The experiments were conducted from October 2022 to February 2023 (wet season) and from July to November 2024 (dry season) in tidal swamplands at Petak Batuah Village, Dadahup Sub-district, Kapuas Regency, and from August to December 2023 (dry season) in sandy soils at Sidodadi Village, Bukit Batu Sub-district, Palangka Raya City, Central Kalimantan Province, Indonesia.

This study used 12 varieties of sorghum ( Table 1). The Cereal Crop Instrument Standard Testing Centre (CCISTC) is the source of all seeds. Table 1 shows some of the main characteristics of these varieties. Other materials needed include soil conditioners such as dolomite and chicken manure. The inorganic fertilizers are Urea, NPK, SP-36, and KCl. Several insecticides were applied as required.

The experiment was conducted in tidal swamplands of type C ( Inceptisols) and sandy soils ( Entisols). Intensive tillage was practiced. After one week, two seeds were planted per planting hole, with 0.6 m between rows and a 0.25 m planting distance. A replanting operation was performed 7–14 days after planting. Thinning was conducted 30 days after planting, leaving a single plant per pot. Weeds were controlled manually, with hoeing 26 and 46 days after planting.

The trials were arranged in a randomized complete block design (RCBD) with two-factor treatments and three replications. The first factor was tested environments consisted of E1 = tidal swamplands applied with 500 kg ha ⁻¹ chicken manure in the wet season, E2 = tidal swamplands applied with 1000 kg ha ⁻¹ chicken manure in the wet season, E3 = tidal swamplands applied with 500 kg ha ⁻¹ chicken manure in the dry season, and E4 = tidal swamplands applied with 1000 kg ha ⁻¹ chicken manure in the dry season, E5 = sandy soils applied with 500 kg ha ⁻¹ chicken manure in the dry season, and E6 = sandy soils applied with 1000 kg ha ⁻¹ chicken manure in the dry season. The second factor was 12 varieties of sorghum ( Table 1). Each plot consisted of eight 5.0-m long rows and sixteen 4.0-m long rows. The utilized area was defined as the area occupied by the central row. The entire plot was applied with 1000 kg ha ⁻¹ of dolomite. The observed traits are given in Table 2.

2.4.1 Analysis of variance

Multivariate Analysis of Variance for all traits according to the following model: Y ijkt = μ t + β k + E i + V j + ( EV ) ij + ϵ ijkt [1]

Where Y ijkt is the observed t-th traits at k-th block under the i-th environment of the j-th variety, β k is the k-th block effect, i = 1, 2…e; j = 1, 2, 3 … v; k = 1, 2, 3; t = 1, 2 … p. E i is the i-th environmental effect, V j is the j-th variety effect, ( EV ) ij is the interaction of the variety and the environment, and ϵ ijkt is the experimental error at the t-th trait of the j-th variety planted at the experimental unit under the i-th environment and k-th block. Multivariate analysis of variance (MANOVA) was conducted for p traits based on model (1). Based on the MANOVA results, the means of the significant effects are extracted to construct two-way tables with variety means or a combination of variety-environment means in rows and traits in columns. The elements of the two-way tables are then rescaled so that all columns have values 0-100 as follows ^{31, 34} r V ij = max nj − min nj max oj − min 0 j x ( v ij - max oj ) + max nj [2]

Where max nj and min nj are the maximum and minimum values of traits j in V ij after rescaling, respectively; max 0 j and min 0 j are the original maximum and minimum value of the trait j, and v ij is the original value for the jth trait of the i-th variety, for traits with higher values, max nj = 100 and min 0 j = 0 ; conversely, if the lower values are desired, then max nj = 0 and min nj = 100.

2.4.2 Factor analysis

The V ^* = (rV _ij) _vxp , i.e., the rescaled V, are then subject to factor analysis to group variables based on their correlation. All variables within a particular group are expected to be highly correlated with one another but have relatively small correlations with variables in different groups.

