Research Article

G×E Interaction Analysis by Ammi Model for Fodder Yield of Dual Purpose Barley Genotypes

Ajay Verma, V. Kumar, A. S. Kharab and GP Singh

  • Page No:  051 - 056
  • Published online: 13 Mar 2020
  • DOI : HTTPS://DOI.ORG/10.23910/IJBSM/2020.11.1.2064

  • Abstract

Numerous statistical methods have been proposed to estimate the yield behavior of genotypes to diverse environmental conditions. Large number of research studies has shown a significant effect of environmental as well as of G×E interaction yield of genotypes. G×E interaction has been analyzed by the additive main effects and multiplicative interaction model as this combines the analysis of variance for the genotype and environmental main effects and the principal component analysis with multiplicative indices.Combined AAMI analysis of variance, for 16 dual purpose barley genotypes evaluated across 08 environments of the country, showed significant differences for genotypes, environments and their interactions. Most of type 1 measures selected (EV1, AMGE1, SIPC1 and D1), genotypes G5, G6, G8 and G10; while type 2 favoured (EV2, AMGE2, SIPC2, D1 and ASV), genotypes G11 G14 G10  and G9; due to type 3 of AMMI parameters (EV4, AMGE4, SIPC4 and D4), genotypes G13, G14, G7 and G8; according to the type 5 measures accounted for maximum G×E interaction signal  pointed towards ( EV5, AMGE5, SIPC5 and D5) G13, G14, G8 and G16 desirable genotypes. Hierarchical clustering of AMMI based measures along with yield could be clustered with four distant groups. Group I contains AMGE3, AMGE5, IPCA2, IPCA3, IPCA4 and average yield. Group II contains only SIPC1, SIPC2 SIPC3 SIPC5 measures. Group III contains EV2, EV3, with IPCA5 and IPCA6. Largest group IV joined D1, D2, D3, D5, ASV, ASTAB1, ASTAB2 and ASTB5.

Keywords :   AMMI, genotype×environment interaction

  • Introduction

    Genotype×environment interaction resulted from differences in the genotypes response to the environmental conditions and leads to inconsistent performances of genotypes (Akbarpour et al., 2014, Bocianowsk et al., 2019a). This limits the efficiency of selection of superior genotypes. Genotypes whose GxE effects are not significant are said to be stable (Kendaland Tekdal, 2016, Edwards, 2016). Several methods have been used to assess the GxE effect and stability in crop performances (Carlosand Wojtek, 2006, Ferraudo et al., 2014).  AMMI model is comprised of additive main effects of genotype and environment, and the multiplicative effect of G×E interaction, and thus can explain more information compared to other methods (Kilic, 2014,Guilly et al., 2017, Tena et al., 2019). AMMI model fits the sum of several multiplicative terms rather than only one multiplicative term in assessing the performance of genotypes in different environments (Mortazavian et al., 2014, Kamila et al., 2016). AMMI analysis can be used to determine stability of the genotypes across locations using the PCA (principal component axis) scores (Sabaghnia et al., 2012, Naroui et al., 2013, Nowosad et al., 2016, Regis et al., 2018). Zobel (1994) introduced averages of the squared eigenvector (EV) values as the AMMI stability parameter. AMGE and SIPC stability parameters of AMMI model to describe the contribution of environments to G×E interaction suggested by Snelleret al. (1997). AMMI stability value (ASV) benefits from the first two IPCA of AMMI analysis (Purchase, 1997). The Euclidean distance from the origin of significant interaction IPCA axes as D parameter was suggested by Annicchiarico (1997). One or all of these measures may also be of interest for barley improvement programs as an alternative to the conventional stability methods (TekdalandKendal., 2018, Nowosad et al., 2018). Present study was conducted to evaluate the effect of G×E interaction on the fodder yield of dual purpose barley by AMMI based measures.

  • Materials and Methods

    Sixteen dual purpose promising barley genotypes were evaluated at research fields during cropping season of 2017-2018 at eight major barley producing locations of the country via randomized complete block design with four replications. Fields were prepared to favour good germination and growth of barley. All agronomic managements were done as per the recommendations to harvest potential yield of the crop. More over fodder yield was analysed further to estimate the G×E interaction component by AMMI analysis. Parentage details along with environmental conditions of considered locations were described in Table 1 for ready reference.

