Various Genotype-by-Environment Biplots

Various Genotype-by-Environment Biplots

Although we have recommended using a GGE biplot in studying genotype-by-environment tables, there are other types of biplots that have been used in studying such data (DeLacy et al., 1996). All biplots can be useful as long as they are interpreted correctly. Some comparisons of six types of GE-containing biplots are briefly given below.

The COMM biplot, based on the completely multiplicative model (i.e., SVD of the original two-way table without centering). This biplot contains E, G, and GE, and is often inflated with the grand mean. This biplot is useful for visualizing the real data but is effective only when the grand-mean is close to 0, as in the case of the covariate-effect biplot. Such a biplot can be generated using GGEbiplot by setting Centering = 0.

The SHMM biplot, based on the shifted multiplicative model (Cornelius et al., 1996). This biplot also displays a mixture of E, G and GE, but can be inflated by the shifting factor. GGEbiplot does NOT generate the SHMM biplot because GGE biplots are more effective in addressing the crossover issue, for which SHMM was specifically developed.

The PCA biplot, based on SVD of grand mean-centered (Centering = 1)genotype-by-environment data (Zobel et al., 1988). This biplot contains E, G, and GE, with E often predominating over G and GE. This biplot is least useful. (NOTE BUT: usually PCA biplot are GGE biplots; the terms used here followed Zobel et al 1988 but it is confusing)

The GE biplot or AMMI2 biplot, based on SVD of double-centered (Centering = 3) genotype-by-environment data (Gauch, 1992). Since G and E are removed prior to SVD, it displays GE only. This biplot is useful for visualizing gene expression data (Chapman 2002).

The AMMI1 biplot, plotting genotype and environment main effects against interactive PC1 scores (Gauch, 1992). This "biplot" displays E, G and GE but usually explains more variation. It does not have the interpretation of a normal biplot, however.

The GGE biplot, based on SVD of environment-centered (Centering = 2) or standardized genotype-by-environment table. As its name suggests, the GGE biplot displays G and GE (Yan et al., 2000).

For more detailed comparison between GGE biplots and AMMI biplots, see Yan et al.(2007, Crop Science).