Integrating Multivariate and Univariate Statistical Models to Investigate Genotype–Environment Interaction of Advanced Fragrant Rice Genotypes under Rainfed Condition

Specialty fragrant rice is sold at a premium price in both local and international trade because of its superior grain qualities. In this research, 40 advanced fragrant rice accessions were evaluated in different environments. The primary objective was to identify genotypes with high grain yield and high stability using multivariate (GGE biplot) and univariate analysis (regression slope, deviation from regression, Shukla’s stability variance, Wricke’s ecovalence, and Kang’s stability statistic). The field experiment trials were laid in a randomized complete block design in three replications. The analysis of variance showed highly significant differences among genotypes, locations, seasons, and the interactions between genotype, locations, and seasons. The environment significantly explained about 43.32% (37.01 and 6.31% for locations and seasons) of the total sum of squares. Based on average ranking generated from multivariate and univariate stability measured, rice accessions were classified into three major categories, viz., genotypes having high trait performance, and high stability as category 1. The second category consists of genotypes that exhibit high mean performance but low stability, while the third category includes genotypes with high stability but low trait performance. Our results showed that breeding for yield performance was possible, and the identified genotypes could be recommended for commercial cultivation.


Introduction
Rice (Oryza sativa L.) is the most widely consumed staple food for over 3.5 billion people, especially in Asia, where average consumption is more than 80 kg per person per year [1]. Therefore, challenges arise due to the need to fulfill the remarkable demand for rice as conditioned by population increase across the globe. The major problems hindering rice production are grain quality, pests, diseases, and weather extremes [2][3][4]. For grain quality, the aromatic trait is one of the qualities used in rice classification. The chemical compound present in the plants resulting in fragrance provides a premium price in the international market. Fragrance or aromatic rice has the highest price globally, accounting for 15-18% of the rice trade [5]. Fluctuations in prices of agricultural commodities affect the world rice market trade. However, the price of fragrant rice remains unchanged. Instead, there is a continuous increase in the price of aromatic rice globally. Aromatic rice is valued at over USD 1050 per metric ton (t), while non-aromatic rice is priced at USD 440-580/t on the world trade market [5]. Generally, three main factors are identified in fragrant rice, viz., ing genotypes with similar performance evaluated under rainfed conditions. Biplots or PCA is a comprehensively used graphical display of interaction patterns for visualizing inter-relationships between genotypes, environments, and GEI to identify stable genotype(s) across environments or genotypes that are well adapted to particular environments. The recent and widely used biplot models are GGE biplots (genotype-plus-genotype-byenvironment) and AMMI biplot (additive main effects and multiplicative interaction). Yan et al. [13] proposed using GGE biplots based on a standardized or singular-value environment-centered decomposition. The biplot displays both genotype (G) and genotype by environment (G × E), which are the main source of variation relevant to genotype evaluation [13]. Several researchers have reported the use of GGE biplot analysis to identify the mega environment, evaluate genotype ranking, and determine the discriminative power and representativeness among tested environments [8]. Therefore, this study was conducted to evaluate G × E's effect on advanced fragrance rice genotypes and to identify rice genotypes with high stability based on yield performance.

