An interactive biplot implementation in R for modeling genotype-by-environment interaction

  • Elisa Frutos
  • M. Purificación Galindo
  • Víctor LeivaEmail author
Review Paper


Classical and GGE biplot methods are graphical procedures that allow multivariate data to be analyzed. In particular, the GGE biplot displays the genotype main effect (G) and the genotype by environment interaction (GE) in two-way data. The GGE biplot originates from data graphical analysis of multi-environment trials (MET). Thus, agronomists, crop scientists and geneticists are potential users of this method. However, it can also be used to visualize and analyze other types of data. In this paper, we propose a new interactive computational implementation in R language to perform the main functions of the classical and GGE biplot methods, so it is also useful for MET data visual analysis. This implementation is organized in an R package named GGEBiplotGUI . This package is the only interactive, noncommercial and open source software that currently exists, offering a free alternative to available commercial software. In addition, it can be used without to practically have knowledge of the R programming language. Here, we present and discuss the capabilities and features of the GGEBiplotGUI package and illustrate them by using real data. The GGEBiplotGUI package graphically addresses the questions that a researcher likely asks. This R package is not only a tool for visual data analysis of multi-environment trials, useful for plant breeders and geneticists, in order to study yields from genotypes and interactions between genotype and environment, but also data from other areas can be analyzed by the GGEBiplotGUI package.


Graphical display Least squares method Multivariate data analysis Singular value decomposition Statistical models Statistical software 

Mathematics Subject Classification

62H99 62-04 



The authors wish to thank the Editor-in-Chief, Professor George Christakos, an Associate Editor, and anonymous referees for their comments on an earlier version of this manuscript, which resulted in this improved version. The research of Victor Leiva was partially supported by FONDECYT 1120879 grant from the Chilean government.