    AMMI is a combination of ANOVA for the main effects of the genotypes and the environment together with principal components analysis (PCA) the genotype-environment interaction (Shahriari et al., 2018; Tena et al., 2019). AMMI models are usually called AMMI (1), AMMI(2), ….,AMMI (n), depending on the number of principal components used to study the interaction effects. Under biplot analysis, the first principal component represents responses of the genotypes that are proportional to the environments, which are associated with the GxE interaction. The second principal component provides information about locations that are not proportional to the environments, indicating that those are responsible of the GxE crossover interaction. In Biplot analysis with two PCA axis, second PCA scores of genotypes and environments are plotted against their respective first PCA scores. The better description of the interaction, first and second PCA scores of genotypes and environments may be considered for graphical representations. The description of AMMI based measures was mentioned for completeness in following Table 2.

  • Results and Discussion

    Combined analysis of variance was explained significant effects of environment, genotype, and their interactions on fodder yield of dual purpose barley genotypes. Effects of locations were 47.3, genotypes (6.5%) and their interactions (37.8%) were highly significant (Table 2). Highly significant GxE interactions indicated complicated crossover and non-crossover types of interaction. Large magnitude of GxE interaction for yield was also observed in other crops (Ndhlela et al., 2014; Sabaghnia et al., 2013, Bocianowsk et al., 2019b). Additive Main effect and Multiplicative Interaction (AMMI) is a statistical tool which leads to identification of stable genotypes with their adaptation behaviour in an easy manner. AMMI first calculate genotype and environment additive effect using analysis of variance (ANOVA) and then analyse residual from these model using principal components analysis (PCA).

    Five types of AMMI based measures were calculated as EV1, AMGE1, SIPC1 and D1 parameters (using only one IPCA), ASV, EV2, AMGE2, SIPC2, ASTAB2 and D2 parameters (considering IPCA1 and IPCA2), EV3, AMGE3, SIPC3 and D3 parameters (using the first three IPCAs), EV5, AMGE5, SIPC5 and D5 parameters (using the first five IPCAs). Considering explained variation due to each IPCAs, type 1-based measures benefits 67.4%, type 2-based parameters benefits 79.1%, type 3-based parameters benefits 88.3%, and type 5 – based used 96.4 of GxE interaction variations (Table 3). Calculating AMMI stability parameters considering larger numbers of significant IPCAs results in the most usage of GxE interaction variations. GxE signal was about 93.9% and corresponding noise was restricted to 6.03% of total interaction sum of squares.

    Ranking of genotypes as per lower values of EV1 are G9,G6,G14, G1, whereas by D1 are G9 G6, G14, G1, measures ASTAB1 identified as G9, G6, G14, G 1, AMGE1 identified G3, G5, G4, G7, and by SIPC1 are G3, G5, G4, G7 genotypes (Table 4). AMMI stability value (ASV) was proposed to quantify the stability measure by considering relative weight of IPCA1 and IPCA2 scores. First two IPCAs in ASV measure used 79.7% of GxE interaction and have different values and meanings. ASV measure used the Pythagoras theorem to get estimated values between IPCA1 and IPCA2 scores to produce a balanced measure between the two IPCA scores (Purchase, 1997). Also, ASV parameter of this investigation used advantages of cross validation due to computation from first two IPCAs. ASV considered two IPCA’s identified as G6, G9, G1, G11 and the values of  EV2 pointed out G6, G1, G11, G9  and by D2 as G6, G1, G9, G11. Stable genotypes based on ASTAB2 are G6, G9, G1, G11 and of  SIPC2 are G14, G3, G7, G5. AMMI based measured defined by significant three principal components as  EV3 selected G15 G9, G6, G11, and by  D3 measures as  G9, G6, G15, G11 whereas by SIPC3 as G14, G7, G5, G11 and values of  ASTAB3 pointed towards G9, G6, G15, G11, and measure AMGE3 selected G3 G1, G8, G5 as desirable genotypes (Mohammadi et al., 2015, Vaezi et al., 2017, Bocianowsk et al., 2019c).

    Since five based measures had considered most of the interaction variation their selection of genotypes would be more appropriate to recommend as by values of  D5 for  G9, G6, G11, G15, and by EV5 values as G9, G11, G10, G7, measure SIPC5 pointed towards G14, G11, G5, G7 and stable genotypes as per ASTAB5 are G9, G6, G11, G15 and lastly by  AMGE5 are G3, G8, G1, G11 (Table 5).

    Finally according to the most of type 1 of AMMI parameters (EV1, AMGE1, SIPC1 and D1), genotypes G5, G6, G8 and G10; based on the type 2 of AMMI parameters (EV2, AMGE2, SIPC2, D1 and ASV), genotypes G11 G14 G10  and G9; due to type 3 of AMMI parameters (EV4, AMGE4, SIPC4 and D4), genotypes G13, G14,G7 and G8; according to the type 5 of AMMI parameters (EV5, AMGE5, SIPC5 and D5)desirable genotypes would be G13, G14, G8 and G16 (Rahmatollah et al., 2016).

