Sites Regression GGE Biplot Analysis of Haricot Bean <i>(Phaseolus vulgaris </i>L.<i>)</i> Genotypes in three Contrasting Environments

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Table 2. Description of the 14 haricot bean genotypes tested across 3 different environments during 2007-2009 cropping season

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2.2. Statistical Procedures

The grain yield data were subjected to General Linear Model (PROC GLM) procedure using SAS version 9.0 ^[24] to determine the existence of significant difference between the genotypes for grain yield performance at each environment and combined over environment. Error mean squares from each environment were tested for homogeneity of variance to ensure the combined analysis across environments was appropriate. Separation of the additive main effect was done using Duncan’s Multiple Range Tests (DMRT). A stratified ranking for grain yield based on the technique suggested by ^[15] was done using the SAS program developed by ^[19] to determine the “top, middle and lower” third genotypes across the environments. Sites regression GGE biplots were produced using the SAS program following the procedures of ^[17] as modified by ^[4].

The following sites regression linear-bilinear model was used for analysis of G x E interaction:

where is the mean of the i^th genotype in the j^th environments; is the overall mean; is the site effect; () are scaling constants (singular values) that allow the imposition of orthonormality constraints on the singular vectors for genotypes, α_ik=(α_1k,…,α_gk ) and sites, γ_jk=(γ_1k,…,γ_ek), such that and for k≠k′; for k=1,2,3,… are called “primary,” ”secondary,” “tertiary,”. . . etc. effects of genotypes and sites, respectively; is the residual error assumed to be NID (0, ) (where is the pooled error variance and r is the number of replicates). Least squares estimates of the multiplicative (bilinear) parameters in the k^th bilinear term are obtained as the k^thcomponent of the deviations from the additive (linear) part of the model. In the sites regression model, the main effects of cultivars (G) plus the G x E interaction is absorbed into the bilinear terms.

3. Result and Discussion

3.1. Mean Performance of Genotypes and Environments

Pooled analysis of variance of grain yield (kg ha^-1) of 14 haricot bean genotypes tested in 9 environments indicated that genotypes, environments and G × E interaction were significantly (p ≤ 0.001) different, with coefficient of variability of 24.9% and coefficient of repeatability (R²) being 89% (Table 3). Environmental effect (E), which accounted for (50.13%) of the yield variation was found responsible for the greatest part of the total variation, followed by genotype (G) and G x E interaction effects explained 29.11% and 18.28%, respectively. Separate year analysis also revealed that the largest yield variation was accounted by environmental effect than the other source of variations (data not shown). Similar result was reported in northern Ethiopia in bread wheat ^[18]. The environments average grain yield across genotypes was ranged from as low as 448 kg ha^-1 for E9 to 4298 kg ha^-1 for E7 followed by 2978 kg ha^-1 for E2 (Table 4). A large yield variation explained by environments indicated that the existence of both spatial and temporal diversity in test-environments, with large differences among environmental means causing most of the variation in grain yield. The genotypes average grain yield across environments was ranged from the lowest of 860 kg ha^-1 for COLL/06-1 to 3323 kg ha^-1 for the genotype 213-FOT-15 (Table 4). The standard cultivar ZEBRA scored the best yield of 5680 kg ha^-1 at the best yielding environment E7, whereas, GORBANCILION yielded the best of 685 kg ha^-1 at the lowest yielding environment E9 (Table 4). According to the rank of ^[15], genotype 213-FOT-15 ranked first in 78% of the nine test environments. Similarly, other three better performing genotypes including 551-SEQ-1024, GORBNCILION and ZEBRA were ranked first in 67% of the test environments. However, genotypes BM-06-01, COLL/06-1 and BM-06-02 were found in the lower 78-100% of the test environments (Figure 1).

Figure 1. Performance rank (%) of the 14 haricot bean genotypes in the “TOP, MIDDLE and LOWER” third of the test envirnments according to (Fox et al., 1990)

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Table 3. Combined analysis of variance for grain yield (kg ha^-1) of 14 haricot bean genotypes evaluated at 9 environments of Ethiopia

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Table 4. Mean performance of 14 haricot bean genotypes tested at 3 locations over 3 years

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3.2. Sites Regression GGE Biplots Analysis

