Identification of stable chickpeas under dryland conditions by mixed models

Chickpea (Cicer arietinum L.) is one of the most important legume crops, mainly grown in tropical and subtropical climates. Evaluation of yield performance in crops under multienvironments is applied to verify the stability of cultivars. The aim of this study is to apply the analytical and experimental models to identify the high‐yielding and stable genotypes of chickpea under dryland conditions. Sixteen chickpea lines and two control cultivars were cultivated in randomized complete block design with three replications in four regions at three cropping seasons (2016–2019). Third type of biplot showed that G4, G15, G10, G9, and G18 were highly productive and widely stable. A selection index based on different weights of seed yield and WAASB stability indicated genotypes G7, G9, G15, G4, G16, G18, G12, and G5 were high yielding and stable. Data mining showed that high rainfall in winter can lead to high yield. Partial least squares regression (PLSR) analysis indicated that rainfall in autumn and spring and low temperature in all of the three seasons involved in genotype by environment interaction (GEI). Factorial regression (FR) also indicated that temperature during spring and winter plays an important role in GEI. In conclusion, based on all experimental approaches, G15, G16, and G5 were stable and high‐yielding genotypes. The PLSR biplot indicated G15 was the genotype that less affected by high temperature in three seasons and lack of rainfall in spring and autumn, it can be used in cultivar introduction processes for dryland cultivation.


| INTRODUCTION
Chickpea (Cicer arietinum L.) is one of the important legume crops, mainly grown in tropical and subtropical climates with 400 mm of annual rainfall (Farshadfar et al., 2013).In dryland conditions, particularly in dry spring, the seed yield of winter sowings is significantly higher than that of spring sowings for annual legume species (Sayar et al., 2013).
Evaluation of yield performance in crops under multienvironments is applied to verify the stability of cultivars (Acuña et al., 2008).Additionally, determining the extent of genotype by environment interaction (GEI) and stability of genotypes helps cultivar recommendation (Fikre et al., 2018).The desirable and superior genotypes, adaptable to the wider environmental variation, are characterized by the low value of GEI for important agronomic traits (Kizilgeci, 2018).The recommended varieties of crops would indicate stable performance under different environments, particularly in an area with a wide range of climatic conditions.Therefore, it is essential to develop cultivars with a high degree of adaptability to diverse environments and pedoclimatic conditions for a prosperous utilization of their inherent potential (Sharifi et al., 2021).
Statistical methods for analyzing GEI are classified into analytical and experimental approaches (van Eeuwijk et al., 1996).The "biological" or "analytical" approach focuses on the integration of climatically/agronomical variables, while the "experimental" or "empirical" approach refers to performance-based selection (Richards, 1982).The analytical and experimental approaches are considered as "predictive" and "postdictive" strategies, respectively.
The first approach is used for recommendation purposes, while the latter handles the repeatability of GEI (Basford & Cooper, 1998).
Stability of genotypes in different environments was evaluated by several empirical methods such as parametric and nonparametric univariate stability and multivariate analyses (additive main effects and multiplicative interaction [AMMI], genotype main effects and genotype by environment interaction [GGE] biplot, etc.).Recently, a new methodology based on restricted maximum likelihood (REML)/ best linear unbiased prediction (BLUP) provided a better and deeper understanding of the GEI (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019).Improving the predictive accuracy of random effects is the other reason for using BLUP (Smith et al., 2005).Olivoto, Lúcio, da Silva, Sari, and Diel (2019) proposed a stability index, namely, WAASB (weighted average of absolute scores based on singular value decomposition [SVD] of BLUP), which is the weighted average of absolute scores based on SVD of the matrix of BLUPs for the GEI effects obtained by linear mixed-effect model (LMM).In addition to WAASB, the superiority index introduced by Olivoto, Lúcio, da Silva, Sari, and Diel ( 2019) is called WAASBY (WAASB and grain yield), which enables weighting between mean performance and stability (MPE).These two indices combine the graphical tools of AMMI and the predictive accuracy of BLUP for stability analysis.
More IPCAs can be necessary to account for the variation.
Therefore, WAASB and WAASBY plots are used to identify the stable genotypes.All significant principal components were used to calculate the WAASB index.One of the most important advantages of the WAASB index is using a mixed-effect model in its calculation; thus, its prediction accuracy is higher than the fixed-effect modelsor even a random model.The second advantage of this procedure is using all significant principal component axes (IPCAs) in its calculation (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019).Some researchers used this methodology in the evaluation of seed yield stability in rice (Sharifi et al., 2021), lentil (Karimizadeh et al., 2021), forage (Santos & Marza, 2020), barley (Ahakpaz et al., 2021), and wheat (Verma & Singh, 2020).Mosaic plot is another graphical tool in multienvironment trials (METs), which established a link between the partitioning of the total sum of squares (TSS) of GEI obtained by SVD and the partitioning of this TSS provided by the ANOVA (Laffont et al., 2007).
In the analytical approach, individual environmental variables such as rainfall, temperature, and fertility are used to determine the factors responsible for GEI or stability/instability and explain GEI (Kang, 2020).This procedure significantly increases the reliability of predictions concerning cultivar performance.Partial least squares regression (PLSR) and factorial regression (FR) models, as analytical approaches, directly incorporate a large number of environmental and genotypic variables with GEI analysis (Reynolds et al., 2002).
Besides the conventional analytical and experimental approaches, data mining can also help assess the effect of climatic factors on seed yield.The process of reviewing and analyzing datasets to discover patterns, extract relevant knowledge, and obtain rules is called data mining (Vercellis, 2009).Rotili et al. (2020) applied data mining techniques to derive a guiding principle for farmers that distinguish high and low yielding crop designs across various environmental conditions.
The purpose of this study was to apply the analytical (PLSR, FR, and data mining) and experimental models (a mixed model based on BLUP) to analyze chickpea stability and identify the high-yielding and stable genotypes in rainfed conditions of Iran.
Seeds were planted in 6-m-long and 1-m-wide plots on five rows with a distance of 25 cm and a density of 50 plants per square meter.Ammonium phosphate (100 kg per ha) and urea (35 kg per ha) were added evenly to the soil during field preparation.After harvest and weighting of seed yield, the collected data were analyzed for the stability of yield performance.Pedoclimatic characteristics in experimental trials, the total amount of annual rainfall, and the average temperature during growth are indicated in Table S2, while seasonal rainfall and average temperature in Table S3.Climatic data were extracted from the facilities of the Department of Meteorology, I.R. of Iran Metrological Organization, which is located in the experimental stations.