  1. Bacon-Shone J (2008) Compositional data analysis in the geosciences: from theory to practice (by A. Buccianti, G. Mateu-Figueras and V. Pawlowsky-Glahn, eds). Stoch Environ Res Risk Assess 22:139–141CrossRefGoogle Scholar
  2. Barros M, Paula GA, Leiva V (2009) An R implementation for generalized Birnbaum–Saunders distributions. Comput Stat Data Anal 53:1511–1528CrossRefGoogle Scholar
  3. Bradu D, Gabriel KR (1978) The biplot as a diagnostic tool for models of two-way tables. Technometrics 20:47–68CrossRefGoogle Scholar
  4. Cárdenas O, Galindo MP (2003) Biplot with external information based on generalized bilinear models. Printed by Council of Scientific and Humanistic Development of the Central University of Venezuela, Caracas. Spanish version can be downloaded from
  5. Choulakian V (1966) Generalized bilinear models. Psychometrika 61:271–283CrossRefGoogle Scholar
  6. Cornelius PL, Seyedsadr MS, Crossa J (1992) Using the shifted multiplicative model to search for separability in crop cultivar trials. Theor Appl Genet 84:161–172Google Scholar
  7. Cornelius PL, Crossa J, Seyedsadr MS (1996) Statistical tests and estimators for multiplicative models for genotype-by-environment interaction. In: Kang MS, Gauch HG Jr (eds) Genotype-by-environment interaction. CRC Press, Boca RatonGoogle Scholar
  8. Crossa J, Cornelius JL (1997) Sites regression and shifted multiplicative model clustering of cultivar trial sites under heterogeneity of error variances. Crop Sci 37:405–415Google Scholar
  9. Denis JB (1991) Ajustements de modelles lineaires et bilineaires sous constraintes lineaires avec donnes manquantes. Stat Appl 39:5–24Google Scholar
  10. Ebdon JS, Gauch HG (2002a) Additive main effect and multiplicative interaction analysis of national turfgrass performance trials I: interpretation of genotype × environment interaction. Crop Sci 42:489–496CrossRefGoogle Scholar
  11. Ebdon JS, Gauch HG (2002b) Additive main effect and multiplicative interaction analysis of national turfgrass performance trials II: cultivar recommendations. Crop Sci 42:497–506CrossRefGoogle Scholar
  12. Eberhart SA, Russell WA (1969) Yield stability for a 10-line diallel of single-cross and double-cross maize hybrids. Crop Sci 9:357–361CrossRefGoogle Scholar
  13. Eckart C, Young G (1939) A principal axis transformation for non-Hermitian matrices. Bull Am Math Soc 45:118–121CrossRefGoogle Scholar
  14. Falguerolles A (1995) Generalized bilinear models and generalized biplots: some examples. Publications du Laboratoire de Statistique et Probabilites. Universite Paul Sabatier, ToulouseGoogle Scholar
  15. Finlay KW, Wilkinson GN (1963) The analysis of adaptation in a plant-breeding programme. Aust J Agric Res 14:742–754CrossRefGoogle Scholar
  16. Fisher RA, Mackenzie WA (1923) The manurial response of different potato varieties. J Agric Sci 23:311–320CrossRefGoogle Scholar
  17. Gabriel KR (1971) The biplot graphic display of matrices with application to principal component analysis. Biometrika 58:453–467CrossRefGoogle Scholar
  18. Gabriel KR (1998) Generalised bilinear regression. Biometrika 85:689–700CrossRefGoogle Scholar
  19. Galindo MP (1986) An alternative for simultaneous representation: HJ-biplot. Questíio 10:12–23Google Scholar
  20. Gauch HG (1988) Model selection and validation for yield trials with interaction. Biometrics 44:705–715CrossRefGoogle Scholar
  21. Gauch HG (2006) Statistical analysis of yield trials by AMMI and GGE. Crop Sci 46:1488–1500CrossRefGoogle Scholar
  22. Gauch HG, Zobel RW (1996) AMMI analysis of yield trials. In: Gauch HG, Kang MS (eds) Genotype-by-environment interaction. CRC Press, Boca Raton, pp 1–40Google Scholar
  23. Gauch GH, Zobel RW (1997) Interpreting mega-environments and targeting genotypes. Crop Sci 37:311–326CrossRefGoogle Scholar
  24. Gauch HG, Piepho HP, Annicchiarico P (2008) Statistical analysis of yield trials by AMMI and GGE: further considerations. Crop Sci 48:866–889CrossRefGoogle Scholar
  25. Golub GH, Reinsch CH (1970) Singular value decomposition and least squares solution. Numer Math 14:403–420CrossRefGoogle Scholar
  26. Gower JC (1992) Generalized biplots. Biometrika 79:475–493CrossRefGoogle Scholar
  27. Gower JC, Hand D (1996) Biplots. Chapman & Hall/CRC, LondonGoogle Scholar
  28. Gower JC, Harding SA (1988) Nonlinear biplots. Biometrika 75:445–455CrossRefGoogle Scholar
  29. Gower JC, Gardner-Lubbe S, Le Roux N (2011) Understanding biplots. Wiley, New YorkCrossRefGoogle Scholar
  30. Greenacre M (2010) Biplots in practice. BBVA Foundation, MadridGoogle Scholar
  31. Householder AS, Young G (1938) Matrix approximation and latent roots. Am Math Mon 45:165–171CrossRefGoogle Scholar
  32. Kang MS (1988) Using genotype-by-environment interaction for crop cultivar development. Adv Agron 62:199–252CrossRefGoogle Scholar
  33. Kempton RA (1984) The use of biplots in interpreting variety by environment interactions. J Agric Sci 103:123–135CrossRefGoogle Scholar
  34. Leiva V, Hernandez H, Sanhueza A (2008) An R package for a general class of inverse Gaussian distributions. J Stat Softw 26:1–21Google Scholar
  35. Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc A 135:370–384CrossRefGoogle Scholar
  36. R Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. Available at
  37. Samonte SOPB, Wilson LT, McClung AM, Medley JC (2005) Targeting cultivars onto rice growing environments using AMMI and SREG GGE biplot analysis. Crop Sci 45:2414–2424CrossRefGoogle Scholar
  38. Ukkelberg A, Borgen O (1993) Outlier detection by robust alternating regressions. Anal Chim Acta 277:489–494CrossRefGoogle Scholar
  39. Van Eeuwijk F (1995) Multiplicative interaction in generalized linear models. Biometrics 51:1017–1032CrossRefGoogle Scholar
  40. Vicente-Villardón JL, Galindo MP, Blázquez A (2006) Logistic biplots. In: Grenacre M, Blasius J (eds) Multiple correspondence analysis and related methods. Chapman & Hall, New YorkGoogle Scholar
  41. Yan W, Falk DE (2002) Biplot analysis of host by pathogen interaction. Plant Dis 86:1396–1401CrossRefGoogle Scholar
  42. Yan W, Hunt LA (2002) Biplot analysis of diallel data. Crop Sci 42:21–30CrossRefGoogle Scholar
  43. Yan W, Kang MS (2003) GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC Press, Boca RatonGoogle Scholar
  44. Yan W, Kang MS (2006) GGEbiplot. Available at
  45. Yan W, Rajcan I (2002) Biplot evaluation of test sites and trait relations of soybean in Ontario. Crop Sci 42:11–20CrossRefGoogle Scholar
  46. Yan W, Tinker NA (2006) Biplot analysis of multi-environment trial data: principles and applications. Can J Plant Sci 86:623–645CrossRefGoogle Scholar
  47. Yan W, Hunt LA, Sheng Q, Szlavnics Z (2000) Cultivar evaluation and mega-environment investigation based on GGE biplot. Crop Sci 40:597–605CrossRefGoogle Scholar
  48. Yan W, Kang MS, Ma B, Woods S, Cornelius PL (2007) GGE biplot vs. AMMI analysis of genotype-by-environment data. Crop Sci 47:643–655CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Elisa Frutos
    • 1
  • M. Purificación Galindo
    • 1
  • Víctor Leiva
    • 2
    Email author
  1. 1.Departamento de EstadísticaUniversidad de SalamancaSalamancaSpain
  2. 2.Departamento de EstadísticaUniversidad de ValparaísoValparaisoChile

Personalised recommendations