thus, it is very informative since it explains 83.5 % of the treatment SS. The lines with PC1 scores close to zero expressed general adaptation whereas the larger scores depicted more specific adaptation to environments with PC1 scores of the same sign (Ebdon and Gauch 2002). Therefore, a line such as G9 with larger PC1 score was better adapted to Mogan in 2004 with larger PC1 score with the same sign (Figure 1). In contrast, line G1, was adapted to Lorestan in 2004 and Gachsaran in 2006 with larger negative PC1 scores. The relative magnitude and direction of lines along the abscissa and ordinate axis in biplot is important to understand the response pattern of genotypes across environments. The best genotype should combine high yield and stable performance across range of production environments. Therefore, the four high yielding (averaged over environments) lines G1, G14, G11 and G2 (with 4256, 4206, 4122 and 4097 kgh^-1, respectively) can best judged based on their stability. G2 and G11 that combined low absolute PC1 score and high yield would be best overall winners with relatively less variable yield across environments. Gorgan had relatively smaller variation in the interaction (PC1 score) from year to year while year differences were very high for Lorestan, Mogan and Gachsaran. This underlines the importance of evaluating multi-location yield trials over different seasons. Also, Figure 1 indicated that the relative ranking of genotypes were stable at Gorgan than other locations.

Figure 1. AMMI1 biplot for IPCA1 vs main effect, to show genotype performance in relation

to stability of 18 barely advanced lines evaluated across 12 environments 

Winning genotype and mega-environment

The Figure 2 polygon is a summary of the GEI pattern of the 18 barely lines with 12 environments. According to this analysis, ideal cultivars are those that should have large PC1 scores (high mean yield) and small (absolute) PC2 scores (high stability). Also, ideal test environments should have large PC1 scores (more power to discriminate genotypes in terms of the genotypic main effect) and small (absolute) PC2 scores (more representative of the overall environments) (Yan et al. 2000). This polygon is formed by connecting the lines that are further away from the biplot origin in a way that all other lines are contained in the polygon. With the present data set, the lines G1, G2, G9, G17, G10, G6 and G8 expressed a highly interactive behavior. The genotypes at vertex are the winners in the sites included in that sector. Six rays in Figure 2 divided the biplot into six sectors and the environments fall into two of them. Three (or four) environments, Mogan2004, Mogan2005 (probably also Mogan2006) and Lorestan 2005, fell into the first sector and the vertex line for this sector was G9. Therefore, Mogan in all years clustered in one sector indicating repeatable performance of the lines observed in this location and it could be considered as separate mega-environment for barely variety evaluation and recommendation. The rest of environments (Gorgan in three years, Gachsaran in three years and Lorestan on two years) fell into the second sector. The vertex line for this sector was the G1. The length of an environmental vector is an estimation of discriminating power of the environment (Yan et al. 2007). Test environments with longer vectors (Lor6 in Figure 2) are more discriminating of the genotypes. A test environment close to the biplot origin (Mog6 and Lor5 in Figure 2) means that it exhibited low interaction and relative performance of all genotypes is similar. Therefore, Mog6 and Lor5 provided little or no information about the genotype differences. On the hand, the nearly additive behavior of Mogan in 2006 indicated that genotypic yield in that environment was highly correlated with the overall genotypic means across environments. Gorgan was relatively closer to biplot origin in all years and hence less interactive location and could be a suitable location for the selection of genotypes with average adaptation.

Visualizing the mean yield and stability of the genotypes

The mean yield and stability of genotypes are evaluated by defining an average tester coordinate (ATC) method (Yan 2001). In this method, the average environment is indicated by a circle and shows the positive end of the ATC x axis (Figure 3). A line known as the average environment axis and serves as the abscissa of the AEC is then drawn to pass through this average environment and the biplot origin. The ordinate of the AEC is the line that passes through the origin and is perpendicular to the AEC abscissa (Figure 3). Unlike the AEC abscissa, which has one direction, with the arrow pointing to greater genotype main effect, the AEC ordinate is indicated by double arrows, and either direction away from the biplot origin  indicates   greater  GEI  effect  and  lower

Figure 2. Polygon views of the GGE biplot based on symmetrical scaling for which won

where pattern for genotypes and environments.

