## 3 Results
### Relevance of Genotypic, Environmental, and Genotype-Environmental Effects  
A two-way analysis of variance (ANOVA) was employed to evaluate the performance of 10 sugarcane varieties cultivated over three periods in five different sectors. The results demonstrated that there is genotypic variation in response to the environment (Table 3), with high significance both in the independent effects of \(\mathrm{G}\), \(\mathrm{S}\), and \(\mathrm{Y}\) (\(p<0.001\)) and in the interactive effects \(\mathrm{G}\times\mathrm{S}\) (\(p<0.01\)), \(\mathrm{G}\times\mathrm{Y}\) (\(p<0.01\)), and \(\mathrm{S}\times\mathrm{Y}\) (\(p<0.001\)). This indicates that sugarcane yield was affected by the cultivation period, sector, and the specific variety used. However, the triple interaction among genotype, sector, and year (\(\mathrm{G}\times\mathrm{S}\times\mathrm{Y}\)) was not statistically significant, suggesting that some interactions do not decisively influence yield under the study conditions. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Genotypes**} & \multicolumn{4}{c}{**Average Total Yield (\(\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{ \mathrm{ }}}}}}}}}}}}}}\)\)**} & \multicolumn{4}{c}{**Score 02**} & \multicolumn{4}{c}{**Sector 03**} & \multicolumn{4}{c}{**Sector 04**} & \multicolumn{4}{c}{**Sector 05**} \\ \cline{2-13}  & **2018** & **2019** & **2020** & **2018** & **2019** & **2020** & **2018** & **2019** & **2020** & **2018** & **2019** & **2020** & **2018** & **2019** & **2020** \\ \hline CC-8592 & 70.45 & 69.22 & 72.71 & 57.85 & 63.34 & 77.1 & 83.68 & 92.09 & 72.42 & 79.14 & 79.52 & 84.64 & 96.63 & 75.83 & 78.51 \\ CC-34181 & 66.97 & 60.62 & 66.69 & 71.91 & 59.03 & 65.25 & 78.71 & 91.52 & 73.66 & 54.41 & 64.28 & 69.98 & 78.74 & 67.14 & 72.01 \\ CLONES & 63.69 & 88.24 & 111.68 & 77.85 & 100.28 & 72.99 & 99 & 107.61 & 72.95 & 88.94 & 59.08 & 101.45 & 11.67 & 72.81 & 75.53 \\ CC-74250 & 70.03 & 64.76 & 74.85 & 65.75 & 61.79 & 72.60 & 81.56 & 95.09 & 78.37 & 72.76 & 64.98 & 74.68 & 88.36 & 76.24 & 70.86 \\ EC-20 & 70.95 & 67.81 & 91.03 & 53.39 & 60.01 & 86.95 & 88.09 & 103.06 & 81.79 & 86.95 & 81.75 & 91.55 & 106.18 & 82.44 & 85.62 \\ EC-03 & 58.14 & 50.02 & 64.13 & 60.57 & 62.72 & 59.09 & 71.96 & 87.97 & 59.44 & 67.88 & 67.9 & 69.28 & 89.98 & 48.56 & 64.67 \\ EC-05 & 86.66 & 60.73 & 74.19 & 57.68 & 61.76 & 72.56 & 77.64 & 83.56 & 81.93 & 71.47 & 72.17 & 70.92 & 84.35 & 49.74 & 50.85 \\ EC-07 & 87.77 & 47.94 & 97.28 & 57.77 & 72.03 & 83.32 & 99.32 & 109.72 & 81.68 & 82.09 & 88.82 & 92.11 & 106.31 & 74.91 & 85.74 \\ EC-08 & 77.63 & 78.32 & 84.42 & 75.72 & 75.14 & 78.92 & 82.3 & 102.06 & 78 & 77.05 & 85.9 & 90.51 & 99.36 & 73.17 & 79.82 \\ EC-01 & 77.42 & 70.06 & 73.36 & 67.94 & 71.33 & 84.28 & 92.24 & 95.3 & 84.83 & 85.79 & 75.58 & 87.62 & 91.37 & 80.87 & 82.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average yield of sugarcane genotypes across five sectors. The yield of sugarcane shows that it predominantly contains variation patterns influenced by factors not present in the model or due to the natural variability inherent in sugarcane cultivation (69.41%). On the other hand, the portion explained by the model (30.59%) indicates that all its interactions are significant, with the (G \(\times\) S) interaction, which outlines the differences in yield between varieties and sectors, having the highest explanatory power among the groups. The GGE biplot analysis shown in Figure 1 utilized the singular value decomposition (SVD) method with symmetric scaling (standard deviation) and has an explanatory power of 74.77% of the total variance that evaluates the G \(\times\) S \(\times\) Y interaction [15]. The proximity of genotypes in a specific environment indicates that the selected sugarcane varieties may have a better response in a corresponding environment [20].