| Mixed model
In this experiment, g genotypes are tested in e environments (combination of cultivation year and location) in a randomized complete block design (RCBD) with b replications.The analysis of response variable (e.g., seed yield) was performed by LMM method.The effects of environment and GEI were assumed random and the effects of genotype and block within-environment were assumed fixed (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019).The linear model of this experiment is given in Equation (1).
where y ijk is the response variable of the kth block of the ith genotype the grand mean; α i is the main effect of the ith genotype; τj is the main effect of the jth environment; (ατ) ij is the interaction effect of the ith genotype with the jth environment; γ jk is the effect of the kth block within the jth environment; and ε ijk is the random error assuming ε ijk $ NID(0,σ2), where NID means normally, identically and independently distributed (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019).
Environmental (E), GEI, residual, and environmental/block components of variance were estimated by REML.The significance of the random effects (environment and GEI) tested by a likelihood ratio test (LRT), which compares the À2(Res) log likelihoods for two models, one with full model (all random terms) and other with reduced model (without one of the random terms).The probability is obtained by a two-tailed chi-square test with one degree of freedom (χ 2 1 ).In WAASB i , the weighted average of absolute scores based on SVD of BLUP interaction effects of genotype i or environment, was calculated by Equation ( 2) to assess the stability of genotypes (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019): where interaction principal component axis (IPCA) ik is the genotype i (or environment) score in the k th IPCA, and the explained principal (EP) k is the amount of the variance explained by the k th IPCA.
WAASBY index for simultaneous selection based on mean performance (seed yield, Y) and stability (WAASB) is obtained by Equation (3) (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019): where WAASBY i is the superiority index for the genotype i and θ Y and θ S are the weights of seed yield and stability (WAASB).Twentyone scenarios varying θ Y and θ S (100/0, 95/5, 90/10, …, 0/100) were planned.G i and W i are the response variable (Y) and the WAASB values for i th genotype.rG i and rW i are the rescaled values (0-100) for the response variable and WAASB, respectively.

