Gge Biplot Full Version

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Abstract:In this study, 12 maize hybrids were planted and evaluated to determine the effect of genotype and genotype-environment interaction (GEI) base GGE (genotype plus genotype-by-environment) using a Graphical biplot technique in four research stations (Arak, Birjand, Shiraz and Karaj) within two years using a Randomized Complete Blocks Design (RCBD). The combined analysis of variance showed that the effects of the environment, genotype and genotype-environment interaction (GEI) were significant in the one percent probability level. GGE biplot results indicated that the first and second principal components (PC1 and PC2) explained more than 83% of the grain performance variation. Simultaneous study of grain performance and hybrid stability using the biplot of average environment coordinates showed that the KSC705 genotype had the highest yield and stability. Polygon view divided the studied areas into two mega-environments (MEs) and identified the best genotypes in each mega-environment (ME). In the first mega-environment (ME1), the Karaj and Shiraz with KSC706 and KSC400 genotypes were detected, and were the best; and in the second mega-environment (ME2), Arak and Birjand with KSC704 and KSC707 genotypes performed better. The biplot graph for the correlation between the genotypes categorized the studied hybrids into four groups positively related to each other based on the angles between vectors. The KSC704 and KSC707 genotypes were desirable in the yield in Shiraz and Karaj and KSC706 were in Arak and Birjand. Additionally, Arak-Birjand, Karaj-Shiraz showed a positive and significant correlation. Birjand and Karaj had most genotype interaction with each other.Keywords: adaptability; stability; correlation coefficient; mega-environments (MEs); graphical technique

FIGURE 1. Average environment coordination views of the GGE biplot based on location-focused scaling of mean performance and stability of genotypes. (A) Pod yield. (B) Seed yield.

An example of a GGE (genotype plus genotype-by-environment) biplot similar to figure 12 of Yan and Tinker (2006). The flip argument can be used to flip the x and y axes so that biplots are oriented as desired. Because the SVD factorization is not unique,

As seen above, the environment vectors are fairly long, so that relative performance of genotypes in environments can be assessed with reasonable accuracy. In contrast, a biplot based on principal components 2 and 3 has shorter vectors which should not be interpreted.

When \\(\\bf X\\) is a genotype-by-environment matrix, a genotype-focused biplot is easily obtained. The genotype coordinates are can be obtained from the SVD using the first two columns of \\(\\bf G_{gf} = U S\\) or equivalently from NIPALS \\(\\bf G_{gf} = T\\).

Note that GGE biplots are environment-focused. In particular, this provides the interpretation that the correlation of genotype performance in two environments is approximated by the cosine of the angle between the vectors for those two environments.

The SVD and NIPALS methods provide the same principal components for complete-data, except that a principal component from SVD and the corresponding principal component from NIPALS might point in opposite directions (differ by a factor of \\(-1\\)) as in some of the examples above. The corresponding biplots would therefore be mirror-reversed along that component. For biplots from SVD and NIPALS that are visually consistent, each principal component can be directed to point in a direction that is positively correlated with the overall genotype means. In other words, if the correlation of the genotype means and the ordinate of the genotypes along the principal component is negative, the principal component is multiplied by \\(-1\\).

As with all biplots, the environment vectors can be arbitrarily scaled so that the genotypes and environments uses a similar amount of area on the plot. The algorithm that physically centers the biplot and scales it on the page is not perfect and has opportunities for improvement.

Genotype environment (GE) interaction is an important source of variation in soybean yield, which can significantly influence selection in breeding programs. This study aimed to select superior soybean genotypes for performance and yield stability, from data from multi-environment trials (METs), through GGE biplot analysis that combines the main effects of the genotype (G) plus the genotype-by-environment (GE) interaction. As well as, through path analysis, determine the direct and indirect influences of yield components on soybean grain yield, as a genotype selection strategy. Eight soybean genotypes from the breeding program of Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) were evaluated in field trials using a randomized block experimental design, in an 8 x 8 factorial scheme with four replications in eight different environments of the Cerrado of Northeastern Brazil during two crop seasons. Phenotypic performance data were measured for the number of days to flowering (NDF), height of first pod insertion (HPI), final plant height (FPH), number of days to maturity (NDM), mass of 100 grains (M100) and grain yield (GY). The results revealed that the variance due to genotype, environment, and GE interaction was highly significant (P < 0.001) for all traits. The ST820RR, BRS 333RR, BRS SambaíbaRR, M9144RR and M9056RR genotypes exhibited the greatest GY stability in the environments studied. However, only the BRS 333RR genotype, followed by the M9144RR, was able to combine good productive performance with high yield stability. The study also revealed that the HPI and the NDM are traits that should be prioritized in the selection of soybean genotypes due to the direct and indirect effects on the GY.