The requirement of “near-perfect correlation” (r=0.95) between genotype IPC1 scores and genotype main effects ^{[8, 31, 33, 35, 36]}, which commonly occurs when genotype sum of square is 40% or more of GGE sum of squares ^[34] has been met in the present dataset (i.e., r = 0.994 or genotype sum of square = 60.4% of GGE sum of squares). Therefore, the yielding ability and stability of genotypes, and discriminating ability and representativeness of the test environments can be effectively visualized using the sites regression GGE biplots. Hence, the application of GGE model for partitioning of G × E interaction revealed that the first (IPC1) and second (IPC2) multiplicative component sum of squares, with their cumulative degrees of freedom of 38, were explained 85.76% of the interaction sum of squares (Figure 2). This showed that there was a differential yield performance among the haricot bean genotypes across the nine test environments due to the presence of significant G × E interaction effects. Similar result was reported in ^[18] in bread wheat genotypes where the first two multiplicative interaction components of GGE were accounted for 88.97% of the G × E interaction sum of squares. Since further interaction principal component axes and the residual captured mostly noise and did not help to predict validation observations, first and second multiplicative components with their largest proportion of sum of squares of G × E interaction were adequate enough to cross-validate the current haricot bean grain yield and test environment variation. The prediction assessment also indicated GGE with only first two multiplicative component axes was the best predictive model ^[31].

The relative position of 14 haricot bean genotypes on IPC2 vs. IPC1 GGE biplot is displayed in Figure 2. This biplot classified the genotypes into high and low yielding types, and the two productivity classes into stable and unstable performance. All genotypes that had IPC1 scores greater than zero including ZEBRA, 551-SEQ-1024, 213-FOT-15, BAYOMADERO-75, 720-FOT-49, CARIOCA, GORBANCILLION, MAM-36 and 630-ESLES were found above average yielding and adaptable, while all genotypes that had negative IPC1 scores, namely EXRSCO-230, 855-POMPADOURG, BM-06-01, COLL/06-1 and BM-06-02 were found below average yielding and non-adaptable (Figure 2 and Table 4). This revealed that the sites regression GGE was 100% efficient in exhibiting the existing G × E interaction in the present haricot bean dataset. Similar result was reported in ^[39], whereas, inconsistencies in which some low yielding genotypes demonstrated greater than zero IPC1 scores and vice-versa has been reported in barley ^[41] and field pea ^[26]. According to ^[31], an ideal genotype is a genotype that had high mean performance across environments with high positive IPC1 value and near zero absolute value of IPC2 score. Thus, high yielding genotypes ZEBRA, BAYOMADERO-75, 551-SEQ-1024 and 213-FOT-15, with their 28.47, 24.63, 26.84 and 26.16 IPC1 values and 0.93, 2.22, 2.17 and 6.89 absolute IPC2 scores, respectively (Figure 2), were found stable across test environments and considered as ideal genotypes.

Figure 2. GGE Biplot visualizing the relative position of 14 haricot bean genotypes tested over 9 environments

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Figure 3. Genotype plus genotype × environment (GGE) biplot obtained from sites regression analysis showing the yielding ability (“which-won-where”) of 14 haricot bean genotypes tested over 9 environments

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3.3. Mega-environment Analysis

The “which-won-where” view of the GGE biplot, which consisted of an irregular polygon formed by connecting vertex genotypes and a set of lines drawn from the biplot origin and intersecting the sides of the polygon at right angles, was indicated in Figure 3. The vertex genotypes in this case were GORBANCILION, ZEBRA, 213-FOT-15, 630-ESLES, BM-06-02, COLL/06-1 and EXRSCO-230. Figure 3 helped to seek opportunities to sub-divide the target environment into sub-regions (mega-environments). Thus, it classified the environment markers into two sectors (i.e., two mega-environments). This revealed that no single genotype had highest yield in all environments. Five environments including E1, E2, E3, E4 and E6 were grouped into the same mega-environment, whereas, the remaining four environments namely E5, E7, E8 and E9 were grouped into another mega-environment (Figure 3). None of the test locations across all years were clustered into the same sector, indicating the inconsistency in performance of genotypes over years at a given single location. On the other hand, environment IPC1 scores had all positive values leading to non cross-over type G × E interaction. Unlike environment IPC1, environment IPC2 scores had both negative and positive values. This indicated that there was a difference in ranking orders among genotypic yield performances across environments leading to crossover G × E interaction (Figure 3). This result was consistent with previous reports ^{[34, 39, 40]}.

The distances from the origin (0, 0) are indicative of the amount of interaction exhibited by genotypes over environments or environments over genotypes ^[30]. Unlike the vertex genotypes, those that were located near the biplot origin, for example 855-POMPADOURG, had demonstrated less responsive to the changing environments. According to ^[37], vertex genotypes, because they are farthest from the origin, they are either best or poorest in some or all test environments. Therefore, they positively or negatively expressed a highly interactive behaviour and contributed more to the exhibited G × E interaction. Thus, vertex genotypes ZEBRA, GORBANCILION and 213-FOT-15 were found the best performer but EXRSCO-230, COLL/06-1 and BM-06-02 were the poorest across environments and manifested their high contribution to the existed G × E interaction. Similarly, those near origin environments, for example E6 and E9, exhibited nearly additive behavior over genotypic performance (Figure 3). This showed that genotypic yield in E6 and E9 were highly associated with over all environments mean yield, i.e., these two environments have average response to all genotypes. In contrast, E2 and E7, with their longest projection from the biplot origin, showed higher variation. This showed that performance consistency of the genotypes over seasons was better at E6 and E9 than it was at E2 and E7. Environments within the same sector of the polygon are assumed to share the same winner genotypes. Accordingly, genotypes ZEBRA, 551-SEQ-1024 and GORBANCILION were winner in mega-environments E1, E2, E3 and E4, whereas, 213-FOT-15 was a winner genotype in E5, E7 and E8 (Figure 3). Genotypes, which were not associated with any of the tester environments found poorly performed. For example, genotypes EXRSCO-230, COLL/06-1, BM-06-01 and BM-06-02 had shown their poor performance across the test environments (Figure 3; Table 4).