| Incorporating rainfall covariables for explaining GEI
Data mining, FR, and PLSR methods, which are analytical approaches, were used to evaluate the effects of covariates in GEI.Weka software based on the decision tree method (Kumar & Vijayalakshmi, 2011) and artificial neural network analysis method (Abiodun et al., 2018) was used on the dataset for data mining.Integration of external data into GEI analysis by PLSR and FR methods carried out by GEA-R software (Pacheco et al., 2015).In addition, the data discretization operation was performed, and then the features affecting the analysis using various rough set algorithms were discovered using Rosetta software.
Finally, it revealed that the Holt algorithm with the highest left hand side coverage (LHS) detection value and the accuracy (0.69) was the best algorithm in this stage (Wang et al., 2010).

PLSR
Seasonal rainfall and the average temperature of autumn, winter, and spring are used as environmental covariables (Table S3).The PLSR model includes independent matrices X (rainfall and average temperature data) and a dependent matrix Y (seed yield) and the latent variables t as follows (Vargas et al., 1998): where matrixes T, P, and Q contain X-scores, X-loadings, and Y-loadings, respectively.F and E are the residuals of the unexplained variation.A biplot was build based on the first two PLSR factors to investigate the relationships among covariables, genotypes, and environments.

FR
The FR model is also as follows (van Eeuwijk et al., 1996): where Yge is the yield of the genotype g in environment e, μ is the grand mean, αg and βe are the genotype and environment deviations from μ, respectively, Zih is the environmental covariates, ζjh are the genotype factor, H is the number of environmental covariates, and εij is the error.The heterogeneity in the ξi's for successive z1, …, zK variables accounts for the interaction, while the sum of multiplicative terms P H g¼1 Z ih ξ jh approximates the GE interaction.The Akaike's information criterion (AIC) (Akaike, 1974) is used to determine the number of covariables included in the model.

| Evaluation of random and fixed factors, estimation of variance components
The LRT showed that the effect of environment and GEI was significant on seed yield.Analysis of variance indicated the considerable influence of genotype on seed yield.Estimated variance components by REML showed environmental, GEI, residual and environmental/ block variances contributed 71.74%, 3.43%, 22.28%, and 2.53% of phenotypic variance, respectively (Table 1).Because in the mixed model, the genotype is considered fixed, the variance of the fixed effects (genotype in present case) is not accounted.

| Principal component analysis and estimation of predicted means
The scree test indicated the proportion of explained variance by the first four principal components of the total variance was more than 10%, and the proportion of variance explained by the other principal components (eight PCAs) was less than 10% (Figure S1a).Thus, the first and second principal components only explained 26.12% and 24.20% of the total variation, respectively.The mosaic plot divided the TSS into the genotypic sum of squares (GSS) and GEI sum of squares (GESS).In this plot, the dark region shows the variation due to genotypic effects, 17.67% of TSS.The light-colored region displays the variation due to GEI, 82.33% of TSS (Figure S1b).The columns of this plot represent the axes of the principal component. of GESS.The third to fifth principal components explained 18.41%, 11.49%, and 6.11% of TSS, respectively.Each column, which represents the axis of the principal component, is divided into two parts by the rows of the mosaic plot resulting from GSS and GESS.In the first principal component axis, the contributions of G and GE were 33.31% and 66.68%, respectively.In the second principal component axis, the contributions of G and GE were also 26.38% and 73.62%, respectively.Moreover, in the third and fourth principal components, the contribution of GEI, with 98.37% and 85%, was much higher than that of the contribution of genotype with 1.63% and 15%, respectively.