Planting Material, Environments, and Cultural Practices
Thirty-eight genotypes of BC 2 F 2 generation from our previous research on introgression of BADH2 fragrance gene from Basmati 370 to the genetic background of high-yielding MR269 were used in this study [13]. The thirty-eight planting materials and the parents (Basmati 370 and MR269) were subjected to multi-environmental field trials. The field trials were conducted repeatedly across two locations in two cropping seasons in Peninsular Malaysia (2018-2019). The locations represent major granary areas with different agronomic and environmental conditions such as management practices, water regulations, and varying temperatures. Details of the environmental conditions are presented in Table 1. The field experiment was laid out in a randomized complete block design (RCBD) in three replications at each location. The plot size was 40 × 16 m 2 with a subplot unit of 1.5 m 2 for the respective genotype in each replication following Oladosu et al. [8]. In this research, the land was mechanically plowed following the local farmer's normal cultural practices in the study locations. Pest and disease control were carried out when the need arose. Thiamethoxam (640-700 mL/ha), a commonly used pesticide, was used in controlling bugs on the rice field. The optimal transplanting date conformed to the farmer's schedule at each location. The experiment was fully irrigated, and the water level was maintained from 7 to 12 cm until two weeks before harvesting throughout the trials to control weeds. Regular hand weeding was conducted when the need arose, while selective herbicide halosulfuron methyl was applied at a concentration of 1.5 L per hectare to control broadleaf weeds. Fertilizers were applied following the Malaysian Agricultural Research and Development Institute (MARDI) recommendation. Phosphorus (in the form of triple superphosphate) and Potassium (applied in the form of Murate of potash) fertilizers were applied at 15 days after transplant (DAS) at the rate of 57 and 42 kg per hectare, respectively, while NPK fertilizer was applied at 15, 55, and 75 DAS at the rate of 140, 107, and 50 kg per hectare, respectively. Nitrogen was applied as urea fertilizer at 30 DAS at 80 kg/ha, 55 DAS at 12 kg/ha, and 75 DAS at 20 kg/ha. At each location, data on grain yield in tonne per hectare was estimated from the weight of threshed grains from all panicles in 1 m 2 for each genotype from each replication excluding border rows following the International Rice Research Institute (IRRI) standard evaluation system (SES) [14].

Statistical Analysis
The morphological trait was subjected to analysis of variance (ANOVA) to determine phenotypic variations among the genotypes, locations, seasons, genotype by location, genotype by season, and genotype by location by season (genotype by environment) using SAS version 9.4. The genotypes were treated as fixed variables, while the environments were considered random variables. An additional statistical analysis was carried out if there was a significant interaction between the environment and the genotype to determine the stability level among the 40 genotypes across environments. The G × E SAS code developed by Dia and Wehner [15] was used for stability analysis. The G × E SAS output consists of ready-to-use input files in R-package for multivariate analysis and univariate stability results. The univariate stability parameter measure includes corrected means by least squares (M), regression coefficient (bi), deviation from regression (S 2 d ), Wricke's ecovalence (W 2 i ), Shukla's stability variance (σ i 2 ), and Kang's stability statistic (YS i ). Simple correlation coefficients were determined using Spearman's rank (a simplified version of R statistical software) developed by the R Core Team [16]. The Graphical user interface (GUI) package of R studio was used for GGE biplots, consisting of two concepts, the biplot concept [17] and the GGE concept [13]. The GGE biplots are a graphical picture to illustrate G × E interaction and genotype ranking based on mean and stability. The graph generated is based on megaenvironment evaluation (which-won-where pattern), Genotype evaluation (mean versus stability), and tested environment raking (discriminative versus representative). The GGE biplots were constructed using the first and second principal components (PC1 and PC2) that were derived by subjecting environment-centered means grain yield to singularvalue decomposition. The options used for data analysis were environment centering (Centering = 2), no standardization (Scale = 0) and no transformation (Transform = 0). The biplot was based on environment-focused singular-value partitioning (SVP = 2), which is suitable for picturing the relationships among the genotypes and locations.