The estimation of the factorial scores for each row in V ij is according to the following model: X = μ + L f + ϵ [3]

Where X is a px1 vector of a row of rV ij (the rescaled values of V ij ), μ is the px1 vector of the standardized mean, L is a px f matrix of factorial loadings, f is a px 1 vector of common factors, and ϵ is a px 1 vector of residuals. p and f are the number of traits and common factors retained. The initial loadings are computed considering only factors with eigenvalues of the correlation matrix of rV ij or rVE ij higher than 1. The varimax rotation criteria are used for the analytic rotation and estimation of final loadings. The scores are then obtained as follows. S = V ∗ ( A T R − 1 ) T [4]

S is a v x f matrix with factorial scores, V ^* is a v x p matrix with rescaling means, and A is a p x f matrix of canonical loading. R is a p x p correlation matrix between the traits, and f is the number of factors retained. Factors associated with the eigenvalue of the matrix greater than one are maintained.

2.4.3 Multitrait -Genotype-Ideotype-Distant Index (MGIDI)

The MGIDI _i for the i-th treatment, defined as the Euclidean distance between the scores of the i-th treatment and the ideal type, is computed as follows. MGIDI i = [ ∑ j = 1 f ( γ ij − γ j ) 2 ] 0.5 [5]

Where γ ij is the score of the i- th treatment in the j- th factor (i = 1, 2, …, t; j = 1, 2, …, f ), being t and f the number of treatments and factors, respectively; and γ j is the jth score of the ideotype or ideal treatment. The treatment with the lowest MGIDI is closer to the ideal treatment, presenting the desired values for all the p traits. The traits are prioritized by putting the following weights (number in the bracket in front of the traits): (0.4) PH, (0.6) LC, (0.4) INC, (0.4) INL, (0.7) SD, (0.7) LW, (0.7) LL, (0.6) PL, (0.5) (PDW), (1.0) LWW, (0.3) BRIX, (1.0) SWW, (1.0) GY. The analysis was performed using R software version 4.3.3. ⁵¹

2.4.4 GGE Biplot

The mean yield of variety i in environment j according to model (1) is: Y ij = μ + E i + V j + ( EV ) ij

If we delete E _i from Y _ij, then the environmental-centered data matrix M with the ij-th element m ij = Y ij ` − μ − V j can be subjected to singular value decomposition, i.e., m ij = ∑ k = 1 p ξ ik ∗ η jk ∗

Where ξ ik ∗ = λ k a ξ ik ; η jk ∗ = λ k 1 − a η jk , being λ _k the kth eigenvalue from the SVD (k = 1,2, …, p) with p ≤ min ( e , v ) ; a is the single value partition factor for the Principal Component (PC) k; ξ ik ∗ and η jk ∗ are the PC score for variety i and environment j, respectively.

A Genetic plus Genetic-Environment interaction (GGE) biplot was used to examine the stability and adaptability of the varieties. The biplot’s abscissa represents the first principal component (PC1), indicating the phenotypic performance of the varieties, while the ordinate represents the second principal component (PC2), indicating the stability of the varieties. The two components account for the variation in varieties and the interaction between varieties and environments. By joining the variety’s coordinates that were most distant from the origin, a polygon was created that can be used to determine which varieties were the best (won) and where ( Figure 5 and Figure 10). The biplot is divided into sectors by drawing a dotted line perpendicular to the polygon’s sides from the origin of the biplot. The sectors depict environments that are most comparable to one another. The varieties with the best phenotypic performance in environments within a sector were those found near the polygon’s vertices in the sector. A group of environments where the same variety performs the best is called a mega-environment. Varieties in a sector without allocated environments are considered unfavorable to any environment and exhibit low phenotypic performance responsiveness. Figure 1.

The average environmental point, with coordinates representing the average PC1 and PC2 scores of the environments, was initially defined to create the Average Environmental Coordination (AEC). The AEC’s X-axis is a line between the biplot’s origin and the average environmental point. Simultaneously, the Y-axis is the line that runs perpendicular to the AEC’s X-axis in the biplot’s origin. The ordinate shows the interactions between each variety and its environment, whilst the AEC abscissa shows the phenotypic performance of varieties in the average environment. The arrow in the AEC axis indicates the direction of ascending phenotypic performance. The projection of each variety on the X-axis of AEC measures the mean phenotypic performance across environments.

