AMMI an GGE biplot analysis of grain yield for drought-tolerant maize hybrid selection in Inner Mongolia

Due to the ongoing global warming, maize production worldwide is expected to be heavily inflicted by droughts. The grain yield of maize hybrids is an important factor in evaluating their suitability and stability. In this study, we utilized the AMMI model and GGE biplot to analyze grain yield of 20 hybrids from the three tested environments in Inner Mongolia in 2018 and 2019, aiming at selecting drought-tolerant maize hybrids. AMMI variance analysis revealed highly significant difference on main effects for genotype, environment, and their interaction. Furthermore, G11 (DK159) and G15 (JKY3308) exhibited favorable productivity and stability across all three test environments. Moreover, G10 (LH1) emerged as the most stable hybrid according to the AMMI analysis and the GGE biplot. Bayannur demonstrated the highest identification ability among the three tested sites. Our study provides accurate identification for drought-resilient maize hybrids in different rain-fed regions. These findings can contribute to the selection of appropriate hybrids that exhibit productivity, stability, and adaptability in drought-prone conditions.


Plant materials and experimental site
A total of 20 hybrids, including 19 tested hybrids and one control hybrid (XY335), were used in the droughttolerant maize hybrid selection trials conducted in Inner Mongolia.The experiment took place over two planting seasons in 2018 and 2019.The hybrids were planted at three different locations: Hangjinhouqi Experimental Station of Bayannur Academy of Agriculture and Animal Husbandry Sciences, Bayannur (107.15°,40.88°, sandy soil with a pH of 7.4, bulk density of 1,584 kg.m −3 , organic carbon content of 0.17% m/m, and organic matter content of 13.15 g/kg); Maize Research Center of Inner Mongolia Agricultural University, Salaqi (110.52°,40.56°, sandy soil with a pH of 7.2, bulk density of 1,578 kg.m −3 , organic carbon content of 0.23% m/m, and organic matter content of 14.17 g/kg); and Chengzi Experimental Station of Chifeng Academy of Agriculture Sciences, Chifeng (118.93°,42.29°, sandy soil with a pH of 7.1, bulk density of 1,586 kg.m −3 , organic carbon content of 0.21% m/m, and organic matter content of 13.63 g/kg).This constituted a 2-year, three-location trial, the pedigree information of 20 tested hybrids and the rainfalls of three locations are shown in Tables 1 and 2. Collection of plant material, must fully comply with relevant institutional, national, and international guidelines and legislation.

Experimental design
The experiment was conducted using a randomized complete block design.The 20 tested hybrids underwent two replications of drought-tolerant trials.The experimental plots were arranged in four rows, with a row spacing of 60 cm and a row length of 5 m.The planting density was determined to be 75,000 plants per hectare.Four protective rows were included around the experimental area.The plants were only watered before sowing, and no additional irrigation was provided throughout the entire growth period.During harvest, the two middle rows were selected, and the first and last plants from each row were removed for yield measurement.
Table 1.Pedigree of 20 maize hybrids used in this study.

Statistical analysis
In this experiment, the AMMI model was employed to analyze the interaction between genotypes and environments, effectively capturing the interaction components of each genotype or environment.The AMMI model for analyzing yield data in maize hybrids is represented by the following equation 10,24 : where Y ge represents the yield of genotype (G) in the environment (E); μ is thegrand mean; α g is the genotype average deviation; λ n is the eigenvalue of the n th principal component (PCA) axis, N is the total number of PCA, γ gn and η en are the genotype and environmental PCA scores for the n th PCA axis, and θ ge is the residual.The AMMI stability value (ASV) was calculated according to Purchase, Hatting and Van Deventer 18,25 as follows: where SS is the sum of squares of the IPCAs and IPCA1 and IPCA2 are the first and second interaction principal component axes, respectively.Means of the genotypes were used for GGE biplot analysis.
GGE biplot: The grain yield data collected from three experimental sites were organized into a three-column data table of genotype-environment-yield, where each value represents the average yield of the corresponding genotype in the respective environment, known as the phenotype value (Yger).The linear statistical model for GGE biplot analysis is presented as follows 16,26 : where Y ger represents the yield value of genotype g in environment e for the rth replication; μ is the overall mean; β e represents the main effect of environment e; ρge is the residual of genotype g in environment e; εger represents the overall error; λn is the singular value of the nth principal component; γgn is the genotype g's score for the nth eigenvector; δge is the environment e's score for the nth eigenvector.The parameters λnγgn and γnδen are defined as the GGE principal component scores for genotype g and environment e, respectively, also known as IPCAn or PCn.The data analysis was performed using Microsoft Excel 365 and Genstat 23 software on the Windows operating system.