Citation: Silva WJdS, Alcântara Neto Fd, Al-Qahtani WH, Okla MK, Al-Hashimi A, Vieira PFdMJ, et al. (2022) Yield of soybean genotypes identified through GGE biplot and path analysis. PLoS ONE 17(10): e0274726.

Thus, considering the strong influence of the environment on the phenotype of plants, this study aimed to select soybean genotypes for performance and yield stability accessed by GGE biplot analysis. Furthermore, based on the environments identified by the GGE biplot graphical tool, to verify using the path analysis the relative contribution (direct and indirect effects) of yield components on GY as a breeding strategy.

All phenotypic data were collected from five randomly selected and tagged plants in each plot. NDF were recorded as the period between sowing and the start of flowering, when 50% of the flowers are open (stage R1) to R2 (full flowering). HPI was measured with a graduated ruler, from the soil to the insertion point of the 1st pod. FPH was measured from the base of the plant at full maturity stage to the upper end of the main stem. NDM were recorded as the period between sowing to full maturity (95% of the pods have reached their full mature color).

All of the trials were harvested manually. The GY and M100 were determined in the useful area of each plot (4 m2), five days after the plants reached full maturation. The pods were manually threshed and the harvested grains were stored in properly identified paper bags for later determination of the grain mass per useful area of each plot. The GY (kg ha-1) was estimated with the humidity adjustment to 13% as determined by the drying oven method at 105C for 24 h [23]. The M100 was determined by separating the grains according to the method established by Brasil [23], and the masses quantified using a precision balance.

To explain the GE interaction, the multivariate stability analysis was performed graphically based on the GGE biplot model [26] using R package GGEBiplotGUI. Singular value decomposition (SVD) of the first two principal components was used to fit the GGE biplot model according to the equation below:where GGE is the matrix of the effects of genotypes added to the effects of the interaction; λk is the k-th singular value of the original matrix interactions (GE); γik is the element corresponding to the i-th genotype in the k-th singular vector of the GE matrix column; αjk is the element corresponding to the j-th environment in the k-th singular vector of the GE matrix row; and ρij is the residual related to the adjustment.

GGE biplots are graphical tools to demonstrate the GE interaction and the classification of genotypes based on the mean and stability obtained for an evaluated character. The generated graph is based on METs evaluation for environmental stratification (who-won-where pattern), genotype evaluation (mean versus stability) and tested environment ranking (discriminatory versus representative). The classification of genotypes was established in ascending order of each stability parameter. The biplots were based on partitioning with singular value = 2, transformed (transform = 0), centered on the environment (centering = 2) and standardized with standard deviation (scaling = 0).

Considering the GY, it is observed that the environments account for the greatest variation in relation to G x E interactions, while the genotypes show the smallest variation. The magnitude of the mean square of the G x E interaction of GY, resulting from the product of the mean square with the degree of freedom, was about 3.23 times greater than the magnitude of the genotypes, reinforcing the significant differences in the genotypic response in the MET of this study. The GGE biplot based on this data set is shown in Fig 1, with the scores of PC1 on the x-axis and the scores of PC2 on the y-axis, for genotypes and environments.

The \"which-won-where\" graph (Fig 1A) allows for visual grouping of test environments based on G x E crossing between the best genotypes. The genotype at the vertex of the polygon performs best in the environment falling within the sectors. The vertices of the polygon are formed by the genotypes: BRS 333RR, BRS 8990RR, ST820RR and M8766RR. The eight environments