| Understanding the extend of GEI through biplot interpretation
The nominal yield plot showed that G4, G3, G18, G1, G9, and G2 had a small contribution to the GEI due to the low scores of the first principal component (regression coefficient or line slope) and were more stable genotypes (Figure S3a).On the other hand, genotypes G17, G11, G12, G5, G15, and G13 were unstable genotypes due to their higher regression coefficient.These apparently unstable genotypes may be adapted to certain environments due to the specific adaptation shown, since, as exploiting GEI might be a valuable strategy to reach local adaptation.This plot also indicated that E4, E6, E8, and E12 had high scores in the first principal components and were the most informative (discriminating) environments.Another use of this plot is to identify the appropriate genotypes for each environment.
According to the type III biplot (seed yield vs. a weighted absolute average score of BLUP (WAASB)), genotypes G1, G2, G13, and G8 in the first quarter were unstable or with specific adaptation due to their high contribution to GEI (Figure S3b).Despite their low general stability, these genotypes are compatible with E1, E5, E8, E12, and E6.
Additionally, E6 in this quarter had a high ability to discriminate genotypes due to their highest WAASB stability index.The seed yield of genotypes G4, G5, G12, G11, and G17 was higher than the average yield in the second quarter, but these genotypes were unstable due to their high WAASB index.In this quarter, environment E4 was highly discriminative and representative.In the third quarter, genotypes G7, G14, G3, and G6 had lower seed yield than the total average seed yield, but they could be considered stable genotypes due to the low WAASB values.Genotypes G4, G15, G10, G9, G18, and G16 were very productive and stable in the fourth quarter due to the significant response variable (high yield) and high stability (low WAASB values).

| Genotype ranking according to the different weighting of stability and seed yield
The plot of response variable (SY) Â WAASB (Figure S4), which interprets stability and seed yield simultaneously, allows the use of the other significant components to the ranking of genotypes (Olivoto, Lúcio, da Silva, Marchioro, et al., 2019).Equal weight for seed yield and stability (50:50) was used for drawing this plot.According to this plot, G16, G18, G5, G12, and G6 were high-yielding and stable genotypes.
Figure 1 shows that the ranking of genotypes changes according to the weight of response variable (SY) and stability (WAASB).
In the first left column of this heatmap, which is ranked only based on the WAASB stability index, genotypes G16, G18, G3, G6, G7, G9, and G5 are more stable than other genotypes.From left to right, the weight of the response variable (seed yield) in each column increases by 5%, and the weight of the stability index (WAASB) decreases by 5%.As in the last column on the right, the ranking of genotypes were only based on seed yield, according to which G5, G12, G11, G17, G4, and G15 had the highest seed yield.The clusters shown on the left of this plot can be used to identify genotypic groups with similar stability and yield patterns.
In the first cluster, genotypes G1, G2, G13, G10, G14, and G8 were low-yielding and unstable.In the second cluster, genotypes G11 and G17 were high-yielding but unstable.These two genotypes are also high-yielding but stable according to the third type of biplot (Figure S3b).In the third cluster, genotypes G3 and G6 were stable but low-yielding.Genotypes G7, G9, G15, G4, G16, G18, G12, and G5 were high yielding and stable in the last cluster.

| Data mining
According to the decision tree algorithm, average seasonal temperature and rainfall affected seed yield, and the algorithm's accuracy was 0.677.In general, the decision tree of the chosen algorithm was selected by examining the results of different methods in terms of LHS, accuracy, effective features and interpretability.The discovered tree from this algorithm is indicated in Figure 2. As shown, the average temperature and rainfall in autumn and winter affect seed yield.If the temperature in autumn is less than and equal to 14.33 C, high yield is predicted, and if the autumn temperature is more than 14.13 C and less than and equal to 14.86 C, intermediate seed yield is predicted.If the autumn temperature is more than 14.86 C and the winter rainfall is less than and equal to 85.3 mm or the autumn temperature is more than 14.86 C, the autumn rainfall is more than 42.3 mm, and the winter rainfall is more than 85.3 mm, low yield is predicted.

| Stability performances are linked to environmental variables by PLSR and FR
The stepwise FR model based on Akaike's information criterion (AIC) indicated genotype by temperature interaction in spring and winter were significant (Table 2).The first and second factors in the PLSR biplot explained 59.87% and 19.6% of the GEI variance, respectively (Figure 3).PLSR analysis indicated that rainfall in autumn and spring and temperature in all three seasons were involved in GEI.PLSR biplot revealed that E11 and E12 had the longest vectors and the highest seasonal rainfall values in spring and autumn for germination, establishment, and growth stages (Table S3).Genotypes G7 (1014 kg per F I G U R E 2 Discovered tree to predict seed yield according to seasonal rainfall and temperature.
F I G U R E 1 Ranks of 18 chickpea genotypes with different weights for stability and yield.
ha in E11), G17 (1552 kg per ha in E12), G18 (1292 kg per ha in E11), and G10 (1,119 kg per ha in E11) had the best performance in these environments.E1, E 5, E6, and E9 had the highest average temperature in autumn, winter and spring (Table S3).Genotypes G5, G8, G11, and G16 were the most affected by these conditions and had the lowest seed yield compared to other genotypes (Table S4).However, other environments were less affected by these covariates and had a distribution close to the origin of biplot.