Combined Analysis of Variance for Grain Yield
Combined analysis of variance used to describe the main effect and quantify the interactions among and within the source of variations is presented in Table 2. The mean square of locations, seasons, genotypes, genotypes by seasons (G × S), genotypes by locations (G × L), and genotypes by locations by seasons (G × L × S) showed highly significant differences (p ≤ 0.01) in yield per hectare. Highly significant differences for locations, seasons, and genotypes are conceivably due to changes in environmental conditions and genotype characteristics, which vary from one environment to another (i.e., combination locations × seasons). The partitioning of the percentage of genotype by environment interaction (% of GE) estimated from the total sum of square in Table 2 explains the variation percentage. The environment significantly explained about 43.32% (37.01 and 6.31% for locations and seasons, respectively) of the total sum of squares. However, variance components partitioning for the environment revealed that both unpredictable (seasons) and predictable (locations) components were important sources of variation. As Dehghani et al. [18] reported, when the genotype by environment interaction resulted from predictable variation factors, breeders can either develop broadly adapted genotypes that perform well under a wide range of conditions or select genotypes for specific environments. Nevertheless, when genotype by environment interaction is due to unpredictable factors, the development of relatively stable genotype performance under a wide range of environmental conditions is required. In this study, a remarkable variation explained by locations indicated that tested environments were diverse, with large differences among environmental effects causing the most variation for yield per hectare among the rice genotypes. As indicated by Kang and Pham [19], GE interactions minimize genotype effectiveness by limiting yield performance. However, to better understand GE interaction, Becker and Leon [20] revealed that yield-stability assessment across different locations and seasons could increase both heritability and repeatability of studied traits. As Oladosu et al. [7] reported, the analysis of variance lacks a detailed explanation of the GEI. Hence, supplementary statistics analysis such as multivariate and univariate are more resourceful in describing and understanding the GEI. Oladosu et al. [7] stated that estimation of stability and adaptability are the major factors for evaluating genotypes over a wide range of environments. As reported by Yan et al. [13], two types of G × E interactions in a multi-local yield trial constitute a combination of non-crossover and crossover interaction. Non-crossover indicates constant yield performance among the evaluated genotypes in diverse environments, while crossover shows the relative change in genotype ranking across the environments. The important effect of GE interaction establishes the fact that genotypes responded differently to different locations or environments which indicates the need for genotype evaluation in multiple environments. Similarly, this interaction also reveals the problems encountered by plant breeders during the selection of an ideal genotype for commercial cultivation prior to its release. Hence, the partitioning of environmental variance components into the season by location (unpredictable) and location (predictable) showed the significance of the source of variations.

Multivariate Analysis as Explain by GGE Biplot Graph
In the absence of GEI, crop cultivation in any part of the world regardless of the environment should perform equally, thereby having a universal result. Similarly, in the absence of biasness, replications become irrelevant [8]. Hence, one replication at any trial would be sufficient in any location [21]. However, in the presence of GEI, plant breeders/agronomists repeatedly evaluate advanced breeding lines in a diverse array of locations and seasons. As Haldane [22] reported, GEI is essential in a condition where a cultivar performs differently in a diverse environment. Therefore, plant breeders evaluate advanced breeding lines in different environments to explore the impact of GEI to accurately and efficiently measure the selected lines' performance before releasing them as commercial varieties [13]. As reported by Yan et al. [17], genotype main effect (G) plus genotype by environment interaction (GE) are the two major significant sources of variation in the evaluation of cultivar in multilocation yield trials. The biplot is perfectly and specially used for three main components, viz., (i) mega-environment analysis or which-won-where pattern identification based on the correlation between genetic (genotype) and environment, (ii) genotype evaluation based on their stability and mean performance across the environment, and (iii) test environment evaluation based on their representativeness and discriminating ability. The "bi" in biplot refers to displaying two distinct things, e.g., genotypes and environments on the same graph. It is a two-dimensional representation matrix that does not refer to the fact that the graph has two axes. First, the data was centered, followed by partitioning the singular value into genotype and environment scores for each of the principal components (PC1 and PC2), followed by plotting the PC1 scores against the PC2 scores to generate a biplot. The large PC1 score represents high-yielding ability while the small PC2 score represents stability. The first two principal components (PC1 and PC2) of the GGE explained 82.95% of the sum of squares with PC1 = 67.90% and PC2 = 15.35% for yield per hectare of the GGE sum of squares using a standardized environment model.

