Identifying Adaptable Varieties of Sorghum (Sorghum bicolor L) in Tidal Swamplands and Sandy Soils by MGIDI and GGE Biplots

2.1 Experimental sites

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.

The experimental site's soil has very low levels of exchangeable K, Na, Ca, and Mg. With a pH range of 3.62 to 3.8, the swampland area's soils were likewise highly acidic. Base saturation was extremely low, whereas cation exchange capacity was extremely high. Organic-C values ranged from moderate to extremely high. While accessible P and exchangeable K, Na, Ca, and Mg were at extremely low levels, total N was at a moderate level.

Rainfall in tidal swamplands ranges from 184.9 cm to 302 cm during the wet season, and from 77.8 cm to 416.5 cm during the dry season; in sandy soil, it ranges from 28.4 to 317 cm during the dry season. The weather in the trial sites appears to be approaching the start of the wet season at the end of the dry season.

2.2 Plant material

This study used 12 varieties of sorghum. 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 primary genetic sources of the twelve tested varieties are Numbu and Kawali varieties. Super 1-2, Suri 3-4, and Soper are the result of Numbu introduction and selection; Soper 7-9 is the result of a cross between Kawali and indigenous varieties; and Bioguma is a result of Numbu mutant breeding. For MGIDI-based multi-trait genotype selection and GGE biplot-based mega-environment stratification, the founder-dominated pedigree structure is quite advantageous. More than 70% of the genetic base of Indonesia's released cultivars comes from Numbu and Kawali.

2.3 Experimental design and observation

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. The plot size was 5x4 cm with planting distant between row 0.6 m and within row 0.25 m. 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. Irrigation by watering the plants with a hose for 4-5 hours during the early growth and seed filling. Fungicides with the active ingredients difenokonazol and azoksistrobin were used to control fungal disease, whereas insecticide with the active ingredient karbofuran was used to control pests.

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 2). 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 Data analysis

2.4.1 Analysis of variance

Multivariate Analysis of Variance for all traits according to the following model:

Where Y_ijkt is the observed t-th traits at k-th block under the i-th environment of the j-th variety, μ_t is the grand mean of the t-th trait, βk 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, Vj is the j-th variety effect, (EV)_ij is the interaction of the variety and the environment, and ϵ_ijkt is the experimental error and k-th block. The 1xp vector $e_{\mathit{ijk}}^{\prime }$ =(ϵ_ijk1, ϵ_ijk2, ϵ_ijk3,… ϵ_ijkp.) is assumed to be multivariate normal with mean = 0 and positive definite covarianc matrix ∑. 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. Let denote the two ways tables in matrices form as V = (V_ij)_vxp and EV = (EV_ij)_evxp, for variety means or variety-environment combination means in rows and traits in columns, respectively. The rows of the two matrices are then rescaled so that all columns have values 0-100 as follows.^40,43

for the column of V. The column of EV rescaled in the same way. Where ${\mathit{max}}_{\mathit{nj}}$ and ${\mathit{min}}_{\mathit{nj}}$ are the new maximum and minimum values of traits j in column of V or EV after rescaling, respectively; ${\mathit{max}}_{\mathit{oj}}$ and ${\mathit{min}}_{\mathit{oj}}$ are the original maximum and minimum value of the trait j in the i-th variety or variety-environment combination. The values of ${\mathit{max}}_{\mathit{nj}}$ and ${\mathit{min}}_{\mathit{nj}}$ determined based on whether we expect the highest value and the lowest value in the “ideotype”. If we expect that the “ideotype” has the highest value for the traits then we set, ${\mathit{max}}_{\mathit{nj}}$ = 100 and ${\mathit{min}}_{\mathit{nj}}$ = 0; otherwise, ${\mathit{max}}_{\mathit{nj}}$ = 0 and ${\mathit{min}}_{\mathit{nj}}$ = 100.

2.4.2 Factor analysis

The V^* or EV^* = i.e., the rescaled V and EV respectively 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 the two matrices (V* and EV*) is according to the following model:

Where X is a 1xp vector of a row of V* or EV*, μ is the 1xp vector of the standardized mean, L is a pxf matrix of factorial loadings, f is a px1 vector of common factors, and ϵ is a px1 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 rVij or rVEij 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 is a vxf matrix with factorial scores, X is a vxp scaled matrix (V* or EV*), and A is a pxf matrix of canonical loading. R is a pxp 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 retained.

