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Applying the generalized additive main effects and multiplicative interaction model to analysis of maize genotypes resistant to grey leaf spot

  • C. R. L. ACORSI (a1), T. A. GUEDES (a1), M. M. D. COAN (a2), R. J. B. PINTO (a2), C. A. SCAPIM (a2), C. A. P. PACHECO (a3), P. E. O. GUIMARÃES (a3) and C. R. CASELA (a3)...


Analysing the stability and adaptation of cultivars to different environments is always necessary before recommending them for planting on large areas. Additive main effects and multiplicative interaction (AMMI) models have been used to analyse genotype-by-environment interactions (G × E). AMMI models require data with homogeneous variance, normal errors and additive effects. However, agronomic data do not always conform to these statistical assumptions. The objective of the present study was to analyse G × E interactions for severity and incidence of grey leaf spot, a foliar disease in maize caused by Cercospora zeae-maydis, using a generalized AMMI model. Data were collected and evaluated for 36 maize cultivars from experiments carried out in nine Brazilian regions in 2010/11 by the Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA – Milho e Sorgo). Only two of three stable genotypes defined by a quasi-likelihood model with a logistic link function could be recommended for their desirable agronomic characteristics. Four growing locations in which the genotypes were stable were identified, but in only one of these was stability associated with very severe grey leaf spot disease. Cultivars adapted to specific locations with low percentage disease severity were also identified.