Figure 4. The average environment axis (mean-vs-stability) view of the GGE biplot obtained from the sites regression

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3.4. Genotype Evaluation

The mean-vs-stability view of the GGE biplot (Figure 4), which is defined by the average of the first two interaction principal component scores of all test environments in the biplot, is an effective display for visual evaluation of the current haricot bean genotypes in both mean performance and stability aspects ^{[39, 40]}. According to ^[34], superior genotype is a genotype that has both high mean performance and high stability across a mega-environment. The “average environment axis (AEA)” arrow (Figure 4) points to higher mean performance for the genotypes ^[40], and consequently help to rank the genotypes according to their mean performance. Thus, the current haricot bean genotypes were ranked according to their mean performance as follows: ZEBRA > 551-SEQ-1024 > 213-FOT-15 = BAYOMADERO-75 > GORBANCILION > 720-FOT-49 = CARIOCA > MAM-36 = 630-ESLES > “mean yield” > 855-POMPADOURG > BM-06-01 > EXRSCO-230 > BM-06-02 > COLL/06-1. This genotypic performance ranking based on AEA is nearly coincided with the mean performance of the genotypes in Table 4. Such consistence in this study was occurred due to the near perfect correlation (r = 0.994) obtained between genotypic main effect and first interaction principal component scores.

According to ^[40], the double-arrowed line that passes through the biplot origin and perpendicular to the AEA helps to estimate the genotypes contribution to the exhibited G × E interaction variance, both arrows indicating to the higher performance variability or lesser stability of the genotypes in both directions. Based on this principle, genotypes BAYOMADERO-75 and 855-POMPADOURG, which were located either almost on or very close to the AEA (Figure 4), were found the most stable genotypes with above and below average mean performance, respectively. This showed that the rank of these two genotypes were highly consistent across environments within their respective mega-environment. In contrast, 630-ESLES and CARIOCA, and EXRSCO-230 and BM-06-02, with their longest projection onto the AEA, were the two least stable genotypes with above and below average mean performance, respectively (Figure 4).

3.5. Test Environment Evaluation

Test environment evaluation is important to identify locations that can be used effectively to select superior genotypes for mega-environment. The “discriminating vs. representativeness” view of the GGE biplot, which is an important measure to evaluate the test environments ^[10], was indicated in (Figure 5). The length of vectors of an environment from the biplot origin, which is proportional to the genotypic mean standard deviation within the respective environment, is used to measure the discriminating power of the test environments ^{[38, 40]}. Those environments, which have longest projection from the biplot origin, for example E2, E7, E3 and E1, were found more discriminating of the genotypes. On the other hand, E9 and E6, with their shortest vector from the biplot origin, were found less discriminating of the test genotypes (Figure 5). In such an environment, all genotypes tend to perform uniformly and one can draw little or no information about the genotypic performance difference. Therefore, these environments could be considered as less important environments for selection of haricot bean genotype.

The AEA of Figure 5 is another benefit of the GGE-biplot to indicate the test-environments representativeness of the target environment. Based on ^[38], a test environment that has a smaller angle with the AEA is more representative of other test environments. Consequently, E4 and E2 are more representative of the other test environments whereas, E3, E1 and E8, with their wider angle from the AEA, are the least representative of the other test environments. As described by ^[40], an “ideal” test environment is an environment that had the ability to discriminate the genotypes and must be representative of the target environment. Hence, E2 was identified as an ideal environment that has both discriminating ability of the genotypes and representative of the other test environments. Therefore, this environment can be used to effectively select superior haricot bean genotypes that can perform consistently best across environments. For instance, genotypes ZEBRA and 213-FOT-15 were winner at E2, and found superior across all the remaining environments. On the other hand, if the testing environments sub-divided in to mega-environments, the environment that best discriminate the genotypes but not representative of the other environments would help to select specifically adapted genotypes ^[38]. Therefore, E1 and E3, which has high discriminating ability of the genotypes but not representative of the other test environments (Figure 5), would be used to select specifically adapted genotypes.

Figure 5. Discriminating ability vs. representativeness view of the GGE biplot obtained from the sites regression

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