Genotype Plus Genotype × Block of Environments Biplots

ABSTRACT Biplots have been widely used in recent years for the analysis of multi‐environment trials through the genotype plus genotype × environment (GGE) biplot analysis or through the additive main effects and multiplicative interaction analysis. Sometimes the environments are structured in blocks of environments, for example, regions or years. In this paper, we propose a new biplot technique for describing genotype × environment interactions that takes into account this additional information. We call it a GGB biplot for genotype plus genotype × block of environments biplot. This biplot has interesting geometrical properties that will be covered in this paper. Similarly to what was done for the GGE biplot (Laffont et al., 2007), we also establish a link between the partitioning of the total sum of squares provided by the GGB biplot and the partitioning provided by the analysis of variance. Simulated and real data are used to illustrate this new biplot.