| DISCUSSION
A number of statistical methods were employed to analyze MET data to recommend suitable genotypes across the different regions in the study.Because much of the effort in the final stages of breeding programs are based on multienvironmental experiments, predictive accuracy is crucial for correct genotype selection, cultivar recommendation, and mega-environment identification (Yan & Kang, 2003).Screening genotypes in several environments and identifying stable and high-yielding ones are ongoing challenges for breeders (Alwala et al., 2010).In other words, finding the applicable information hidden within the multienvironment is the major challenge of plant breeders.The significant effect of GEI in this study indicates that the seed yield of one genotype may differ from environment to environment.Previously, some researchers reported the considerable effects of G, E, and GEI on seed yield of chickpea (Bakhsh et al., 2011;Danyali et al., 2012;Farshadfar et al., 2011Farshadfar et al., , 2013;;Fikre et al., 2018;Kanouni et al., 2015).In agreement with the high contribution of environmental (E) variation in total variation, other researchers also reported a higher contribution of the environment than the other two components (G and GE) (Bakhsh et al., 2011;Erdemci, 2018;Farshadfar et al., 2011;Kanouni et al., 2015;Pouresmael et al., 2018;Sayar, 2017).The enormous value of environment sum of squares infers that environment has a central role in determining variation for seed yield in dryland cultivation of chickpea in Iran.
A mosaic plot links the TSS obtained by SVD and TSS provided by the ANOVA and facilitates the interpretation of GEI (Laffont of TSS, respectively, and therefore the latest components in the TSS cannot be ignored.Farshadfar et al. (2011Farshadfar et al. ( , 2013)), Kanouni et al. (2015), and Pouresmael et al. (2018) also reported the low and medium contribution of two first principal components in total variance.Fikre et al. (2018) evaluated 20 chickpea genotypes in 18 environments, indicating that the first two principal components explained 28.5% and 19.6% of GEI sum of squares and that the stable genotypes were distinguished with ASV and ssiASV.Considering the high contribution of the third and fourth principal components in TSS and the increased contribution of GE in these two components, it seems that the stability analysis based on the first and second principal components is faulty in this experiment.Therefore, it is better to use the other main components for stability analysis (Olivoto, Lúcio, da Silva, Sari, & Diel, 2019).
The BLUPs were estimated due to the significant effect of GEI.
The stability analysis was performed by the AMMI method on these BLUPs.Other researchers have also used the AMMI method on BLUPs of GEI matrix to identify stable genotypes of rice (Sharifi et al., 2021), lentil (Karimizadeh et al., 2021), forage (Santos & Marza, 2020), barley (Ahakpaz et al., 2021), and wheat (Verma & Singh, 2020).The nominal yield plot indicated genotypes G4, G3, G18, G1, G9, and G2 are more stable based on a small contribution to the GEI.This plot also finds E4, E6, E8, and E12 the most informative (discriminating) environments; therefore, it provides much information on the genotypes and should be employed as the test environments.
Since the drawing of this plot is based on the first principal component, which explains only 26.12% of the GEI, to achieve a better interpretation, it is necessary to drawings plots, which use all of the significant principal components.
WAASB and WAASBY plots were used to identify the stable genotypes.Environment E6 in the first quarter of type III biplot had a high ability to discriminate genotypes due to their highest WAASB stability index.In the fourth quarter of this biplot, genotypes G4, G15, G10, G9, G18, and G16 were very productive and stable.This biplot shows better stability; therefore, the selected genotypes with this index and biplot have more reliable stability.
High environmental contribution in total variation indicates that climatic factors have played a significant role in expressing seed yield in chickpea genotypes.Therefore, the evaluation of climatic factors such as high rainfall, proper temperature, and good rainfall distribution can help assess GEI on seed yield more accurately.Since the performance of a genotype is the sum of the main genotype effect and susceptibility of the genotype to the stress covariate, predicting the impact of environmental factors as a covariate is very useful for identifying superior genotypes (Rotili et al., 2020).Therefore, in the present study, a data mining process was used on the data set.The different analysis methods found different subsets of genotypes to be stable, so it is completely not clear as to what the recommendation of the analysis is in terms of genotype selection.Still, when we use analytical methods, we can achieve a better result.