Which-Won-Where vs. Mega Environment View GGE Biplot Graph
The polygon view of the GGE biplot can be employed as a useful method for visualizing the mode of interaction between genotypes and environments to confirm the absence or existence of crossover interaction, which is useful in assessing the presence of different mega-environments [23]. The conception of the "which-won-where" pattern in multilocation yield trials is important for studying the presence of different mega-environments with a target location [24]. Figure 1 represents a polygon view of 40 rice accessions evaluated in four different environments in this study. In this biplot, a polygon was constructed, joining the vertex genotypes with straight lines with the remaining genotypes encapsulated within the polygon. The straight lines that originated from the center of the biplot perpendicularly to the polygon denote a putative environment in which the two genotypes at the two sides of the polygon perform equally [8]. The perpendicular line runs from the biplot center divides the biplot into sectors, with each sector having its winning genotype. Theoretically, the winning cultivar is located at the vertex where two sides of the polygon join, whose perpendicular lines form the sector's borderline ( Figure 1). Yan et al. [13] also reported that the genotype at the vertex of each sector had the highest yield in the environment that falls within that particular sector. Oladosu et al. [8] reported that genotypes situated inside the polygon closer to the origin are insensitive to environmental variations [8]. If all environment markers fall into one sector, this indicates that a single genotype performs best in all environments. However, suppose that the environment markers fell into different sectors. In that case, it indicates that different genotypes won in different environments, indicating the different mega-environment, which is an essential property of the GGE biplot that was rendered by the biplot's inner product property [23]. Contrarily, the genotype located at the vertex of sectors with no environment performed poorly in all tested environments. In this study, the GGE biplot constructed based on 40 rice accessions tested in four environments was divided into seven clockwise fan-shaped sectors for yield per hectare. Given this information, G1 and G6 are the highest yielding and have the highest stability performance in TKM, MDO, and MDM, while genotype G21 is the best in the TKO environment for yield per hectare.

Mean Versus Stability Views of GGE Biplot and Ideal Genotype Comparison
The average-environment coordination (AEC) or average-environment axis (AEA) view of the GGE biplot is used for genotype ranking based on average means performance and their stabilities ( Figure 2). This graph is comprised of two lines, the AEC abscissa (vertical line) and the AEC ordinate (horizontal line). The AEC abscissa is the single arrowed line that passes through the hypothetical average environment and through the biplot origin defined by the average scores of PC1 and PC2 of all environments, denoted by the small circle at the tip of the arrowhead ( Figure 2). The arrowhead direction on the AEA abscissa points towards higher mean values for yield performances. In this study, the highest and lowest yield per hectare was obtained in G1 and G32, respectively. The second line in the figure measures stability. The line, which is the AEC ordinate, perpendicular to the AEC abscissa that passes through the biplot center, signifies the genotypes' stability. Genotype vectors farther from the AEC denote higher variability or instability in either direction. Hence, the shorter the distance or projection from AEA, the less variable or more stable the genotype performance among the tested environments, and vice versa. Therefore, G15 is the most stable genotype while G21 is the most unstable among the tested genotypes, (Figure 2). For an extensive selection, the ideal genotypes should typically have both high mean and stability. In this biplot, genotypes G1, G6, and G15 can be described as ideal due to relatively short vectors which are nearer to the AEC. Another reason for the idealness of the AEC is its proximity to the small circle. Generally, yield in the genotypes located on the left side of the line is less than the average mean, whereas genotypes positioned on the right side performed better than the average mean. The genotype with the highest yielding performance but low stability is G1, whereas G15, which was highly stable, had a low yield. The assessment for yield performance is primarily founded on two concepts which are mean and stability; thus, breeders utilize the information obtain from performance assessment to choose genotypes with optimal