AMMI analysis of grain yield for drought-resilient maize hybrid selection
The average grain yield differences of the experimental hybrids varied widely, ranging from 8.46 to 15.94 ton per hectare.Table 3 displays the two-year grain yield of the 20 maize hybrids across three environments in Inner Mongolia.AMMI variance analysis revealed highly significant (P < 0.001) main effects for genotype, environment, and their interaction.The interaction between genotypes and environments were decomposed into interaction principal component axes 1 (IPCA1), interaction principal component axes 2 (IPCA2) and interaction principal component axes 3 (IPCA3) (Table 4).IPCA1 and IPCA2 were found to be highly significant, explaining 59.51% and 37.34% of the total variation of G × E interaction (Fig. 1a), respectively.G11 (DK159) exhibited the highest average yield across all tested sites (Fig. 1b and Table 3) and also demonstrated broad adaptability, as indicated by its proximity to the origin (Fig. 1a).In contrast, G16 and G13 were highly influenced by environmental interaction (Fig. 1a).All of the environments were positioned far from the origin, indicating strong interaction forces with genotype, and the angles between the tested environments suggested distinctiveness in selecting drought-tolerant hybrids (Fig. 1a).

GGE biplot analysis of G × E interaction
Which won where model A "which-won-where" polygon view was presented, illustrating the relationship between genotypes and environments (Fig. 2).The biplot analysis accounted for 76.84% of the total observed variation, with 50.02% explained by the first principal component (PC1), and 26.82% by the second principal component (PC2).Genotypes G11, G9, G3, G18, G17 and G16 were situated at the corners of the "which-won-where" polygon, indicating their exceptional performance in specific environments (Yan and Ticker.2006).Among these genotypes, G11 exhibited the highest grain yield in four out of six tested environments: Ba18, Ba19, Sa18, and Sa19.The CK (G9) outperformed in terms of yield in the Cf18 and Cf19 environments(Fig.2).

Environmental vector view
The "Environmental vector view" function plot of GGE biplot was utilized to analyze the hybrids.The angles between the Ba and Cf environments were greater than 90 degrees, suggesting a negative correlation and opposite ranking of hybrids between these two environments (Fig. 3).On the other hand, the angles between all other environments were less than 90 degrees, indicating a positive correlation among them.The length of the environmental line represents the discrimination ability of the test sites for the hybrids.Among the test environments, Ba18 had the strongest the discrimination ability (Table S1).The mega-environment function plot revealed that Cf formed a distinct type, while Ba and Sa belonged to another type (Fig. 2 and Supplemental Fig. 1).

Ranking biplot mean vs stability view
In the positive direction, the biplot indicates that G11 has the closest projection onto the Average Environment Coordinate (AEC) axis, suggesting G11 exhibited significantly higher yield compared to the other hybrids.
The stability analysis of each hybrid shows that G10 have the shortest perpendicular distance to the AEC axis, indicating the highest stability in yield.Conversely, G16 and G3 have the longest vertical distance, indicating the lowest stability in grain yield (Fig. 4).

Best hybrid and best environment by GGE biplot
Based on the best genotype comparison biplot, the top-performing hybrid across the three tested environments was G10, followed by G15 and G11, which consistently displayed above-average grain yield in all environments (Fig. 5a).Other desirable genotypes, including G9 and G19, which were located on the second concentric circles, respectively.The AEC view comparing environments relative to an ideal environment is presents.It indicates that environments Sa18 and Sa19 were closer to the center of the concentric circle (Fig. 5b).Compared to the other two locations, Salaqi was identified as the ideal environment (Fig. 5b).

