3.1| Combined analysis and mean comparison
The combined analysis of variance indicated significant effects by the year and interactions of year- cultivar and year- harvest date- cultivar across all investigated traits. Notably, distinct differences among various harvest dates were observed regarding SY at the 1% probability level, as well as in RY and WSY at the 5% probability level. The year- harvest date interaction significantly influenced all traits, except for RY. Moreover, the studied cultivars significantly varied in SC and MS (Table 3).
The highest RY (86.67 t. ha-1) was obtained from HD4, followed by HD3 and HD2, while the lowest RY was recorded by HD1 (47.40 t. ha-1) (Figure 1). Asia and Shokoufa showed the highest RY in the third year, averaging 83.75 and 82.75 t. ha-1, respectively, yet insignificantly differing from Paya, Perfecta, and Arya in the third year, Ekbatan in the first year, and Perfekta in the second year. Notably, Asia exhibited the lowest RY in the first year (52.28 t. ha-1) (Table 4). The mean comparison demonstrated that SC was highest (17.01%) for HD3 in the third year, and lowest (11.61%) for HD1 in the first year. It remained higher across all four harvest dates in the third year compared to the other two years (Table 5). Perfekta showed the highest SC in the second (15.50%) and third years (15.45%), with no significant difference from Arta, Ekbatan, and Asia in the third year. The lowest SC was attributed to Paya (11.31%) and Asia in the first year (11.25%) (Table 4). The research found the highest SY in the third year on HD4 (13.52 t. ha-1) and in the second year on HD3 (13.33 t. ha-1), while the lowest SY was recorded for plants harvested on HD1 in the second year (4.60 t. ha-1) (Table 5). Results revealed that Perfekta (12.51 t. ha-1) and Asia (12.48 t. ha-1) produced the highest SY in the second and third years, respectively, showing no significant difference from Perfekta and Shokoufa in the third year. Asia exhibited the lowest SY in the first year (5.91 t. ha-1) (Table 4). The study also revealed an increase in WSC across all three years due to delayed harvesting, with the highest WSC obtained from HD3. Notably, HD3 in the third year (14.49%) exhibited the highest, and HD1 in the first year (7.62%) had the lowest WSC (Table 5). Among the studied cultivars, Perfekta in the third and second years (13.16% and 12.69%, respectively) and Ekbatan in the third year (12.80%) showed the highest WSC. The lowest WSC was associated with Paya and Asia in the first year (6.89% and 6.47%) (Table 4). The highest WSY was linked to HD4 and HD3 in the third year (10.56 and 10.19 t. ha-1, respectively) and HD3 in the second year (10.11 t. ha-1), while it was lowest on HD1 in the first and second years (3.86 and 3.46 t. ha-1, respectively) (Table 5). Perfekta demonstrated the highest WSY in the third and second years (10.54 and 10.30 t. ha-1, respectively), followed by Asia and Shokoufa (10.21 and 10.14 t. ha-1) in the third year. Asia exhibited the lowest WSY in the first year (3.40 t. ha-1), and it's worth noting that Ekbatan had the highest WSY in the first year (Table 4). The ECSs were notably highest (84.97%) for HD3 in the third year and lowest (65.35%) for HD1 in the first year (Table 5). Based on the mean comparisons, Perfekta, Ekbatan, and Shokoufa cultivated in the third year exhibited the maximum ECS (85.02%, 84.70%, and 83.65%, respectively). Asia recorded the lowest ECS in the third year (57.07%). Ekbatan had the highest ECS in the first year, while Perfekta obtained the highest ECS in the second year compared to other cultivars (Table 4). The highest ALC was observed (10.89%) when harvested in HD3 during the first year, while it was minimized (2.92%) in HD2 in the second year. The highest ALC across all three years of experiments was attributed to HD3 (Table 5). Ekbatan in the first year (10.89%) and Arya in the second year (2.99%) exhibited the highest and lowest ALC, respectively. All cultivars displayed their highest ALC in the first year, except for Sharif and Shokoufa (Table 4). The highest and lowest MS were linked to HD3 in the first year (3.50%) and HD3 in the third year (1.92%). It was higher across all four harvest times in the first year than in the other two years (Table 5). Among the studied cultivars, the highest MS was recorded by Asia (4.18%) in the first year, and the lowest was related to Ekbatan, Perfekta, and Shokoufa in the third year (1.68, 1.68, and 1.78%, respectively). Notably, the cultivars exhibited the highest MS in the first year among all three years (Table 4).
Table 3 Combined analysis of variance for the observed traits of sugar beet cultivars
Figure 1 Comparison of root yield averages across varying harvest dates over three years
Table 4 Mean comparison of the interaction between cultivars and years for studied traits of sugar beet cultivars
Table 5 Mean comparison of the interaction between harvest dates and years for studied traits of sugar beet cultivars
3.2| Stability analysis
The AMMI analysis of variance for WSY demonstrated statistically significant differences between genotypes and environments (additive effects) and the GEI (multiplicative effects) at a 1% probability level (Table 6). Genotype and environment significantly contributed to the variance in data, accounting for 3.05% and 32.10%, respectively. The GEI was further analyzed, yielding IPC1 and IPC2. Both IPCA1 and IPC2 were found to be significant at 1% probability level. IPC1 contributed 5.01%, while IPC2 contributed 1.72% of the total sum of squares. These components accounted for 60.20% and 15.21% of the sum of squares of the GEI effect, respectively. Combined, IPC1 and IPC2 explained 75.41% of the total GEI variance (Table 6).