    Association among the AMMI based stability measures studied by using Ward’s hierarchical clustering procedure. Biplots help to visualize relationships among genotypes & environments; by depicting both main as well as interaction effects. Biplots enables to identify target breeding environments and to choose representative testing sites in those environments along with varieties with good adaptation to target breeding environments. Graphical analysis based on biplots reflected four major clusters for the twenty one studied the AMMI stability parameters along with mean yield (Figure 1).

    Group I contains AMGE3, AMGE5, IPCA2, IPCA3, IPCA4 and average yield. Group II contains only SIPC1, SIPC2SIPC3SIPC5 measures. Group III contains EV2, EV3, with IPCA5 & IPCA6. Largest group IV joined most of the AMMI based measures as D1, D2, D3, D5, ASV, ASTAB1, ASTAB2 and ASTB5.

  • Conclusion

    Each of the AMMI based measures correlates to a different concepts of stable performance and will be useful to plant breeders to select stable genotypes with respect to yield across environments. At the same time, there is not a way to consider all of these measures simultaneously, and few of them should be used in MET vis-a-vis number of significant IPCAs. AMMI analysis has been observed as useful for exploring complex GxE interaction, improving selections and increasing experimental efficiency (Tena et al 2019).

  • Reference
  • Akbarpour, O., Dehghani, H., Sorkhi, B., Guach, G., 2014. Evaluation of Genotype×environmentinteraction in Barley (Hordeum vulgare L.) based on AMMI model using developed SAS Program. Journal of Agricultural Science and Technology 16, 919–930.

    Annicchiarico, P., 1997. Joint regression vs AMMI analysis of genotype×environment interactions for cereals in Italy. Euphytica 94, 53–62.

    Bocianowsk, J., Warzecha, T., Nowosad, K., Bathelt, R., 2019b. Genotype by environment interaction using AMMI model and estimation of additive and epistasis gene effects for 1000-kernel weight in spring barley (Hordeum vulgare L.). Journal of Applied Genetics 60, 127–135.

    Bocianowski, J., Niemann, J., Nowosad, K., 2019a. Genotype-by-environment interaction for seed quality traits in interspecific cross-derived Brassica lines using additive main effects and multiplicative interaction model. Euphytica 215,7.

    Bocianowski, J., Nowosad, K., Szulc, P.,2019c. Soil tillage methods by years interaction for harvest index of maize (Zea mays L.) using additive main effects and multiplicative interaction model. Acta Agric Scand Sect B Soil Plant Science 69(1), 75–81.

    Carlos, T.D.S.D., Wojtek, J.K., 2006. Choosing Components InThe Additive Main Effect And Multiplicative Interaction (AMMI) models, Scientia Agricola (Piracicaba, Braz.), 63(2), 169–175.

    Edwards, J.W., 2016. Genotype×environment interaction for plant density response in maize (Zea mays L.). Crop Science 56, 1493–1505.

    Ferraudo, G.M., Perecin, D., 2014. Mixed model, AMMI and Eberhart-Russel comparison via simulation on genotype×environment interaction study in sugarcane. Applied Mathematics 5, 2107–2119.

    Guilly, S., Thomas, D., Audrey, T., Laurent, B., Jean-Yves, H., 2017. Analysis of multi environment trials (MET) in the sugarcane breeding program of Re´union Island. Euphytica 213, 213.

    Kamila, N., Alina, L., Wiesława, P., Jan, B.,2016. Genotype by environment interaction for seed yield in rapeseed (Brassica napus L.) using additive main effects and multiplicative interaction model. Euphytica 208, 187–194.

    Kendal, E., Tekdal, S., 2016. Application of AMMI Model for Evolution Spring Barley Genotypes in Multi-Environment Trials. Bangladesh Journal of Botany 45(3), 613–620.

    Kilic, H., 2014. Additive Main Effect and Multiplicative Interactions (AMMI) Analysis of Grain Yield in Barley Genotypes across Environments. Journal of Agricultural Science 20, 337–344.

    Mohammadi, M., Sharifi,P., Karimizadeh,R., Jafarby,J.A., Khanzadeh,H., Hosseinpour, T., Poursiabidi,M.M., Roustaii,M., Hassanpour Hosni, M., Mohammadi, P., 2015. Stability of grain yield of durum wheat genotypes by AMMI model. Agriculture & Forestry 61(3), 181–193.