Like in the data mining findings, the results of PLSR and FR were also produced with the entry of covariates, that is, seasonal rainfall and temperature, to the GEI analysis; it was found that rainfall and temperature in some seasons do not affect the GEI pattern.According to the results of FR the temperature during spring and autumn seasons plays a vital role in GEI.Identifying the most effective seasonal rainfall and temperature in the GEI can be useful in introducing stable genotypes for current and future conditions with changes in the pattern of seasonal rainfall and temperature.Stability analyses identified genotypes G5, G15, and G16 as superior genetics based on yield performance and stability.The rainfall in spring and autumn had a positive effect on these genotypes, which are sensitive to rainfall deficiency at the beginning of the season.Instead, PLSR biplot indicated genotypes G5 and G16 were affected by high temperatures in three seasons, while G15 was the only genotype that was not affected by high temperatures in three seasons and lack of rainfall in spring and autumn, which makes it a suitable genotype for rainfed cultivation.Therefore, high temperature in autumn, winter, and spring is one of the most significant factors affecting the reduction of yield performance of these genotypes; these genotypes, which can be considered sensitive to high temperature.This shows that considering the choice of a superior genotype based only on experimental methods (based on REML/BLUP in this case) can lead to errors in the conclusion and the use of environmental variables as a covariate can lead to better and accurate results.Differences between the PLSR and FR models in the introduction of covariates have already been observed in former studies (Ahakpaz et al., 2021;Mohammadi et al., 2020).Under rainfed condition, contrast, analysis of variance was used to assess the significance of the fixed effect (genotype) on seed yield.Simple and combined analysis of variance, estimation of WAASB (weighted average of absolute scores based on SVD of BLUP) and WAASBY (simultaneous selection based on WAASB and yield) and drawing graphs were performed by multienvironment trial analysis (METAN) R packages(Olivoto & Lúcio, 2020).The WAASB is computed considering all interaction principal component axes (IPCA) from the SVD of BLUP.The PCA was done as follows: First, standardize the range of continuous initial variables and then compute the covariance matrix to identify correlations.In the following, compute the eigenvectors and eigenvalues of the covariance matrix to identify the principal components.The mosaic plot was mapped with GGE(Wright & Laffont, 2018) R packages.
The average rainfall and temperature in the three seasons of autumn, winter, and spring were considered predictor variables and seed yield dependent variables.This procedure was used to evaluate the effects of seasonal average temperature and rainfall on the yield of chickpea genotypes.Data mining indicated that rainfall and temperature in some seasons have no effect on the GEI pattern.Recognizing the most influential seasonal rainfall and temperature in the GEI can introduce stable genotypes for such conditions.With the ongoing climatic situation, the patterns of seasonal rainfall and temperature rainfall are changing.For the second case of low predicted yield by data mining (autumn temperature more than 14.86 C, autumn rainfall more than 42.3 mm, and winter rainfall more than 85.3 mm) (Figure3), the favorable conditions at the beginning of the season have caused high vegetative growth and other uncontrollable factors have a negative effect and reduced seed yield.If the autumn temperature is more than 14.8 C, the winter rainfall is more than 85.3 mm, and the autumn rainfall is less than 42.3 mm, the seed yield performance is good.Rotili et al. (2020) also derived "rules of thumb" to distinguish high and low yielding crops across various environmental conditions using data mining.
Stepwise factorial regression model for seasonal rainfall and temperature based on Akaike's information criterion(AIC)., 2007(AIC).,  , 2013)).The low contribution of the GSS (17.67%) than GESS (83.33%) in TSS, in the mosaic plot, can be due to the selection of superior genotypes in terms of seed yield in previous years in the chickpea breeding programs as well as different reactions of genotypes in different environments.The magnitude of GEI sum of squares obtained from this mosaic plot indicates considerable differences in genotype responses across environments.The first five principal com-