Stability of finger millet ( Eleusine c oracana L.) yield using additive main effects and multiplicative interaction analysis

tons ha -1 (Kako-01). AMMI stability value ranged from 0.23 (genotype Bako-09) to 1.55 (Boneya), and yield stability index ranged from 3 (genotype Bako-09) to 19 (Bareda). AMMI1 and AMMI2 biplots explained 87.28% and 82.63% of the treatment sum of squares, respectively. In the present study, because of its high yield (4.27 tons ha -1 ) and stability across test environments, genotype Bako-09 would be recommended for widespread cultivation.


Introduction
In the mid-and lowlands of Ethiopia, where rainfall is erratic, finger millet (Eleusine coracana L.) is an important cereal crop. The grain of finger millet is used to make porridge, kita (a thin flatbread), and traditional beverages like areke and tela, and the straw is used as livestock feed. The grain contains 7.4% protein, 74.0% carbohydrate, 3.2% fiber, and 2.6% ash. It is rich in calcium, phosphorus, iron, and tryptophan, cysteine, and methionine amino acids (NRC, 1996). Finger millet is the sixth most valuable cereal crop in area coverage and production, after tef (Eragrostis tef), maize, sorghum, wheat, and barley. It covers 456,172 hectares (4.46% of the cereal-growing area) and produces 1,017,059 tons (4.01% of cereal grain production) of grain per year (CSA, 2017). The average yield of finger millet is low (2.23 tons ha-1), partly due to variety instability and low yield potential.
Yield is a complex polygenic trait usually influenced by genotype, environment, and genotype by environment (GE) interaction.
Because the same gene can have different effects in different environments (Yan et al., 2017), a genotype's performance can vary from one environment to the other. Among the various statistical methods used in stability analysis, additive main effects and multiplicative interaction (AMMI) have been widely used to identify genotypes with wide and specific adaptations across various environments (Zobel et al., 1988). Unlike traditional analysis of variance, which divides sources of variation into effects due to genotypes, environments, and GE interaction. AMMI model combines analysis of variance for additive main effects of genotypes and environments with principal component analysis for multiplicative component, or nonadditive, GE interaction. Furthermore, AMMI biplots make it simple to visualize multienvironment data and identify genotypes with wide and specific adaptations (Zobel et al., 1988;Gauch and Zobel, 1997). This study used AMMI analysis to identify finger millet genotypes with high yield and wide adaption.

Materials and Methods
Field experiments were conducted on-farm in Boricha and Dore Bafano districts and on-station in Halaba district, Southern region, Ethiopia, from early May to October, during the main cropping seasons of 2018 and 2019. Boricha is located at 6 o 56'04"N and 38 o 20'88"E, with an elevation of 1907 m above sea level, and Dore Bafano is at 7 o 04'68"N and 38 o 22'18"E, with an elevation of 1717 m above sea level, while Halaba is located at 07 o 18'44"N and 37 o 06'50"E, with an elevation of 1763 m above sea level. The annual average rainfall in Boricha, Dore Bafano, and Halaba is 915, 997, and 912 mm, respectively. For Boricha, Dore Bafano, and Halaba, the average cropping season rainfall was 482, 602, and 480 mm in 2018 and 1112, 853, and 798 mm in 2019. Boricha, Dore Bafano, and Halaba have annual average temperatures of 20.10, 20.09, and 21.74 o C, respectively, with silt loam, sandy clay loam, and loam as their respective soils.
A randomized complete block design with four replications was used to grow eleven finger millet genotypes (ten improved and one local check). Each plot consisted of four rows with 2.5 m row length. The space between rows, plots, and replications was 40, 80, and 120 cm, respectively. The seed was drilled at a rate of 10 kg ha -1 . Plots were given 65 kg ha -1 of nitrogen in the form of urea and NPS, as well as 38 kg ha -1 of P2O5 in the form of NPS at planting. Manual weeding was also used to control weeds.
The AMMI analysis was based on the following AMMI model: Y ge = μ + α g + β e + ∑ λ n ζ gn η en + θ ge N n=1 Where, Y ge is the yield of genotype (g); in the environment (e); μ is the grand mean; α g is the genotype mean deviation; β e is the environment mean deviation; λ n is the eigenvalue of the PC axis, n; ζ gn η en are the genotype and environment PC axis scores for the PC axis, n; N is the number of PC axes retained in the model; and θ ge is the residual (Zobel et al., 1988). Moreover, Genstat version 18.1 (VSN International, 2015) was used for AMMI analysis.
In order to compensate for differences between PC1 and PC2 in explaining the GE sum of squares, the AMMI stability value (ASV) was calculated as: PC1 sum of squares PC2 sum of squares (PC1 score)] 2 + (PC2 score) 2 Where, the smaller ASV scores suggest a less interactive environment and a more stable genotype (Purchase et al., 2000).
Yield stability index (YSI) was calculated as:

YSI= RASV + RY
Where, RASV is the rank of the AMMI stability value (ASV), and RY is the rank of a genotype's mean yield across environments, with 1 being the highest yield and the lowest AMMI stability value. Low YSI values are linked to high yield and genotype stability (Bose et al., 2014).