Mean Versus Stability Views of GGE Biplot and Ideal Genotype Comparison
The average-environment coordination (AEC) or average-environment axis (AEA) view of the GGE biplot is used for genotype ranking based on average means performance and their stabilities (Figure 2). This graph is comprised of two lines, the AEC abscissa (vertical line) and the AEC ordinate (horizontal line). The AEC abscissa is the single arrowed line that passes through the hypothetical average environment and through the biplot origin defined by the average scores of PC1 and PC2 of all environments, denoted by the small circle at the tip of the arrowhead (Figure 2). The arrowhead direction on the AEA abscissa points towards higher mean values for yield performances. In this study, the highest and lowest yield per hectare was obtained in G1 and G32, respectively. The second line in the figure measures stability. The line, which is the AEC ordinate, perpendicular to the AEC abscissa that passes through the biplot center, signifies the genotypes' stability. Genotype vectors farther from the AEC denote higher variability or instability in either direction. Hence, the shorter the distance or projection from AEA, the less variable or more stable the genotype performance among the tested environments, and vice versa. Therefore, G15 is the most stable genotype while G21 is the most unstable among the tested genotypes, (Figure 2). For an extensive selection, the ideal genotypes should typically have both high mean and stability. In this biplot, genotypes G1, G6, and G15 can be described as ideal due to relatively short vectors which are nearer to the AEC. Another reason for the idealness of the AEC is its proximity to the small circle. Generally, yield in the genotypes located on the left side of the line is less than the average mean, whereas genotypes positioned on the right side performed better than the average mean. The genotype with the highest yielding performance but low stability is G1, whereas G15, which was highly stable, had a low yield. The assessment for yield performance is primarily founded on two concepts which are mean and stability; thus, breeders utilize the information obtain from performance assessment to choose genotypes with optimal adaptation to particular environments [13]. Genotype G1 had the highest yielding performance in environment MDM, G6 was highly adapted to TKM, while G21 was best suited to TKO. Figure 3 presents the ranking of genotypes relative to an ideal genotype view with concentric circles. The ideal genotype (i.e., high mean and the most stable) is used as a standard for genotype assessment [23]. Therefore, concentric circles were drawn where the ideal genotype was theoretically located at the center to help visualize the distance between the ideal genotype and each genotype. Since no genotype marker falls within the center of the concentric circle, genotype markers that fall next to the innermost circles are then considered. Thus, G1 and G15 can be considered ideal genotypes for yield per hectare. adaptation to particular environments [13]. Genotype G1 had the highest yielding performance in environment MDM, G6 was highly adapted to TKM, while G21 was best suited to TKO. Figure 3 presents the ranking of genotypes relative to an ideal genotype view with concentric circles. The ideal genotype (i.e., high mean and the most stable) is used as a standard for genotype assessment [23]. Therefore, concentric circles were drawn where the ideal genotype was theoretically located at the center to help visualize the distance between the ideal genotype and each genotype. Since no genotype marker falls within the center of the concentric circle, genotype markers that fall next to the innermost circles are then considered. Thus, G1 and G15 can be considered ideal genotypes for yield per hectare.

Discriminative vs. Representative View of GGE Biplot (Relationship among Test Environments)
The most essential breeding strategy for the effective selection of superior genotypes is the identification of ideal test sites. Representativeness and discriminative power of all environments are the two characteristics of an ideal test environment [21]. The discriminative power of an environment or location refers to its ability to differentiate genotypes while the representativeness refers to the ability of a tested environment to represent other tested environments [21]. In this study, Figure 4 shows the representativeness view vs. discriminative power of the GGE biplot analysis. The cosine of the angle between the average-environment axis and environment vector approximates the correlation coefficient between the genotype means across the environment and the genotype values in that environment [17]. Because the average-environment coordinate (AEC) abscissa is the average-environment axis (AEA), test environments that form small angles with the AEA can better represent the environments compared to those forming large angles. The small circle represents the mean of the environment while the arrow adjacent to the circle signifies the direction of the AEA. The length of the vector estimates the standard deviation (the discriminating ability) of the studied environment. The vector length of a study location provides a measurement of its magnitude (discriminating power) to differentiate genotypes in the environments. Following the above, the short vector locations such as TKM and MDO for yield per hectare can be considered as independent research locations and may be treated as unique locations. Meanwhile, locations with long vectors i.e., MDM and TKO were more influential in discriminating among the rice accessions. Environments having long vectors and small angles with the AEC abscissa are ideal in the selection of superior genotypes. Environment MDM had a long vector and formed a relatively small angle with the AEC abscissa; thus, it was the most representative and discriminating test location. Based on the representativeness and discriminating ability of the study environment, Yan et al. [17] classified the environment into three major types. Type 1 environments are characterized by short vectors, providing little or no infor-