The stability of WSY and the specific adaptation of cultivars to the studied environment were assessed through the biplot of the first two IPCs (Figure 2). Cultivars with higher WSY (represented on the horizontal axis) and lower values for the IPC1 and IPC2 (defined on the vertical axis) were considered more favorable. Results revealed that Shokoufa exhibited the lowest IPC1 value among the studied cultivars, indicating higher WSY stability. Conversely, Ekbatan and Perfekta displayed both high positive and negative values of IPC1, suggesting lower stability compared to other studied cultivars (Figure 2A). Arya and Arta recorded the lowest IPC2 values, while Perfekta and Asia displayed the highest (Figure 2B). In the 12 environments, Perfekta demonstrated the highest average WSY at 8.84 t. ha-1, followed by Shokoufa, Arya, and Arta. Conversely, Paya exhibited the lowest average WSY at 5.90 t. ha-1. In terms of stability, Arta and Arya displayed lower values for ASTAB, ASI, ASV, AVAMGE, DA, DZ, EV, FA, MASI, MASV, SIPC, ZA, and WAAS, indicating stability in WSY. Conversely, Ekbatan exhibited higher values for the same stability parameters, suggesting instability (Table 7).
Table 6 Analysis of variance of white sugar yield in sugar beet cultivars using the AMMI Model
Figure 2 Scatter plot illustrating the relationship between cultivars and environments, using the mean white sugar yield and the first (A) and second (B) principal components.
Table 7 Mean white sugar yield and various AMMI stability parameters for sugar beet cultivars across 12 environments
Figures 3A and 3B depicts the convex hull generated by the GGE biplot analysis of sugar beet cultivars across 12 environments, utilizing the IPC1 and IPC2 to identify cultivars and environments. The diagram, accounting for 75.35% of the variance in the GEI, illustrates those genotypes closer to a specific environment exhibit specific adaptability, while those nearer to the coordinate origin display general adaptability. The study identified Sina, Arya, and Arta as the most stable due to their proximity to the coordinate origin, while Perfekta, Ekbatan, Paya, and Asia were characterized as the most unstable.
The polygon in the biplot (Figure 3A) represents the cultivars excelling in specific environments, with Perfekta positioned at the polygon's vertex, indicating its high specific adaptability across various environments. Notably, Ekbatan demonstrated significant specific stability in specific environments, including FY-HD1, FY-HD4, FY-HD2, and FY-HD3 times. Conversely, Paya and Asia were deemed unsuitable for the tested environments, as they were positioned at the vertex of the polygon, indicating no suitable environment.
The average environment coordination line, a diagonal line passing through the biplot's center and the ideal point, indicates that genotypes closer to the circle’s center yield higher. Conversely, those further from the perpendicular line to the environmental function’s average line are less stable, exerting a more significant impact on interaction. The study highlighted Shokoufa as a cultivar with higher average WSY and recognized its stability due to its proximity to the ACE line. In contrast, Paya exhibited the most significant distance from the ACE line, indicating weak stability compared to other cultivars (Figure 3B).
Figure 3 (A) Polygon generated through the GGE biplot method to identify optimal cultivars for each environment, and (B) Ranking of cultivars based on average white sugar yield and stability
Three factors, each with an eigenvalue greater than one, were identified, collectively capturing 87.21% of the total variance in the data. The first factor, with an eigenvalue of 5.50, accounted for 50.45% of the total variance. This factor positively influenced SC, WSC, ECS, and WSY, while exerting a negative influence on Na+, K+, and MS (Table 8). The second factor, with an eigenvalue of 2.19, explained 19.62% of the data variance and exhibited high and positive coefficients for RY, SY, and WSY (Table 8). The third factor, with an eigenvalue of 1.88, accounted for 17.13% of the data variance, displaying a high positive factor coefficient for N and high negative factor coefficients for ALC.
The cultivars’ MTSI was computed using quantitative and qualitative factor scores. In Figure 4, cultivars are arranged by MTSI value, with the highest positioned at the center and the lowest at the outermost circle. Cultivars selected based on the MTSI values at 20% selection intensity are denoted by red dots. In this regard, Perfekta and Shokoufa were identified as stable based on all studied characteristics. The cultivars are placed in the outermost circuit to the center of the figure based on the highest to lowest value of the MTSI, respectively. Paya recorded the lowest stability index score, indicating poor stability in different environmental conditions.
Table 8 Factor analysis using principal component analysis: eigenvalues, factor coefficients, relative and cumulative variance, and varimax rotation.
Figure 4 Ranking of cultivars in ascending order based on the multitrait stability index