Research Article

Stability Analysis for Assessment of Yield Performance and Adaptability of Selected Mango (Mangifera indica L.) Genotypes under Multi Location Trials in India

Sai Krishna K., Ram Kumar Chaudhary and Mahesh Kumar

  • Page No:  454 - 462
  • Published online: 31 May 2022
  • DOI : HTTPS://DOI.ORG/10.23910/1.2022.2870

  • Abstract

A study was conducted in April 2020 based on the data collected from the All-India Coordinated Research Project on Sub-Tropical Fruits (AICRP-STF) and Central Institute for Subtropical Horticulture (CISH), Lucknow, India. The objective was to identify the high yielding and stable genotypes of mango using Additive main effects and multiplicative interaction (AMMI) and Genotype plus Genotype×Environment interaction (GGE) biplot analyses. Data on sixteen genotypes of mango tested across four locations, viz., Rewa, Sabour, Sangareddy, and Vengurla, over nine years was considered for the study. Combined analysis of variance showed highly significant differences (p<0.01) for genotype, environmental main effects and genotype×environment interaction (GEI) effects. The significant GEI contributes about 42.81% of the total sum of squares. AMMI analysis partitioned the GEI into fifteen interaction principal component axes and a residual term. The first two interaction principal component axes (IPCA1, IPCA2) collectively accounted for 40.80% of GEI sum of squares. AMMI analysis recommended Zardalu, Mankurad and GGE biplot analysis recommended Totapari, Mankurad as superior mango genotypes for cultivation in all the test locations. GGE biplot analysis classified the test locations into two mega environments. The first mega environment includes Rewa and Sangareddy with Neelum as the best suitable genotype; the second includes Vengurla and Sabour with Suvarnarekha as the best suitable genotype. The present study also concluded that GGE biplot analysis was the best analytical tool for identifying location-specific genotypes of mango, and AMMI analysis was the best for identifying superior genotypes having high yield with stability across all the test locations.

Keywords :   Adaptability, AMMI, biplot, environment, GEI, GGE, mango, stability


    Mango is one of the most important commercially grown fruit crops in India. Major mango producing countries in the world are India, China, Thailand, Indonesia, Mexico, Pakistan, Brazil, Philippines, Nigeria, and Sudan (Anonymous, 2020a).  Mango is cultivated in a vast area of 2,578 t ha-1. The production is around 24.75 mt, accounting for about 45.13% of total world mango production 46.68% of world mango cultivated area (Anonymous, 2020a). The increasing population raises demand for agricultural produce, which is expected to enhance agricultural production. In a view of sustaining hunger, it is required to increase agricultural production per unit area. To encounter this requirement, various crop improvement programs have been initiated all over the world (Anonymous, 2019). In any crop improvement program, the performance of promising genotypes has been tested over different locations each year to identify the genotypes having both high yield qualities and wider adaptability over different environmental conditions (Kumar et al., 2021, Reddy et al., 2022). In Multi-location trials (MLT), most frequently, it is noticed that the genotypes respond differently to the diverse environmental conditions; this differential response of genotypes over diverse environments is known as Genotype environment interaction (GEI) (Pham et al.,1988, Farias et al., 2016, Pagi et al., 2017). Yet there is no single method developed so far that equally satisfies breeders for the study of GEI. There are many different statistical analyses in use today, including parametric and non-parametric methods to study the nature of interactions of genotypes with environments (Kaya et al., 2006, Jeberson et al., 2017, Oladosu et al., 2017, Rao et al., 2022).

    Among various statistical techniques, Genotype plus Genotype×Environment Interaction (GGE) biplot and Additive Main Effects and Multiplicative Interaction (AMMI) models are being used predominantly for evaluating GEI and identifying superior genotypes (Purchase et al.,2000, Gauch Jr., 2006, Oliveira et al., 2010, Zali et al.,2012, Giridhar et al., 2016, Khan et al.,2021). AMMI model was introduced in 1988, and basically, the AMMI model is a combination of Analysis of Variance (ANOVA), which explains the main effects (Reddy et al., 2022), and Principal Component Analysis (PCA) which describes interaction effects (Gauch and Zobel, 1988, Singh et al., 2019). GGE biplot model concurrently depicts mean performance and stability and gives a comprehensive assessment of genotypes by creating a biplot. It can efficiently display the “which-won-where” patterns of MLT data (Singh et al 2019, Siddi et al., 2022). An important characteristic of this GGE biplot is that it removes the environment main effect and retains and combines genotype main effect and GEI. Thus, the biplot generated from the MLT data contains only G and GEI (Kang, 2002, Kumar et al., 2021, Sharma et al., 2016). GGE biplot and AMMI analyses has been carried out in understanding GEI in many crop species including pigeon pea (Rao et al., 2022, Reddy et al., 2022, Kumar et al., 2021, Sharma et al., 2016); wheat (Verma et al., 2021, Singh et al., 2019, Jeberson et al., 2017); ground nut (Khan et al., 2021); maize (Bozovic et al., 2020, Oliveira et al., 2010); rice (Chandra Mohan et al., 2021).