Discriminative vs. Representative View of GGE Biplot (Relationship among Test Environments)
The most essential breeding strategy for the effective selection of superior genotypes is the identification of ideal test sites. Representativeness and discriminative power of all environments are the two characteristics of an ideal test environment [21]. The discriminative power of an environment or location refers to its ability to differentiate genotypes while the representativeness refers to the ability of a tested environment to represent other tested environments [21]. In this study, Figure 4 shows the representativeness view vs. discriminative power of the GGE biplot analysis. The cosine of the angle between the average-environment axis and environment vector approximates the correlation coefficient between the genotype means across the environment and the genotype values in that environment [17]. Because the average-environment coordinate (AEC) abscissa is the average-environment axis (AEA), test environments that form small angles with the AEA can better represent the environments compared to those forming large angles. The small circle represents the mean of the environment while the arrow adjacent to the circle signifies the direction of the AEA. The length of the vector estimates the standard deviation (the discriminating ability) of the studied environment. The vector length of a study location provides a measurement of its magnitude (discriminating power) to differentiate genotypes in the environments. Following the above, the short vector locations such as TKM and MDO for yield per hectare can be considered as independent research locations and may be treated as unique locations. Meanwhile, locations with long vectors i.e., MDM and TKO were more influential in discriminating among the rice accessions. Environments having long vectors and small angles with the AEC abscissa are ideal in the selection of superior genotypes. Environment MDM had a long vector and formed a relatively small angle with the AEC abscissa; thus, it was the most representative and discriminating test location. Based on the representativeness and discriminating ability of the study environment, Yan et al. [17] classified the environment into three major types. Type 1 environments are characterized by short vectors, providing little or no information on the genotypes; thus, they are inappropriate as test environments. Type 2 environments are characterized by long vectors, forming smaller angles with the AEC abscissa, and are useful for selecting superior genotypes. Type 3 environments with long vectors form large angles with the AEC abscissa; therefore, they are inappropriate for the selection of superior genotypes. Despite their limitation, Type 3 environments can be useful in culling unstable genotypes. According to this classification, TKM and MDO for yield per hectare were Type 1 environments (short vectors). They offered little or no information on the genotypes and are inappropriate for use as test environments. This implies that some of these environments were redundant and may not be utilized to save the costs of field trials without loss of information. The GGE biplot identified environment MDM for yield per hectare as the ideal environments (Type 2 environments). The environment would be suitable for selecting superior genotypes due to their remarkable discriminating ability and representativeness. Type 3 environments include TKO for yield per hectare, which should not be used in selecting superior genotypes; however, they may be valuable in identifying unstable genotypes. In general, Figure 5 revealed that environment MDM is the ideal environment. This study implies that the type of genotype studied determined the most appropriate location for multilocation assessment based on the test locations' discriminating power and representativeness. bility 2021, 13, x FOR PEER REVIEW 10 of 15 mation on the genotypes; thus, they are inappropriate as test environments. Type 2 environments are characterized by long vectors, forming smaller angles with the AEC abscissa, and are useful for selecting superior genotypes. Type 3 environments with long vectors form large angles with the AEC abscissa; therefore, they are inappropriate for the selection of superior genotypes. Despite their limitation, Type 3 environments can be useful in culling unstable genotypes. According to this classification, TKM and MDO for yield per hectare were Type 1 environments (short vectors). They offered little or no information on the genotypes and are inappropriate for use as test environments. This implies that some of these environments were redundant and may not be utilized to save the costs of field trials without loss of information. The GGE biplot identified environment MDM for yield per hectare as the ideal environments (Type 2 environments). The environment would be suitable for selecting superior genotypes due to their remarkable discriminating ability and representativeness. Type 3 environments include TKO for yield per hectare, which should not be used in selecting superior genotypes; however, they may be valuable in identifying unstable genotypes. In general, Figure 5 revealed that environment MDM is the ideal environment. This study implies that the type of genotype studied determined the most appropriate location for multilocation assessment based on the test locations' discriminating power and representativeness.