In contrast, the projection on the Y-axis measures the stability of the variety in tested environments ( Figure 6, Figure 11). The ascending direction is the arrow in the abscissa, and the varieties projected above the origin in the direction of the arrow in the abscissa are above the average of the mean phenotypic performance; the higher the ordinate of the variety in the AEC coordinate is, the less stable it is. The best (adaptable) variety is the highest phenotypic performance and stability variety. This imaginary “ideal variety,” i.e., the best variety, is marked as a small circle in Figures 7 and 12. Varieties are ranked by their mean phenotypic performance and stability, as indicated by their closeness to the “ideal variety” ( Figures 7 and 12).

The ideal variety is based on its performance in the AEC. However, one may need to determine a test environment representing the average environment. A line vector was constructed from the biplot’s origin to each environmental point to evaluate the environment’s representativeness and discriminating power. The length of the vector represents the discriminating ability of the environment, while the angle between the vector and the X-axis of AEC measures the representativeness of the environment. The longer the vector and the smaller the angle, the higher the discriminating ability and representativeness of the environment associated with the vector ( Figures 8 and 13). The environment is then ranked based on its discriminativeness and representativeness ( Figure 9 and Figure 14).

The multivariate analysis of variance ( Table 3) found that variety means across environment ( V) and variety-environment interaction ( VE) have significant effects on the vector of traits, based on the Pillai trace Test ( p < 0.0.01), indicating differences in the means of varieties across environments and such differences are affected by environment. The significant effect of variety-environment interaction means that the ranking of varieties within each environment is varied.

Two two-way tables were extracted from the MANOVA: V (V _jt) _vxp and EV (EV _(ij)t) _(ev)xp, where V _jt and EV _(ij)t are the variety and variety-environment combination, respectively, of the t traits. Factorial loading after varimax rotation and their cumulative variance obtained in factor analysis on the variety mean matrix (V) are presented in Table 4. In contrast, the variety-environment combinations matrix (EV) is presented in Table 5. In both tables, four factors associated with an eigenvalue greater than one are retained along with their cumulative variance. The bold-faced numbers (greater than 0.50 in absolute value) in each table are the dominant factor loading of the traits to the associated factor. Hence, for example, in Table 4, internode count (INC), panicle dry weight (PDW), stem wet weight (SWW), and grain yield (GY) are associated with factor 1(FA1). Similarly, plant height (PH), Internode count (INC), internode length (INL), leaf length (LL), and BRIX are associated with the factor (FA2). Factor 3 is associated with panicle length (PL),) and BRIX. Factor 4 is associated with leaf count (LC), stem diameter (SD), leaf width (LW), panicle dry weight (PDW), and Leaf wet weight (LWW). Similar interpretations can also be held for Table 5. The result of factor analysis will then be used to calculate MGIDI.

3.3.1 Selected varieties

Figure 1 shows the ranking of the MGIDI of varieties averaged across environments. The selected varieties based on the MGIDI are Kawali (V10) and Numbu (V8), as indicated by the red dots in Figure 1.

3.3.2 Selected variety-environment combinations

Figure 2 presents the ranking of variety-environment combinations based on MGIDI. The red dot at the outer circle is the selected environment-variety combination. They are E6-V10, E6-V5, E6-V8, E6-V7, E2-V7, E6-V9, E6-V6, E2-V8, E1-V4, and E1-V10, E6_V11, E2_V10, E2_V4, E6_V2, where E _iV _j denotes the j-th variety planted at the i-th environment. The majority of selected varieties are those applied in sandy soil with a high rate of organic fertilizer (E6). Only four varieties (V4, V7, V8, or V10) were selected for tidal swamplands in the rainy season, and they were either applied at a high or low rate of organic fertilizer (E1 and E2).

3.3.3 Selected varieties in each environment

The multivariate analysis of variance, as shown in Table 3, indicates that the interaction between variety and environment is significant. This interaction suggests that the ranking of varieties varies across different environments. Therefore, it is necessary to select varieties in each environment by the MGIDI. The selection procedure is similar to that of average varieties across all environments and variety-environment combinations. However, the result of the factor analysis and the graphs of the ranking are not presented here. Table 6 presents the result of the selection.

