, Volume 202, Issue 3, pp 393–409 | Cite as

Application of mixed models for evaluating stability and adaptability of maize using unbalanced data

  • André Gradowski de Figueiredo
  • Renzo Garcia Von Pinho
  • Heyder Diniz Silva
  • Marcio Balestre


The aim of this study was to use a multi-environment trial approach from a mixed model point of view for factor analysis (FA) of the stability and adaptability of hybrids. Twenty-eight hybrids were analyzed in 35 environments across four seasons/years (summer season 2010, winter season 2011, summer season 2011 and winter season 2012). Several of these hybrids were analyzed during the first seasons and were not evaluated in later seasons or vice versa. Therefore, the dataset used in this study simulated the dynamics of a genetic breeding program with removal and inclusion of genotypes over the years. A biplot of the factor scores and loadings showed that the environments were more similar within seasons than between seasons, thereby suggesting that a given site may behave differently year after year. The season was more effective in discovery mega-environments. The FA models may be directly interpreted as GGE biplot analysis since the first factor score had a perfect fit (\(r^{2} = 0.99\)) with the empirical best linear unbiased predictors of the genotypes. Given the assumption of normality for the factor scores, confidence ellipses could be created to directly compare the genotypes in the biplot. Stability and adaptability could be analyzed in unbalanced experiments with the removal and inclusion of genotypes over time. This approach allowed certain trends in a breeding program to be measured by directly comparing hybrids developed for the first or winter season. The biplot interpretation was direct and intuitive, and it has the same properties as the GGE biplot obtained by singular value decomposition.


Sites regression (SREG) model Confidence ellipse Multi-environment trial (MET) Unstructured matrices (UN) 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • André Gradowski de Figueiredo
    • 1
  • Renzo Garcia Von Pinho
    • 2
  • Heyder Diniz Silva
    • 3
  • Marcio Balestre
    • 4
  1. 1.Departament of Techonology DevelompmentMonsanto do Brasil LTDASão PauloBrazil
  2. 2.Department of AgricultureFederal University of LavrasLavrasBrazil
  3. 3.Monsanto do Brasil LTDAUberlandiaBrazil
  4. 4.Department of Exact SciencesFederal University of LavrasLavrasBrazil

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