Genotype Means Comparison
Grain yield in rice fluctuates significantly with respect to changes in environmental conditions. Therefore, a genotype with a high yield and reasonable stability is desired to develop a new variety to minimize the risk of yield losses in harsh environments and unfavorable low land conditions. In this study, genotype × environment interaction was partitioned, which revealed highly significant differences for genotypes by locations by seasons interaction. These differences are essential in determining GEI. The pooled means across the 4 environments are presented in Table 3. Genotypes G1, G22, and G39 recorded the highest yield at 6.89, 6.03, and 6.16 tons per hectares, respectively, while genotypes G40, G18, and G34 are the bottom-yielding genotypes (Table 3). Yield in rice is a complex trait that is determined by the contribution from yield components traits such as filled grains per panicle, number of effective tillers, and yield per hill/plant [10]. To better comprehend GEI, Becker, and Leon [20] established that genotype evaluation for stability across different seasons and locations could increase both repeatability and heritability of studied traits. Similarly, the significance of GEI indicated changes in genotype ranking or genotype expression across different locations due to the reaction to changes in environmental conditions. Hence, the results from trials conducted in Malaysia indicated that genetic factors control grain yield; however, it is subject to the effect of environmental conditions.

Univariate Stability Methods
Higher linear component value than non-linear value suggested the probability of prediction for yield performance over the environments. Hence, linear regression coefficient (bi) and non-linear deviation from regression (S 2 d) of G × E interactions were considered for phenotypic stability analysis [25,26]. According to Eberhart and Russell [25], a stable genotype across a wide range of environments will be one with a high mean and bi

Genotype Means Comparison
Grain yield in rice fluctuates significantly with respect to changes in environmental conditions. Therefore, a genotype with a high yield and reasonable stability is desired to develop a new variety to minimize the risk of yield losses in harsh environments and unfavorable low land conditions. In this study, genotype × environment interaction was partitioned, which revealed highly significant differences for genotypes by locations by seasons interaction. These differences are essential in determining GEI. The pooled means across the 4 environments are presented in Table 3. Genotypes G1, G22, and G39 recorded the highest yield at 6.89, 6.03, and 6.16 tons per hectares, respectively, while genotypes G40, G18, and G34 are the bottom-yielding genotypes (Table 3). Yield in rice is a complex trait that is determined by the contribution from yield components traits such as filled grains per panicle, number of effective tillers, and yield per hill/plant [10]. To better comprehend GEI, Becker, and Leon [20] established that genotype evaluation for stability across different seasons and locations could increase both repeatability and heritability of studied traits. Similarly, the significance of GEI indicated changes in genotype ranking or genotype expression across different locations due to the reaction to changes in environmental conditions. Hence, the results from trials conducted in Malaysia indicated that genetic factors control grain yield; however, it is subject to the effect of environmental conditions.