stability. The AEC ordinate separates genotypes with below-average means from those with above-average means. Furthermore, the average yield of genotypes is approximated by the projections of their markers to the AEC abscissa. For this study, lines with above-average means (i.e. G1, G14, G2, G11, G5, G15, G12, G9 and G18) were selected, whereas the rest (i.e. G4, G7, G13, G16, G3, G17, G8 and G10) were discarded. On the other hand, a longer projection to the AEC ordinate, regardless of the direction, represents a greater GEI of a genotype, which means it is more variable and less stable across environments or vice versa. For instance, lines G5, G18, G11 and G2 were more stable as well as high yielding. Conversely, G9, G1, G12, G14 and G15 were more variable, but high yielding. The requirement for the use of SREG based GGE biplots in the identification of superior genotypes is to facilitate the identification of such genotypes (Crossa et al. 2002).

Ideal genotype and ideal environment

An ideal genotype is defined as one that is the highest yielding across test environments and is absolutely stable in performance (Yan and Kang 2003). Although such an ideal genotype may not exist in reality, it can be used as a reference for genotype evaluation. A genotype is more desirable if it is located closer to the ideal genotype. Thus, using the ideal genotype as the center, concentric circles were drawn to help visualize the distance between each genotype and the ideal genotype. When an “ideal” cultivar view was drawn (Figure 4), the lines G2, G11 and G1 were the closest to the ideal cultivar (center circle) and may be regarded as desirable genotypes, followed by G14, G5 and G15 as a group.
Ranking of other genotypes as ideal was G18 > G12 > G7 > G4 > G13 > G16 > G9 > G3 > G17> G8 > G10 > G6. On the other hand, the lower yielding genotypes i.e. G7, G4, G13, G16, G9, G3, G17, G8, G10 and G6, are unfavorable because they are far away from the ideal genotype. The relative contributions of stability and grain yield to the identification of desirable genotype found in this study using the ideal genotype procedure of the GGEbiplot are similar to those found in other crop stability studies such as rice (Samonte et al. 2005), wheat (Kaya et al. 2006), barley (Dehghani et al. 2006) and maize (Fan et al. 2007).

Figure 3.  GGE biplot obtained from sites regression (SREG) analysis showing mean and

stability of 18 barely genotypes for yield and GEI.

Figure 4. Comparison of 18 barely advanced lines against the ‘ideal’ genotype for grain

yield and stability of performance across environments

An ideal environment should have more power to discriminate genotypes in terms of the genotypic main effect (large PC1 scores) and at the same time more representative of the overall environments (small absolute PC2 scores). Although such an ideal environment may not exist in reality, it can be used as a reference for genotype selection in the MEYTs. An environment is more desirable if it is located closer to the ideal environment. Thus, using the ideal environment as the center, concentric circles were drawn to help visualize the distance between each environment and the ideal environment (Yan et al. 2000). In Figure 5, the environments are ranked based on both discriminating ability and representativeness. Thus, LOR4 was a relatively favorable test environment, followed by GAC5, with the highest yield, as a group. Overall, the poorest test environments relative to the ideal environment were GAC6, LOR5, MOG4 and MOG6.

Figure 5. Comparison of 12 test environments against the ‘ideal’ environment based on

discriminating ability and representativeness

Comparing performance of two genotypes at all environments

The performance of the top two high yielding and stable lines (G2 and G11) was compared in GGE biplot by a straight line connecting the markers of the two genotypes and a broken perpendicular line passing the plot origin (Figure 6). This perpendicular line divided the environments into two groups; each of these genotypes would yield better than the other at environments with markers on its side of the perpendicular, and vice versa (Yan et al. 2000). Thus, G11 would yield better than G2 at GAC in all years (2004, 2005 and 2006) and at LOR in 2004 and 2006, whereas G2 would yield better than G11 at GOR in all years (2004, 2005 and 2006), MOG in all years (2004, 2005 and 2006) and LOR in 2005. Therefore, G11 is the ideal genotype for planting in Gachsaran and Lorestan and G2 is the best for Gorgan and Mogan.

Figure 6. GGE biplot obtained from site regression (SREG) analysis that clusters the environments into those where G2 out-yields G11 (below the broken line) and where G11 out-yields G2 (above the broken line)