    Genotype environment interaction is a major problem in selecting and recommending superior genotypes to cultivate crops. When dealing with perennial crops like Mango, Guava, etc., this problem gets intensified because choosing unstable cultivars puts the farmers in a risky income situation for many years. To avoid such circumstances and facilitate growth in farmers’ income by recommending superior genotypes, the present study has been taken up.


    2.1.  Source and description of data

    Mango multi location trials were conducted at four locations namely Rewa (Madhya Pradesh), Vengurla (Maharashtra), Sangareddy (Telangana), and Sabour (Bihar) over different years. These trials were carried out in a randomized complete block design with three replications in each location. The present investigation has been carried out in April, 2020 based on the data collected from the All-India Co-Ordinated Research Project on Sub-Tropical Fruits (AICRP-STF) and Central Institute for Subtropical Horticulture (CISH), Lucknow, India. All the four locations contain common data for 16 genotypes of mango tested over nine years from 1997−2005 with three replications, and the same data were taken for the study. For the present investigation, the yield variable, i.e., the number of fruits per tree has been considered for the evaluation of MLT data of Mango. A combination of years and locations were considered as environments. As mango genotypes were grown in 4 different locations over nine different years, it gives 36 environments. Codes of selected mango genotypes, and environments used in the present study are shown in Table 1.

    2.2.  AMMI analysis

    AMMI analysis is a mixture of additive and multiplicative effect analysis. At first, it calculates additive main effects by using ANOVA; briefly ANOVA partitions the total variance into 3 different components like deviations of genotypes, environments, and GEI from the grand mean. The second part, i.e., multiplicative part, divides the deviations of GEI into various IPCAs, these IPCA are tested for significance through ANOVA (Gauch Jr, 1992). Generally, AMMI uses PCA for analysing the multiplicative part of GEI. The AMMI model for T genotypes and S environments is given below,  

    Yij= µ+gi+ej+∑n'(n=1)λnαin γjnij………. (1)

    θij ~ N (0, σ 2); i = (1, 2, 3, 4……...T); j = (1,2, 3……. S), Yij = Average yield of ith genotype in jth environment;µ= Grand Man;  g= ith genotypic main effect; ej= jth environmental main effect; λn= Eigen value of nth IPCA; αin and γjn = ith genotype and jth environment PCA scores for the axis n; θij= Residual; n’= Number of PCA axes retained in the model.

    2.3. Stability parameters

    2.3.1.  AMMI stability value (ASV)

    This measure utilizes only the first 2 IPCAs. The higher value of the ASV score indicates that the genotype is specially adapted to certain environments and lower the scores of ASV, the more will be the genotypic stability across different environments (Purchase et al.,2000). It can be calculated by the following formula.

    ASV=√[(IPCA1 score) (IPCA1sum of squares)/(IPCA2sum of squares)]2+[IPCA2 score]2 )………. (2)

    2.3.2.  AMMI based stability measure (ASTABi)

    ASTABi incorporates all the significant principal components required for explaining the GEI. Genotypes having a lower value of ASTABi are considered stable genotypes (Rao and Prabhakaran, 2005). This measure can be computed by the formula.

    ASTABi=∑N'n=1λn  γ2in    ……… (3)

    = Number of significant IPCAs retained;  = Singular value of nth IPCA;  = ith genotype eigenvector value

    2.3.3. Yield stability index (YSI)

    This measure combines mean yield and stability of a genotype in a single criterion. YSI can be computed by the addition of rank of stability measure (RS) and rank of mean yield (RY) of a genotype. The lower the value of YSI, the higher will be the mean yield and stability of genotype across environments.