Univariate Stability Methods
Higher linear component value than non-linear value suggested the probability of prediction for yield performance over the environments. Hence, linear regression coefficient (bi) and non-linear deviation from regression (S 2 d ) of G × E interactions were considered for phenotypic stability analysis [25,26]. According to Eberhart and Russell [25], a stable genotype across a wide range of environments will be one with a high mean and bi of genotypes approximating unity (bi = 1). When the bi is associated with low mean, then the genotypes are described as poorly adapted to all environments. A bi value greater than unity describes a genotype with higher sensitivity to environmental changes and greater adaptation to specific high-yielding environments. In this study, the bi ranged from −0.51 to 2.80. Genotype G16 is considered the most stable due to a bi value closer to unity, followed by G10. Contrarily, genotype G17 was considered the lowest in rank (Table 3). Eberhart and Russell [25] emphasized the use of deviation from regression as a measure of stability, whereas linear regression could be treated as a measure of varietal response to environments. Based on deviation from the regression (S 2 d ) model, a genotype is considered to be stable when S 2 d is as small as possible (i.e., S 2 d = 0). Genotype G12 is the most stable, followed by G18, G5, and G27, while G28 followed by G17 are highly unstable genotypes (Table 3).
According to Shukla [27] and Wricke [28], a genotype with low W 2 i and σ i 2 is considered stable. Shukla's stability variance (σ i 2 ) is strictly a measure of stability, rather than performance while Wricke's ecovalence (W 2 i ) defines the contribution of each genotype to the G × E interaction sum of squares. According to these two concepts, genotypes with the smallest stability variance are considered the most stable. In this study, the genotype with the least stability variance σ i 2 and W 2 i is ranked highest and considered the most stable. Genotype G5 is considered stable based on σ i 2 and W 2 i concepts followed by G23 and 12, while G1 is considered highly unstable, followed by G14 and G28 (Table 3). According to Becker and Leon [20], the range of variables indicates the level of interaction in response to genotypes across environments. Genotypes with the lowest interaction variance are less responsive to the environment, while larger variances indicate environmental influences. However, it was very difficult to find the same pattern of response to validate this proposition, thus, making selection difficult when considering different stability analyses on genotypes due to a shift in genotype ranking. Although different stability parameters are indicative of low, intermediate, or high stability, the stability statistics alone are not useful and informative in genotype selection except if integrated with yield performances. Hence, efforts have been made to combine stability parameters with yield performance in a single selection criterion [19]. Kang [29] developed a yield-stability statistic (YS i ) as selection criteria once the G × E interaction is significant and demonstrates the significance of emphasizing stability performance for yield selection. Hence, genotypes with a YS i value greater than the mean are considered stable. Based on this concept, all the evaluated genotypes show relatively stable performance except for G12, G18, G29, G34, and G40 (Table 3).

Rank Correlations among the Univariate Stability Models
Spearman's correlation was conducted between the genotype means and the stability parameters that produce stability ranking, as presented in Table 4. The univariate stability parameter measure includes corrected means by least squares (M), regression coefficient (bi), deviation from regression (S 2 d ), Wricke's ecovalence (W 2 i ), Shukla's stability variance (σ i 2 ), and Kang's stability statistic (YS i ). The analysis was used for the identification of agreement among the stability parameters. In this study, YS i was positively and highly significantly correlated with mean, while a negative and highly significant correlation with mean was recorded for all other parameters except for bi where the non-significant correlation was observed (Table 4). Mekbib [30] reported that statistical stability parameters provide information that cannot be quantified from the trait's means. The stability ranking given by the stability parameters of S 2 d was highly correlated with σ i 2 and W 2 i at 0.83. This indicates an agreement in the ranking of stability from one method to the other for the genotypes. These two stability parameters reflect only the genotypes' response to the environment and the G × E interaction, but not the genotypes' performance themselves. However, a non-significant correlation was observed between bi and other stability parameters. Table 4. Spearman rank correlations among univariate stability parameters and trait mean (M) for 40 rice genotypes tested in 4 locations.