Results and Discussion
According to the AMMI analysis (Table 1), the effects of genotypes, environments, and genotype by environment interaction were statistically significant (p < 0.01) and contributed 25.79, 48.85, and 25.36% to the treatment sum of squares, respectively. The more significant contribution of environments (48.85%) to the treatment sum of squares (G + E+ GE) would mean substantial differences across test environments, causing different genotypes to perform differently. Even though, in standard multi-environment yield trials, the environment accounts for 80% of the variation in treatments, while genotype and GE each account for 10% (Gauch and Zobel, 1997), these contributions can differ from trial to trial. For example, the contribution of the environment to the treatment sum of squares has been reported to be 2.21% (Bose et al., 2014), 81% (Rashidi et al., 2013), 75% (Zobel et al., 1988;Hongyu et al., 2014), and 78% (Ali et al., 2018) in different trials.
GE interaction would imply that genotypes differed in their responses to changing environments, which could have been attributed to variations in rainfall and soil types among the test environments, which are often one of the major contributors to GE interaction in crops (Ananda et al., 2009). The genotype and interaction components of the treatment sum of squares are used together for genotype and testenvironment evaluations, but the main effect of the environment is irrelevant for these purposes (Gauch and Zobel, 1997;Gauch et al., 2008). Thus, the variation in G plus GE explained 96.37/188.42, or 51.15% of the treatment sum of squares.
Since it includes the majority of the treatment degrees of freedom, GE interaction contributes the most uncontrolled variation (noise) to the treatment sum of squares compared to the genotype and environment effects, even though the latter still include some noise (Gauch and Zobel, 1997;Anandan et al., 2009). Such noise must be removed because it obscures true winners in test environments by reducing yield estimation accuracy (Gauch and Zobel, 1997;Hongyu et al., 2014;Neisse et al., 2018). Thus, the GE interaction was divided into noise sum of squares and actual structure (Gauch and Zobel, Indeed, the relevant variation for detecting megaenvironments is around 10 to 40% of the treatment variation in a yield trial (Gauch and Zobel, 1997).
Only PC1 and PC2 of the four principal components (PCs) generated by AMMI analysis were statistically significant (p<0.01) ( Table 1), implying that PC3 and PC4 could be considered as noise (Zobel et al., 1988;Crossa et al., 1990;Ebdon and Gauch, 2002). PC1, PC2, PC3, and PC4 contributed 49. 85, 32.78, 9.27, and 7.22%, respectively, to the variation in GE interaction. Indeed, the first two PCs usually account for most of the sum of squares of GE interaction in multienvironment yield trials (Tadesse et al., 2018). Furthermore, PC1 and PC2 together explained 82.63% of the GE sum of squares, which is adequate for cross-validation of the yield variation explained by GE interaction because a model must explain at least 70% of the variation to be considered fairly reliable (Neisse et al., 2018). Genotypes showed considerable variations in yield (tons ha -1 ), PCs, ASV, and YSI ( Genotypes G3, G4, G5, and G10 were the most unstable due to their high PC1 scores, while G1, G4, G7, G8, and G11 were the most unstable due to their high PC2 scores. Since PC1 contributes more to the GE interaction sum of squares than PC2, the AMMI stability value (ASV) is used to compensate for the discrepancies between PC1 and PC2 in measuring stability so that genotypes with low ASV values are the most stable (Purchase et al., 2000). According to their ASV values, genotypes G2 (0.23) and G9 (0.25) were the most durable, while G3 (1.01) and G4 (1.55) were the most unstable. In addition, E2 (1.38) and E6 (0.65) were the most unstable and stable environments, respectively. However, when selecting genotypes, stability should be considered along with yield capacity since the most stable genotypes do not necessarily produce the best yield (Hongyu et al., 2014). Genotype G9, for example, had a low ASV score, but its mean yield (3.21 tons ha -1 ) was less than the average yield (3.61 tons ha -1 ). Thus, the yield stability index (YSI), which combines yield and ASV ranks, has been suggested for selecting high yield and stability simultaneously (Bose et al., 2014;Tadesse et al., 2018). Accordingly, genotypes G2 and G6 were the most desirable because they combined high mean yield with a high level of stability.  (Zobel et al., 1988;Crossa et al., 1990). The abscissa (x-axis) in the AMMI1 biplot depicts the main effects of genotypes and environments, while the ordinate (y-axis) depicts genotype and environment interaction, or PC1 scores (Zobel et al., 1988;Crossa et al., 1990;Gauch et al., 2008;Roostaei et al., 2014;Neisse et al., 2018). The horizontal line passing through the PC1 score of zero in this biplot represents the interaction score of zero, while the middle vertical line represents the average yield. Thus, genotypes G1, G5, G4, G6, G2 and G8, and environments E5, E4 and E3 had above average yield, while genotypes G7, G10, G9, G11 and G3, and environments E2, E6 and E1 had below average yield. High PC1 scores (positive or negative) of genotypes and environments suggest a high level of interaction (Zobel et al., 1988;Crossa et al., 1990;Anandan et al., 2009;Rashidi et al., 2013;Roostaei et al., 2014). As a result, genotypes G9, G1, and G2 were less interactive in test environments, while environments E1 and E2 had a high level of interaction.
