Application of GGE biplot graphs in multi-environment trials on selection of forest trees

Autorzy

• Krzysztof Ukalski Warsaw University of Life Sciences – SGGW, Faculty of Applied Informatics and Mathematics, Department of Econometrics and Statistics, Biometry Division, Nowoursynowska 159, 02-776 Warsaw, Poland
  e-mail: krzysztof_ukalski@sggw.pl
• Marcin Klisz Forest Research Institute, Department of Silviculture and Genetics of Forest Trees
  Sękocin Stary, Braci Leśnej 3, 05-090 Raszyn, Poland

Abstract

In the studies on selection and population genetics of forest trees that include the analysis of genotype × environment interaction (GE), the use of biplot graphs is relatively rare. This article describes the models and analytic methods useful in the biplot graphs, which enable the analyses of mega-environments, selection of the testing environment, as well as the evaluation of genotype stability. The main method presented in the paper is the GGE biplot method (G – genotype effect, GE –genotype × environment interaction effect). At the same time, other methods have also been referred to, such as, SVD (singular value decomposition), PCA (principal component analysis), linear-bilinear SREG model (sites regression), linear-bilinear GREG model (genotypes regression) and AMMI (additive main effects multiplicative interaction). The potential of biplot method is presented based on the data on growth height of 20 European beech genotypes (Fagus sylvatica L.), generated from real data concerning selection trials and carried out in 5 different environments. The combined ANOVA was performed using fixed-effects, as well as mixed-effects models, and significant interaction GE was shown. The GGE biplot graphs were constructed using PCA. The first principal component (GGE1) explained 54%, and the second (GGE2) explained more than 23% of the total variation. The similarity between environments was evaluated by means of the AEC method, which allowed us to determine one mega-environment that comprised of 4 environments. None of the tested environments represented the ideal one for trial on genotype selection. The GGE biplot graphs enabled: (a) the detection of a stable genotype in terms of tree height (high and low), (b) the genotype evaluation by ranking with respect to the height and genotype stability, (c) determination of an ideal genotype, (d) the comparison of genotypes in 2 chosen environments.

Keywords

• AMMI additive main effects multiplicative interaction
• GGE biplot analysis
• multi-environment trial
• PCA principal component analysis
• SVD singular value decomposition
• genotype × environment interaction