The strengths and weaknesses of all varieties and selected varieties-environment combinations, which are accounted for by the proportion of each factor to their calculated MGIDI, are presented in Figure 3 and Figure 4, respectively. Each factor has a specific color line, as indicated by the legend. The closer the variety or variety-environment combinations are to the external edge of the polygon, with a specific color representing a particular factor, the smaller the contribution of the factor to the MGIDI. The smaller the contribution of a factor to the MGIDI of a variety/variety-environment combination, the closer the traits associated with the factor to the “ideal type.” Since we defined “ideal type” as those varieties or variety-environment combinations with the highest values in all traits (as selection goals), it implies that the traits associated with the factor are high in the varieties or variety-environment combinations.

The strengths and weaknesses of all varieties are shown in Figure 3. We should focus attention on the selected varieties, i.e., V8 and V10. Variety V8 is closely related to FA1 and V10 is closely related to FA4. It implies that FA1 has a small contribution to the MGDI of V8, and hence traits like internode count (INC), panicle dry weight (PDW), stem wet weight (weight (SWW), and grain yield (GY), which are associated with FA1, have high values in V8. Similarly, V10 exhibits high values in traits related to FA4, including leaf count (LC), stem diameter (SD), panicle dry weight (PDW), and leaf wet weight (LWW).

Figure 4 illustrates the strengths and weaknesses of selected variety-environment combinations. Unlike Figure 3, Figure 4 presents only the selected variety-environment combinations for simplicity, given the high number of variety-environment combinations. Factor FA1 makes a small contribution to the MGIDI of E1-V10, E6-V10, and E6-V6, indicating that traits associated with this factor in that variety-environment combination are similar to those in the variety-environment idiotype. Therefore, traits such as plant height (PH), internode count (INC), Internode Length (INL), leaf Length (LL), and BRIX have high values in that variety-environment combination. With similar reasoning traits associated with FA2, such as leaf count (LC) and panicle dry weight (PDW), these values must be high in variety-environment combinations E6-V8, E6-V7, E2-V7, E6-V5, and E6-V11. Two economically valuable traits, grain yield (GY) and stem wet weight (SWW), contribute to biomass production associated with FA3. This factor has made a small contribution to the MGIDI of E6-V7, E2-V7, E6-V9, and E6-V8. Therefore, these varieties must possess high values for both traits. Finally, traits that are associated with FA4 must have high values in E1_V4, E1_V10, E2-V4, E6_V2 and E2_V8.

The adaptability and stability of each variety were studied, with valuable traits including grain yield and fresh forage yield (stems and leaves, expressed as wet weight). The GGE biplot on each of the two traits was used to study the adaptability and stability of varieties.

3.5.1 Grain yield

The “Which-won-where view” of the biplot on the grain yield (GY) and its polygon is displayed in Figure 5. Of the total GGE variation, the PC1 and PC2 contributed 52.44% and 33.61%, respectively. PC1 reflects the average performance (mean grain yield) of the varieties, while PC2 reflects the stability (variety-environment interaction) of the varieties/genotypes. Jointly, the two components account for 86.05% of the total genotype plus genotype × environment interaction. The polygon separated the biplot’s five sectors. The highest phenotypic performance (grain yield) variety was the variety at the vertex of the polygon. There are five varieties at the polygon’s vertices, i.e., V3, V7, V8, V11 and V12. These varieties are among the best. There are two mega-environments in the biplot. Mega-environment 1 consists of environments E1, E2, and E6 in one sector, with a variety at the vertex, V7, while mega-environment 2 consists of environments E3, E4, and E5, with a variety at the vertex, V8. Varieties V3, V11, and V12 were found in sectors with no allocated environment. Hence, they were less responsive and exhibited low phenotypic performance (in terms of grain yield) in all tested environments.

