Application of the GGE biplot to Application of the GGE biplot to - PowerPoint PPT Presentation

Application of the GGE biplot to Application of the GGE biplot to evaluate Genotype, Environment evaluate Genotype, Environment and GxE interaction on P. radiata: a and GxE interaction on P. radiata: a case study case study Meimei Ding, Bruce Tier and Weikai Yan Meimei Ding, Bruce Tier and Weikai Yan 11. 04. 2007 11. 04. 2007

GGE biplot Application GGE biplot Application GGE biplot analysis was developed by GGE biplot analysis was developed by W. Yan (2000). W. Yan (2000). Basic functions: Basic functions: - “which “which- - won won- - where" pattern (specific where" pattern (specific - genotypes recommended to specific genotypes recommended to specific environments). environments). - Interrelationship between the trials Interrelationship between the trials - - genotype evaluation (the mean genotype evaluation (the mean - performance and stability) performance and stability) - ranking G and E ranking G and E -

Mathematic model Mathematic model The model based on singular value decomposition The model based on singular value decomposition (SVD) of first two principal components is: (SVD) of first two principal components is: − µ − β = λ ξ η + λ ξ η + ε Y ij j 1 i 1 j 1 2 i 2 j 2 ij where is the measured mean (DBH) of genotype i where is the measured mean (DBH) of genotype i Y µ ij in environment j, is the grand mean, is the main in environment j, is the grand mean, is the main β effect of environment j, being the mean yield effect of environment j, being the mean yield j λ λ across all genotypes in environment j, and are across all genotypes in environment j, and are 1 2 the singular values (SV) for the first and second the singular values (SV) for the first and second principal components (PC1 and PC2), respectively, principal components (PC1 and PC2), respectively, ξ ξ and are eigenvectors of genotype i for PC1 and and are eigenvectors of genotype i for PC1 and i 1 i 2 η η PC2, respectively, and are eigenvectors of PC2, respectively, and are eigenvectors of 1 j 2 j ε environment j for PCl and PC2, respectively, is the environment j for PCl and PC2, respectively, is the ij residual associated with genotype i in environment j. residual associated with genotype i in environment j.

Model Model − − β = + + ε Y u g e g e ij j i 1 1 j i 2 2 j ij λ − = λ ξ = η 1 f f e g l l lj l lj il l il and are PC scores for genotype i and e and are PC scores for genotype i and g lj il environment j, respectively. environment j, respectively. f where is the partition factor for . where is the partition factor for . PCl l f Theoretically, can be a value between 0 Theoretically, can be a value between 0 l and 1, but 0.5 is most commonly used. and 1, but 0.5 is most commonly used.

Results “which- -won won- -where” where” Results “which The first two PCs explain 54.5% : PC1=30.4% PC2=24.9%

Relationship among environments Relationship among environments

Family performance and stability Family performance and stability ideal genotype

Examine genotypes Examine genotypes

Examine environment Examine environment

Discussion and conclusions Discussion and conclusions Jointly use the function of classical GxE Jointly use the function of classical GxE interaction methods. interaction methods. Visually reveal the patterns of GxE interaction. Visually reveal the patterns of GxE interaction. Superior to additive main effects and Superior to additive main effects and multiplicative interaction (AMMI), there are multiplicative interaction (AMMI), there are more visual interpretations. more visual interpretations. Superior to joint regression, not only show the Superior to joint regression, not only show the mean performance and stability, but also show mean performance and stability, but also show the genotype group’s favourite environments. the genotype group’s favourite environments. Visually show the interrelationship between the Visually show the interrelationship between the trials. trials.

Discussion and conclusions Discussion and conclusions GGE biplot analysis may explain only GGE biplot analysis may explain only a small part of total GGE, PC1 and a small part of total GGE, PC1 and PC2 may be insufficient to explain PC2 may be insufficient to explain the GGE. the GGE. Does not have a serious statistical Does not have a serious statistical test. test. Advocate being backed by formal Advocate being backed by formal statistical analysis with integrating statistical analysis with integrating the elegant approach. the elegant approach.