    Mortazavian, S.M.M., Nikkhah, H.R., Hassani, F.A., Sharif-al-Hosseini, M., Taheri, M., Mahlooji, M., 2014. GGE Biplot and AMMI Analysis of Yield Performance of Barley Genotypes across Different Environments in Iran. Journal of Agricultural Science and Technology 16, 609–622.

    Naroui, R., Kadir, M.R.,  Rafii, M., Hawa, M.Y.J., Naghavi, Z.E., Farzaneh, M.R., 2013. Genotype×environment interaction by AMMI and GGE biplot analysis in three consecutive generations of wheat (Triticumaestivum) under normal and drought stress conditions. Australian Journal of Crop Science 7(7), 956–961.

    Ndhlela, T., Herselman, L., Magorokosho, C., Setimela, P., Mutimaamba, C., Labuschagne, M., 2014. Genotype×environment Interaction of Maize Grain Yield Using AMMI Biplots. Crop Science 54, 1992–1999.

    Nowosad, K., Liersch, A., Popławska, W., Bocianowski, J., 2016. Genotype by environment interaction for seed yield in rapeseed (Brassica napus L.) using additive main effects and multiplicative interaction model. Euphytica 208, 187–194

    Nowosad, K., Tratwal, A., Bocianowski, J., 2018. Genotype by environment interaction for grain yield in spring barley using additive main effects and multiplicative interaction model. Cereal Research Communications 46(4), 729–738.

    Purchase, J.L., 1997. Parametric analysis to describe G×E interaction and yield stability in winter wheat. Ph.D. thesis. Dep. of Agronomy, Faculty of Agriculture, Univ. of the Orange Free State, Bloemfontein, South Africa.

    Rahmatollah, K., Asghari, A., Chinipardaz, R., Sofalian, O., Ghaffari, A., 2016. Determining Yield Stability And Model Selection By AMMI Method In Rain-Fed Durum Wheat Genotypes. Turkish Journal of Field Crops 21(2), 174–183.

    Rao, A.R., Prabhakaran, V.T., 2005. Use of AMMI in simultaneous selection of genotypes for yield and stability. Journal of the Indian Society of Agricultural Statistics 59, 76–82.

    Regis, J. A. V. B., Andrade, J. A. C., Santos, A., Moraes, A., Trindade, R. W. R., Henriques, H.J.R., Oliveira, L.C., 2018. Adaptability and phenotypic stability of sugarcane clones. Pesquisa Agropecuária Brasileira 53(1), 42–52.

    Sabaghnia, N., Mohammadi, M., Karimizadeh, R., 2012. The Evaluation of Genotype×Environment Interactions of Durum Wheat’s Yield Using of the AMMI Model. Agriculture & Forestry 55, 5–21.

    Sabaghnia, N., Mohammadi, M., Karimizadeh, R., 2013. Parameters of AMMI model for yield stability analysis in durum wheat. Agriculturae Conspectus Scientificus 78(2), 119–124.

    Shahriari, Z., Heidari, B., Dadkhodaie, A., 2018. Dissection of genotype × environment interactions for mucilage and seed yield in Plantago species: Application of AMMI and GGE biplot analyses. PLoS ONE 13(5): e0196095

    Sneller, C.H., Kilgore-Norquest, L., Dombek,D., 1997. Repeatability of yield stability statistics in soybean. Crop Science 37, 383–390.

    Tekdal, S., Kendal, E., 2018. AMMI Model to Assess Durum Wheat Genotypes in Multi-Environment Trials, Journal of Agricultural Science and Technology 20, 153–166.

    Tena, E., Goshu, F., Mohamad, H., Tesfa, M., Tesfaye, D., Seife, A., 2019. Genotype×environment interaction by AMMI and GGE-biplot analysis for sugar yield in three crop cycles of sugarcane (Saccharum officinirum L.) clones in Ethiopia. Cogent Food & Agriculture 5, 1–14.

    Vaezi, B., Pour-Aboughadareh, A., Mohammadi, R., 2017. GGE Biplot and AMMI Analysis of Barley Yield Performance in Iran. Cereal Research Communications 45, 500–511.

    Zobel, R., 1994. Stress resistance and root systems. In Proceedings of the Workshop on Adaptation of Plants to Serious Stresses. 1–4 August. INTSORMIL Publication 94-2, Institute of Agriculture and Natural Recourses. Lincoln, USA: University of Nebraska.


Verma A, Kumar V, Kharab AS, Singh G. G×E Interaction Analysis by Ammi Model for Fodder Yield of Dual Purpose Barley Genotypes IJBSM [Internet]. 13Mar.2020[cited 8Feb.2022];11(1):051-056. Available from:

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