Discussion
The significant G × E effects observed in recent study indicate that the evaluated genotypes do not exhibit consistent performance across different test environments [27][28][29][30] .This highlights the importance of investigating the nature and magnitude of G × E, which cannot be adequately captured by a standard analysis of variance 18,31 .The AMMI model, which combines PCA and analysis of variance, allows for a comprehensive analysis of genotype and environment interactions and facilitates the identification of interaction patterns 32 .IPCA1 of our AMMI analysis contributed 59.51% to the total variation across the tested environments, which implies genotypes and environments have strong interaction 33 .IPCA1 and IPCA2 accounted for 96.85% of the interaction sum of squares.As a result, IPCA3 did not achieve significantly difference (Table 4).AMMI with the first two multiplicative terms was deemed to be the best predictive model in a previous study 24 .On the other hand, the GGE biplot visually presents data in a graph form, providing an intuitive visualization of the specific characteristics of varieties 7,27 .It complements the AMMI model by offering a graphical representation that facilitates the interpretation of G × E interactions 28,30 .
The AMMI stability values, such as the ASI and ASV, provide additional information on the variation among genotypes 20 .The genotypes with ASV values close to zero are considered stable 34 .In our study, G15 (JKY3308) exhibited an ASV of 3.906, suggesting it may possess genes for adaptability to various agroclimatic conditions   3 and tested sites abbreviations in Fig. 1, the same below.(Table S2).However, it is important to note that while G15 ranked as one of the top stable hybrids based on the GGE biplot (Fig. 5), it may not be the most stable hybrid.Therefore, there might be some differences in the results obtained from the AMMI and GGE biplot analyses.To obtain a more reliable analysis, breeders often combine the insights gained from both approaches 7,35,36 .
The selection of appropriate test locations plays a crucial role in crop breeding programs 37,38 .The effectiveness and accuracy of variety selection are directly influenced by the identification ability of the test environments 39 .In this study, we focused on evaluating three rain-fed regions in Inner Mongolia, each characterized by distinct geographical and ecological conditions, using the AMMI model and GGE biplot (Fig. 1a).An environment with long vector and limited angle offers a richer and more accurate representation 38 .Our findings revealed that the test site in Bayannur demonstrated a stronger overall identification ability throughout the two-year period compared to the other two environments (Fig. 3, Tables 2 and S1).This can be attributed to factors such as lower average annual rainfall and significant day-night temperature differences in Bayannur.In future studies, we intend to incorporate additional ecological test environments and rainproof chambers to further enhance our drought tolerant hybrids identification programs.This will allow us to accurately evaluate the stability and adaptability of hybrids or elite inbred lines.By expanding the scope of our evaluations, we aim to improve the precision and reliability of hybrid selection in maize breeding.

Conclusion
Our comprehensive analysis has revealed insights into the performance of maize in the drought-tolerant hybrid selection trials by AMMI model and GGE biplot.AMMI variance analysis revealed highly significant difference on main effects for genotype and environment.G11 (DK159) and G15 (JKY3308) exhibited highest productivity and stability among 20 hybrids.G10 (LH1) was identified as the most stable hybrid across the three test environments.Three test sites belong to distinctive rain-fed types and Bayannur test site exhibited the highest identification ability among them.The integration of the AMMI model and GGE biplot has provided a robust and comprehensive approach for evaluating and identification of drought-resilient maize hybrids in droughtprone regions of China or similar environments.

Figure 1 .
Figure 1.AMMI biplot showing relationship among test environments and genotypes based on grain yield.(a)Vector view of the AMMI biplot.The genotype scores were presented by green crosses and environments by blue pluses with vectors connecting the environment with the origin.Dotted vertical and horizontal lines indicate points where the PC1 and PC2 axes had respective values of zero.See codes of genotypes (G1 to G20) in Table 3. Ba18, Bayannur 2018; Ba19, Bayannur 2019; Sa18, Salaqi 2018; Sa19, Salaqi 2019; Cf18, Chifeng 2018; Cf19, Chifeng 2019.(b) AMMI1 biplot for additive effects vs IPCA1.The genotype scores were presented by green crosses and environments by blue pluses.Dotted vertical and horizontal lines indicate points where the IPCA1 and mean grain yield axes had respective values of zero.

Figure 2 .
Figure 2. The "which-won-where" view of the GGE biplot showing which genotypes performed best in which environment.Dotted vertical and horizontal lines indicate points where the PC1 and PC2 axes had respective values of zero.Vertices of the polygon indicate superior genotypes in each sector.See the code of genotype in Table3and tested sites abbreviations in Fig.1, the same below.

Figure 4 .
Figure 4. Mean vs stability view of ranking biplot.The straight line with arrows is the environmental average axis.The perpendicular length from the average axis to the genotypes indicates the stability of each genotype.A longer perpendicular length signifies a higher level of instability for that genotype.

Figure 5 .
Figure 5. Best hybrid and best environment by GGE biplot.(a) Best hybrid view of GGE biplot comparing hybrids relative to an ideal hybrid.(b) Best environment view of GGE biplot comparing environments relative to an ideal environment.

Table 2 .
Mean monthly and total rainfall (mm) during the study period in 2018 and 2019 at three field sites.

Table 3 .
Mean grain yield (t ha -1 ) of 20 maize hybrids in three environments under rain-fed condition in Inner Mongolia.

Table 4 .
Variance analysis by AMMI model.