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

The MGIDI_i for the i-th treatment (variety or variety-environment combination), is defined as the Euclidean distance between the scores of the i-th treatment and the ideal type, and computed as follows.⁴⁰

Where γij 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 the retained factors, respectively; and γj 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 4.3.3.⁶⁰

2.4.4 GGE Biplot

The mean yield of variety i in environment j according to model (1) is:

If we delete E _i from Y _ij, then the environmental-centered data matrix M with the ij-th element:

Where ${\xi }_{\mathit{ik}}^{\ast }$ = ${\lambda }_k^a{\xi }_{\mathit{ik}}$ and ${\eta }_{\mathit{jk}}^{\ast }$ = ${\lambda }_{\mathit{jk}}^{1-a}{\eta }_{\mathit{jk}}$ ; are the PC score for variety i and environment j, respectively; ${\lambda }_k\mathit{\text{is}}$ the singular value of Principal Component (PC) k, and a is the partitioning factor i.e, a = 0 for environment focused partitioning and a = 1 for genotype-focused partioning. Environment-focused singular value partitioning was applied to evaluate the discriminating ability and representativeness of test environments, while genotype-focused partitioning was used for genotype evaluation and mega-environment delineation. In R code, a = 1 is coded as SVP = 1 and a = 0 is coded as SVP = 2.

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 connecting 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 or worst and at which environments ( Figure 2a and Figure 3a). 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 or the worst 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 unfavourable to any environment and exhibit low phenotypic performance responsiveness.

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 2b and Figure 3b). 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 Figure 2c and Figure 3c. Varieties are ranked by their mean phenotypic performance and stability, as indicated by their closeness to the “ideal variety”.

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 2b and 3b). The environment is then ranked based on its discriminativeness and representativeness ( Figures 2f and 3f). Relationship among environment ( Figures 2e and 3e) identify redundant environment, detect mega-environment and optimize trial network.

3.1 Analysis of variance

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 < 0.01), 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.

3.2 Factor analysis

Two two-way tables were extracted from the MANOVA: V = (V_ij)_vxp, i.,e., the rows are varieties and the columns are the traits, and EV = (EV_(ij)t)_(ev)xp, i.e., the rows are the variety-environment combinations and the columns are the 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 Selection based on MGIDI

3.3.1 Selected varieties

Figure 1. a. Selected varieties based on MGIDI; b. Strengths and weaknesses of selected varieties; c. Selected genotype – environment combination; d. Strengths and weaknesses of all genotype – environment combinations.

Figure 1a 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 1a. The score for MDIGI on variety averaged across environment and in each environment are presented in Table 6.

Figure 1. a. Selected varieties based on MGIDI; b. Strengths and weaknesses of selected varieties; c. Selected genotype – environment combination; d. Strengths and weaknesses of all genotype – environment combinations.

Figure 2. GGE biplot on grain yield: a. which – won- where, b. mean and stability, c. ranking genotype, d. discriminativeness and representativeness, e. relationship among environments, and f. ranking of environment.

Figure 3. GGE biplot on forage yield: a. which – won- where, b. mean and stability, c. ranking genotype, d. discriminativeness and representativeness, e. relationship among environments, and f. ranking of environment.

3.3.2 Selected variety-environment combinations

Figure 1c 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. Most 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 7 presents the result of the selection.

3.4 The strengths and weaknesses view

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 1b and Figure 1d, 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 1b. 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 1d illustrates the strengths and weaknesses of selected variety-environment combinations. Unlike Figure 1b, Figure 1d 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.

3.5 Adaptability and stability

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. The mean of varieties across environments of the two traits and their confidence intervals is presented in Table 8.

Table 9’s variance components for grain and forage yield revealed a significant G-E interaction for grain yield and a low one for forage yield. This suggests that the application of GGE biplot and MGIDI analysis on grain yield is warranted, while the analysis on forage yield, the result will provide broadly adaptive varieties.

3.5.1 Grain yield

The GGE biplot on grin yield are dislayed in Figure 2. The “Which-won-where view” of the biplot on the grain yield (GY) and its polygon is displayed in Figure 2a. 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 or the lowest phenotypic performance (mean grain yield) varieties were the varieties at the vertices of the polygon. There are five varieties at the polygon’s vertices, i.e., V3, V7, V8, V11 and V12. These varieties are candidates for the best adaptable varieties. 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 2b 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. Additionally, a contrast comparison test ( Table 10) showed that V7 differs significantly from the average grain yield of other varieties. 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 2c. 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 grain yield 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 analysed in Figure 2d. 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 2f). The center of the concentric circles in Figure 2f 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 3a 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 become the candidates for the best varieties in the environment. Variety V11 is the 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 3b) showed that among the three varieties in mega-environment 1, V3 has a phenotypic performance (mean forage yield) below the average, while varieties V4 and V9 are above the average, with almost similar phenotypic performance. In contrast comparison test ( Table 11), V4 and V9 were not statistically different in environments E1, E2, and E6, whereas V3 and V4 were considerably different in environments E2 and E6, with the exception of environment E1. This result may explain why, although V9 is not at the vertex of the polygon. It has greater mean forage yield than V3, and has the same mean forage yield as V4. In genotype rank ( Figure 3c), 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 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 3d analyses the discriminativeness and representativeness of all tested environments. Figure 3f 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).