The mean and stability analysis depicted in Figure 6 shows that V7 has the highest mean in Mega-Environment 1, as it is the furthest left along the green AEC line. Note that the green AEC arrow points to the left; therefore, varieties further in that direction can be interpreted as having a higher mean performance (in grain yield). V8 is the second-highest performance, with similar reasoning. In terms of stability, which is reflected by the ordinates in AEC, V7, and V8 are moderately stable, although they are less stable than other varieties, such as V1, V2, and V10. The ranking of varieties based on their mean performance (in terms of grain yield) and stability is presented in Figure 7. The best varieties, which are the most adaptable, are those closest to the ideal variety (represented by the small circle near the arrow), an imaginary genotype or variety with the highest mean and stability. V7 is the most adaptable variety, followed by V8. Consequently, in mega-environment 1, i.e., tidal swamplands in rainy season applied with high rate (E2) or low rate organic fertilizer (E1), and in sandy soils applied with high rate organic fertilizer (E6), the adaptable variety is Soper 7 agritan (V7), while in tidal swampland at dry season applied with high rate (E4) or low rate organic fertilizer (E3) and in sandy soils applied with low rate of organic fertilizer (E5) the adaptable variety is Numbu (V8).

Since the “ideal variety” in the environmental average is only hypothetical, we may need to determine the phenotypic performance of the varieties in a particular tested environment that represents the average environment. For this purpose, we first determined the tested environment that was more discriminative and representative of the average environment—the discriminativeness and representativeness of all tested environments were analyzed in Figure 8. The highest line vector from the origin of the biplot to the environment “point” was the most discriminative environment. At the same time, the most representative is the line vector with the lowest angle to the average environment. The selected environments are ranked based on their discriminativeness and representativeness ( Figure 9). The center of the concentric circles in Figure 9 represents the ideal environment for selecting genotypes, i.e., the most discriminative and representative ones. The closer an environment is to this center, the better it ranks. Hence, E6 is the most discriminative and representative environment of the average environment. In other words, sandy soil applied with a high rate of organic fertilizer during the dry season (E6) is ideal for selecting broadly adaptive genotypes or varieties based on grain yield (GY).

3.5.2 Forage yield

Figure 10 depicts a biplot of sorghum varieties’ Forage yield (FY) and its polygon. PC1 and PC2 contributed 61.30% and 33.57%, respectively, and jointly accounted for 94.87% of the overall GGE variance. There are two mega-environments in the biplot. The first mega-environment is in the sector that contains E1, E3, and E5 tested environments, and the second mega-environment is in the sector that contains E2, E4, and E6 tested environments. We can define the first mega-environment as the environment applied with a low rate of organic fertilizer since all environments are those applied with a low rate of organic fertilizer (500 kg of chicken manure per hectare) in both types of land at both seasons.

For the same reason, we can define the second environment as the one applied with a high rate of organic fertilizer (1,000 kg of chicken manure per hectare). Varieties V3 and V4 are at the vertices of polygons within mega-environment one and, therefore, become suitable candidates for the best varieties in the environment. Variety V11 is the suitable candidate for the best varieties in mega-environment 2. Varieties V5, V6, and V7 were found in sectors with no environmental conditions, indicating that they are not responsive and exhibit low mean phenotypic performance in any tested environment.

The graph of mean and stability ( Figure 11) showed that among the three varieties in mega-environment 1, V3 has a phenotypic performance (forage yield) below the average, while varieties V4 and V9 are above the average, with almost similar phenotypic performance. In genotype rank ( Figure 12), V9 is closer to the “ideal variety” than V3 or V4 in this mega-environment. However, it is further from the ‘ideal variety’ than V11, V2, and V8, which are in mega-environment 2. Therefore, we can conclude that in mega-environment 1, i.e., the environment in tidal swampland applied with low (E1) or high rate (E2) organic fertilizer and in sandy soils applied with low rate of organic fertilizer, the adaptable varieties are variety Soper nine 9 agritan (V9); while in mega-environment 2, i.e. tidal swamplands and sandy soil applied with high rate organic fertilizer, variety Bioguma agritan (V11) are the most adaptive variety.

Figure 13 analyses the discriminativeness and representativeness of all tested environments. Figure 14 gives the rank of the selected environment. Using the same reasoning as in the GGE biplot on grain yield, the tested environment E2 is the most discriminative and representative environment compared to the average environment. Therefore, tidal swampland applied with a high rate of organic fertilizer during the rainy season (E2) is ideal for selecting broadly adaptive genotypes/varieties based on forage yield (FY).