    YSI = RS + RY………………………. (4)

    YSI1 = Index 1 = RASV + RY …………… (5)

    YSI2 = Index 2 = RASTAB + RY …………. (6)

    2.4.  GGE biplot analysis

    The concept of biplot was introduced by Gabriel in 1971. The prefix ‘Bi’ in the word biplot denotes the dual (genotypes and environment) exposing on the same graph. Biplot is a 2D visualization matrix that has two axes, first data was centered afterward sectionalizing the singular value (SV) into GE scores for individual principal components viz. PC1 and PC2 followed by intrigue the PC1 scores contrary to the PC2 scores to create a biplot (Gabriel, 1971). The greater PC1 value indicates greater yielding ability whereas the lower PC2 value signifies stability (Jeberson et al., 2017, Oladosu et al., 2017, Reddy et al., 2022). Genotypes, environments, and their interactions were portrayed on the biplot. The genotypes which were positioned near to the origin of the biplot origin are considered stable genotypes. However, the genotypes which are positioned far away from the origin of the biplot are considered unstable genotypes.

    For better understanding and easy interpretation, various biplots have been derived from the basic GGE biplots. In the present study, 2 types of biplots namely: “Which-won-where” view and “Ranking genotypes” view of the GGE biplot have been utilized. “Which-won-where” biplot has been used for identifying mega environments and this identification of mega environments helps in classifying similar behaving environments as one group and accordingly genotypes have been recommended for each of the mega environments. “Ranking genotypes” biplot has been used to identify superior genotypes.

    2.5.  Statistical analysis

    To explain the GEI, the multivariate stability analysis was performed graphically based on GGE biplot (Which-won-where view and ranking genotypes view) and AMMI using R studio (a simplified version of R statistical software) developed by the R Core Team. The Metan package of R studio was used for GGE biplots (Anonymous, 2020b), while the Agricolae package was used for AMMI (Mendiburu, 2020).

    2.6.  Data transformation

    To attain normality and homogeneity of error variances across environments, data was transformed using appropriate data transformation techniques. Yield variable data was transformed to normal using the “Ordered quantile normalization technique”. R-package “best Normalize” has been employed for data transformation (Peterson and Cavanaugh, 2019).


    3.1.  AMMI analysis

    One of the vital objectives of the crop improvement program is to identify superior varieties with high yield and stability across diverse locations. A combined analysis of variance has been performed to describe the main effects and quantify the interactions among and within the sources of variation. Due to the significant combined analysis of variance, yield stability of genotypes was studied, and genotypes with specific adaptability to each environment and genotypes with general adaptability to all environments were measured (Reddy et al., 2022).

    The mean squares of genotypes, environments and their interactions (i.e., GEI) showed significant differences (p<0.01) for the yield variable. Genotypes, environments, and GEI effect accounted for 6.95%, 37.78%, and 42.81% of the total sum of squares, respectively. As ANOVA confirmed the presence of significant GEI, additional statistical techniques such as AMMI and GGE biplot analyses were more helpful in unfolding and understanding the GEI (Khan et al., 2021). Application of the AMMI model for the apportioning of GEI revealed 12 significant interaction principal component axes (IPCA). IPCA1 and IPCA2 collectively accounted for 40.80% of GEI. The combined analysis of variance and AMMI analysis results were presented in Table 2.

    Sabaghnia et al. (2008) also observed about 40% of GEI contribution in total variation in the lentil genotypes. Reddy et al. (2022) reported similar findings that stated that the GEI effect contributed 36.49% of the variation for Sterility mosaic disease. Chandra Mohan et al. (2021) observed a highly significant difference in grain yield in rice hybrids by genotype (7.5%), environment (65.47%) and their interaction (21.19%). Further, Giridhar et al. (2016), Kumar et al. (2020), and Rao et al. (2022) also reported highly significant genotype-environment interactions.

    3.2.  Stability parameters of AMMI

    Mango genotypes were ranked based on stability measures as well as simultaneous selection indices for yield and stability (SSIYS) using the interaction principal component axes (IPCA) scores obtained through AMMI analysis. Values and ranks of the stability parameters are presented in Table 3 and Table 4, respectively.

    The genotype G4 exhibited the highest mean yield, followed by G2, G8, and G15. Genotypes with lower scores of ASV and ASTABi are known as stable genotypes (Purchase et al., 2000, Rao and Prabhakaran, 2005). ASV scores were smaller for the genotypes G10, G8 and G7, while the ASTABi scores were minimum for the genotypes G7, G5 and G15; hence these genotypes are known as stable genotypes according to ASV and ASTABi, respectively. G3 was recognized as an unstable genotype due to higher scores of ASV and ASTABi. The genotypes with the lowest and highest ranks of SSIYS are considered the best and the poorest genotypes, respectively. G8, G15 and G4 were identified as the best genotypes by Index 1, while G2, G15 and G7 were identified as the best genotypes by Index 2. However, the SSIYS (Index 1, Index 2) found G1 as the poorest genotype.

    Correlations among the stability measures and SSIYS have been computed and presented in Table 5.