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Agresti, A. (2002). Categorical Data Analysis. New Jersey, USA: John Wiley & Sons.
Allard, R. W. (1999). Principles of Plant Breeding. New York, USA: John Wiley & Sons.
Annicchiarico, P., Bellah, F. & Chiari, T. (2005). Defining subregions and estimating benefits for a specific-adaptation strategy by breeding programs: a case study. Crop Science 45, 17411749.
Bhatia, A. & Munkvold, G. P. (2002). Relationships of environmental and cultural factors with severity of gray leaf spot in maize. Plant Disease 86, 11271133.
Brito, A. H., Von Pinho, R. G., Pozza, E. A., Pereira, J. L. A. R. & Faria Filho, E. M. (2007). Efeito da Cercosporiose no rendimento de híbridos comerciais de milho. Fitopatologia Brasileira 32, 472479.
Cordeiro, G. M. & Demétrio, C. G. B. (2008). Modelos Lineares Generalizados e Extensões. Piracicaba, Brazil: Escola Superior de Agricultura “Luiz de Queiroz” – Universidade de São Paulo.
Crossa, J., Fox, P. N., Pfeiffer, W. H., Rajaram, S. & Gauch, H. G. Jr (1991). AMMI adjustment for statistical analysis of an international wheat yield trial. Theoretical and Applied Genetics 81, 2737.
Cruz, C. D., Regazzi, A. J. & Carneiro, P. C. S. (2006). Modelos Biométricos Aplicados ao Melhoramento Genético. Viçosa, Brazil: Universidade Federal de Viçosa.
Dobson, A. J. A. (2002). Introduction to Generalized Linear Models. New York, USA: Chapman & Hall CRC.
Duarte, J. B. & Vencovsky, R. (1999). Interação Genótipos x Ambientes uma introdução à análize “AMMI”. Monograph Series, 9. Ribeirão Preto, Brazil: Sociedade Brasileira de Genética.
Fantin, G. M., Brunelli, K. R., Resende, I. C. & Duarte, A. P. (2001). A mancha de Cercospora do milho. Campinas, Brazil: Instituto Agronômico de Campinas.
Fornasieri Filho, D. (2007). Manual da Cultura do Milho. Jaboticabal, Brazil: Funep.
Ferreira, D. F. (2008). Estatística Multivariada. Lavras, Brazil: Universidade Federal de Lavras.
Ferreira, D. F., Demétrio, C. G. B., Manly, B. F. J., Machado, A. A., Vencovsky, R. (2006). Statistical models in agriculture: biometrical methods for evaluating phenotypic stability in plant breeding. Cerne 12, 373388.
Gabriel, R. (1998). Generalized bilinear regression. Biometrika 85, 689700.
Gauch, H. G. & Zobel, R. W. (1988). Predictive and postdictive success of statistical analyses of yield trials. Theoretical and Applied Genetics 76, 110.
Gauch, H. G. & Zobel, R. W. (1996). AMMI analysis of yield trials. In Genotype by Environment Interaction (Eds Kang, M. S. & Gauch, H. G.), pp. 85122. New York, USA: Boca Raton CRC Press.
Gollob, H. F. (1968). A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 33, 73115.
Gower, J. C. (1995). A general theory of biplots. In Recent Advances in Descriptive Multivariate Analysis (Ed. Krzanowski, W. J.), pp. 283303. Royal Statistical Society Lecture Notes, 2. Oxford: Clarendon Press.
Hadi, A. F., Mattjik, A. A. & Sumertajaya, I. M. (2010). Generalized AMMI models for assessing the endurance of soybean to leaf pest. Jurnal Ilmu Dasar 11, 151159.
Ientilucci, E. J. (2003). Using the Singular Value Decomposition. New York, USA: Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology. Available from: (verified 27 October 2016).
Kempton, R. A. (1984). The use of biplots in interpreting variety by environment interactions. Journal of Agricultural Science, Cambridge 103, 123135.
Kroonenberg, P. M. (1997). Introduction to Biplots for G × E Tables. Research Report #51. Leiden: Leiden University.
McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models. London, UK: Chapman & Hall.
Pacheco, R. M., Duarte, J. B., Assunção, M. S., Junior, J. N. & Chaves, A. A. P. (2003). Zoneamento e adaptação produtiva de genótipos de soja de ciclo médio de maturação para Goiás. Pesquisa Agropecuária Tropical 33, 2327.
Paula, G. A. (2004). Modelos de Regressão com Apoio Computacional. São Paulo, Brazil: Instituto de Matemática e Estatística da Universidade de São Paulo (IME-USP)..
R Development Core Team (2013). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available from:
Rencher, A. C. (2002). Methods of Multivariate Analysis, 2nd edn. New York, USA: John Wiley & Sons.
Searle, S. R., Casella, G. & McCulloch, C. E. (1992). Variance Components. New York, USA: John Wiley & Sons.
Smith, A. B., Cullis, B. R. & Thompson, R. (2005). The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches. Journal of Agricultural Science, Cambridge 143, 449462.
Sumertajaya, I. M. (2007). Analisis Statistik Interaksi Genotipe Dengan Lingkungan. Bogor, Indonesia: Departemen Statistik, Fakultas Matematika dan IPA, IPB (Abstract in English).
Tarakanovas, P. & Ruzgas, V. (2006). Additive main effect and multiplicative interaction analysis of grain yield of wheat varieties in Lithuania. Agronomy Research 4, 9198.
Turner, H. & Firth, D. (2009). Generalized Nonlinear Models in R: An Overview of the gnm Package (R Package Version 0.10–0). Warwick, UK: University of Warwick.
van Eeuwijk, F. A. (1995). Multiplicative interaction in generalized linear models. Biometrics 51, 10171032.
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika 61, 439447.
Zobel, R. W., Wright, M. J. & Gauch, H. G. (1988). Statistical analysis of a yield trial. Agronomy Journal 80, 388393.

Applying the generalized additive main effects and multiplicative interaction model to analysis of maize genotypes resistant to grey leaf spot

  • C. R. L. ACORSI (a1), T. A. GUEDES (a1), M. M. D. COAN (a2), R. J. B. PINTO (a2), C. A. SCAPIM (a2), C. A. P. PACHECO (a3), P. E. O. GUIMARÃES (a3) and C. R. CASELA (a3)...


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