Genotypes or environments may have similar mean yield and/or interactions in the AMMI1 biplot (Crossa et al., 1990;Rashidi et al., 2013). Thus, except for variations in interactions, genotypes G2 and G8 had similar mean yield, and genotypes G1 and G2 had similar interactions except for the mean yield difference. Similarly, environments E3, E5, and E6 had low and similar interactions, with the exception of differences in mean yield. On the other hand, genotypes and environments situated at diagonal or opposite corners have different main effects and interactions (Ebdon and Gauch, 2002). For example, the yield performances and interactions of environments E1 and E4 were quite different.
The genotypes farthest from the biplot's origin have a high level of interaction (positive or negative) and show particular adaptation to specific environments (Chimonyo et al., 2014;Mafouasson et al., 2018). For example, genotype G6, which had a high mean yield and a large PC1 score, was specifically adapted to environments E3 and 4, which also had a high mean yield and large PC1 score. The additive part (main effects) of the AMMI1 biplot for any genotypeenvironment combination is equal to the genotype mean plus the environment mean minus the grand mean, and the multiplicative part (interaction effect) is the product of genotype and environment PC1 scores (Zobel et al., 1988;Crossa et al., 1990;Gauch and Zobel, 1997;Ebdon and Gauch, 2002 (Zobel et al., 1988;Crossa et al., 1990;Anandan et al., 2009;Rashidi et al., 2013). Thus, genotypes G3 and G11 were adapted to Boricha (E1 and E2) but not Dore Bafano (E3 and E4).
Int. J. Agril. Res. Innov. Tech. 13(1): 60-66, June 2023 The most desirable genotypes (e.g., G2) combine above-average yield with a near-zero PC1 scores (Rashidi et al., 2013). However, since high and low-performing genotypes are usually adapted to different environments, such high performance across environments (both favorable and unfavorable) is rare. On the other hand, the main effects and/or interactions of a location can differ greatly from year to year, making it less predictable (Ebdon and Gauch, 2002). Year-toyear variations in interaction lead to year-to-year changes in genotype rankings, making it difficult to recommend a specific variety to specific locations (Zobel et al., 1988;Ebdon and Gauch, 2002). In the present study, the substantial yearto-year variability in yield of Boricha and Halaba sites would make it difficult to predict the performance of these sites. Figure 1. AMMI1 biplot for yield (main effect) and PC1 of eleven finger millet genotypes and six environments; genotype (G) and environment (E) designations are presented in Table 2.
The abscissa represents PC1 scores, and the ordinate represents PC2 scores in the AMMI2 biplot (Figure 2), which explains 82.63% of the treatment sum of squares. Since the AMMI2 biplot provides information on GE but not G (Gauch et al., 2008), it can be used to distinguish genotypes with similar or different patterns of responses across environments, but it cannot be used to display the specific performance of genotypes across test environments (Gauch and Zobel, 1997;Anandan et al., 2009). The vector length from the origin (0, 0) in the AMMI2 biplot indicates the amount of interaction displayed by genotypes or environments, with genotypes and environments far from the biplot origin (positive or negative) being more interactive than those near the biplot center (Gauch et al., 2008;Anandan et al., 2009). Since genotypes G9 and G2 are close to the biplot origin, they are less interactive than genotypes G11 and G4, which are far from the center. Because of their short vector lengths, environments E4 and E6 were less interactive and discriminative among genotypes, while E1 and E2 were more discriminative.
The acute angle between the vectors of genotypes or environments indicates a positive relationship, the right angle indicates a negligible relationship, and the obtuse angle indicates a negative relationship (Ndhlela et al., 2014). Environments E1 and E2, E3 and E4, and E5 and E6 had similar effects on genotype performance and were most related because their vectors were at acute angles. Similarly, genotypes G3 and G5 had a similar relationship and were supposed to have a similar pattern of responses across the test environments, but this was not the case with genotypes G4 and G11. In the present study, because of its high yield (4.27 tons ha -1 ) and stability across test environments, genotype Bako-09 would be recommended for widespread cultivation.  Table 2.

Conclusion
The substantial contribution of environments to the treatment sum of squares would suggest the differences in test environments, causing different genotypes to perform differently. The significant contribution of PC1 and PC2 to the variation in GE interaction relative to PC3 and PC4 would show that PC3 and PC4 would be considered as noise.
Moreover, the more significant contribution of PC1 to the GE interaction sum of squares than PC2, suggested that AMMI stability value, which compensates for the discrepancies between PC1 and PC2 would be used to measure the stability of genotypes. However, the existence of stable genotypes with below average yield would suggest the use of the yield stability index, which combines both AMMI stability value and yield ranks to obtain highyielding and stable genotypes. Finally, the present study showed that besides identifying specific and widely adapted genotypes, AMMI biplots would be used to distinguish genotypes with similar or different patterns of responses across test environments.