    Correlations were quantified using Spearman’s rank correlation coefficient, and these correlations were tested for significance using a student t-test at a 1% level of significance (Zali et al., 2012). Index 1 and Index 2 have a significant correlation with each other and with mean yield, while ASV and ASTABi have no significant correlation with mean yield. Index 1 has a significant correlation with ASV; however, Index 2 has a significant correlation with ASTABi. For the present study, only SSIYS such as Index1 and Index 2 were chosen to identify superior genotypes among the stability parameters because of their ability to identify the genotypes simultaneously for yield and stability. In contrast, ASV and ASTABi rank the genotypes only based on stability, irrespective of their yields. Spearman’s rank correlation coefficient between SSIYS (Index 1 and Index 2) is highly significant (p<0.01), which implies either of the indices may invariably be used for identifying the best genotypes. The present study’s findings agreed with the report stated by Zali et al. (2012) considered thirteen different stability measures, and Verma et al. (2021) considered different AMMI based stability measures and simultaneous selection index in stability assessment of wheat genotypes. Final ranking order of mango genotypes based on AMMI analysis (Index 1) is G8 > G15 > G4 > G7 > G2 > G11 > G14 > G10.

    3.3. GGE biplot analysis

    3.3.1. “Which-won-where” view of GGE biplot

    Figure 1 illustrates the “Which-won-where” view of the GGE biplot for the yield variable. Each sector of the biplot forms a unique mega environment. The environments falling in the same sector belong to the same mega environment. The genotypes which share the same sector with the test environments in a biplot are specially adopted to those environments (Kang, 2002, Siddi et al., 2022).

    Three mega environments have been identified as environmental indicators positioned in 3 sections of the biplot, with different genotypes winning in each segment. A single test environment, E14, formed the first mega environment with G16 and G13 as winners, and the test environments E9, E10, E11, E12, E13, E15, E16, E17, E18, E24, E25, E28, E29, E30, E31, E32, E33, E34, E35 and E36 collectively formed as the second mega environment with G2 as winner genotype. While remaining test environments, i.e., E1, E2, E3, E4, E5, E6, E7, E8, E19, E20, E21, E22, E23, E26 and E27 constitute the third mega environment with G3 as the winner genotype. The present study’s findings agreed with the report stated by Oladosu et al., 2017, who considered two different cropping seasons across five locations in Malaysia. Comparably, Mary et al. (2019) reported that the biplot for grain yield during the wet season showed that PSBRc82 was the winner genotype in E4 and MS13 in E8 and E9. Rukmini Devi et al. (2020) reported the rice genotypes WGRH-6 and WGRH-10 had better performance in mega environment E3, and the genotype WGRH-18 exhibited better performance in the second mega environment consisting of E1 and E2. Similar results have been reported by Yan et al. (2010).

    3.3.2.  Ranking genotypes view of GGE biplot

    This kind of GGE biplot describes the ranks of genotypes based on their position from the ideal genotype. For an effective selection, an ideal genotype should have both high mean and stability properties (Khan et al., 2021). The genotype located in the innermost concentric circle is highly desirable compared to the genotypes of the outer circle. However, no genotype was positioned within the inner circle in some cases. Consequently, genotypes closer to the inner circle are considered the best ones (Gauch, 2006, Siddi et al., 2022). The genotypes G4, G15, G2, G8, G11, G14, and G7, were regarded as the best genotypes across all test environments because of their closeness to the ideal genotype (Figure 2). So, the genotype ranking based on ideal genotype for yield variable is G4 > G15 > G2 > G8 = G11 > G14>G7. Oladosu et al. (2017) and Chandra Mohan et al., 2021 reported similar findings across mutant rice varieties.


    AMMI analysis recommended Zardalu, Mankurad and GGE biplot analysis recommended Totapari, Mankurad as superior genotypes of mango for all the test locations in India. GGE biplot analysis also revealed that Suvarnarekha was the best-performed genotype in Sabour and Vengurla, while Neelum was the best-performed genotype in Rewa and Sangareddy. The present study concluded that AMMI and GGE biplot analyses were the most valuable tools for identifying the superior genotypes in perennial crops.


    Authors wish to acknowledge AICRP-STF, CISH, Lucknow, India and its centres, Rewa, Sangareddy, Vengurla and Sabour for providing data.

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K SK, Chaudhary RK, Kumar M. Stability Analysis for Assessment of Yield Performance and Adaptability of Selected Mango (Mangifera indica L.) Genotypes under Multi Location Trials in India IJBSM [Internet]. 31May.2022[cited 8Feb.2022];13(1):454-462. Available from:

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