## 2 Materials and Methods
### Statistical Analysis  
In this study, analysis of variance (ANOVA) is used to test the independent effects of G (genotype), S (sectors), Y (years), and their interactions; the yield scores obtained were not subjected to transformations, maintaining their original structure to provide simplicity  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sector**} & \multicolumn{1}{c}{**Sugarcane**} & \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Hectares**} & \multicolumn{1}{c}{**Total Harvested**} & \multicolumn{1}{c}{**Average Yields**} & \multicolumn{1}{c}{**Environment**} \\  & & & & **Material** & **(Ton/Ha)** & **Code** \\ \hline \multirow{3}{*}{01} & \multirow{3}{*}{Ingenio} & 2018 & 15.88 & 1141.15 & 71.85 & A \\  & & 2019 & 16.54 & 1300.73 & 78.62 & B \\  & & 2020 & 16.15 & 1268.12 & 78.53 & C \\ \hline \multirow{3}{*}{02} & \multirow{3}{*}{Ingenio and Isabel maria} & 2018 & 15.23 & 1130.96 & 73.43 & D \\  & & 2019 & 16.39 & 1407.28 & 85.93 & E \\  & & 2020 & 16.42 & 1398.54 & 85.22 & F \\ \hline \multirow{3}{*}{03} & \multirow{3}{*}{Ingenio} & 2018 & 17.36 & 1312.59 & 75.6 & G \\  & & 2019 & 17.33 & 1666.7 & 96.19 & H \\  & & 2020 & 18.18 & 1773.76 & 97.58 & I \\ \hline \multirow{3}{*}{04} & \multirow{3}{*}{Ingenio} & 2018 & 17.08 & 1059.5 & 62.03 & J \\  & & 2019 & 16.76 & 1246.57 & 74.39 & K \\  & & 2020 & 16.48 & 1244.68 & 75.55 & L \\ \hline \multirow{3}{*}{05} & \multirow{3}{*}{Ingenio} & 2018 & 16.25 & 1048.75 & 64.55 & M \\  & & 2019 & 16.17 & 1265.4 & 78.25 & N \\ \cline{1-1}  & & 2020 & 16.63 & 1309.51 & 78.77 & O \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of experimental environments.  
and transparency. On the other hand, the GGE biplot method was employed to analyze high performance and stability. The GGE biplot analysis can be expressed as follows:  
\[\mathrm{Y_{ij}}=\mu+\mathrm{G_{i}}+\mathrm{E_{j}}+(\mathrm{G}\ \times\mathrm{E})_{ij}+\epsilon_{ij} \tag{2}\]  
where \(\mathrm{Y_{ij}}\) is the yield of genotype i in environment j, \(\mu\) is the overall average yield, \(\mathrm{G_{i}}\) is the deviation of genotype i from \(\mu\)[11]; \(\mathrm{E_{j}}\) is the deviation of environment j from \(\mu\); \(\mathrm{(G}\times\mathrm{E)_{ij}}\) is the corresponding genotype-environment interaction; \(\epsilon_{ij}\) is the residual error associated with genotype i in environment j (25).  
The GGE biplot (main genotype effect plus the \(\mathrm{G}\times\mathrm{E}\) interaction) bases its visualization on dimension reduction techniques such as the GH-biplot (13) and the HJ-biplot (14) for simultaneous representation; however, the GGE biplot is more suitable for handling agricultural data and visualizing \(\mathrm{G}\times\mathrm{E}\) interactions.  
In this study, the mean matrix for the GGE biplot was constructed using environmental data with three inputs (genotypes or varieties, sectors, and years), where singular value decomposition (SVD) was applied. Subsequently, a plot was created using the scores from the first two principal components (PC1 and PC2).  
All analyses, including the ANOVA analysis using the \"agricolae\" package and the GGE biplot with \"Metan: Analysis of Trials in Multiple Environments\" (26), were performed in the R Studio environment, version 4.1 (2024).