Comparison of additive main effect–multiplicative interaction model and factor analytic model for genotypes ordination from multi‐environment trials

Abstract

An additive main effects and multiplicative interaction (AMMI) model is used to explore the genotype × environment interaction (GEI) in complete multi‐environmental trials. This model orders genotypes (G) according to their performance across environments (E) on a vectorial plane generated by the first two axes of a principal component analysis (AMMI‐biplot). Alternatively, interaction terms can be regarded as random effects, which can be predicted from linear mixed models using a factor analytic (FA) covariance structure for the GEI terms. Here, an FA‐biplot was obtained by plotting the G and E scores derived from the FA mixed model with complete and incomplete data. The aim of this work was to compare AMMI‐biplot with FA‐biplot for balanced data and then show the impact of the imbalance on the FA‐biplot. The G ordinations were assessed in four scenarios generated using datasets of 3 consecutive years obtained from comparative wheat trials conducted under a complete random block design in different environments across the Argentine network of cultivar assessment. For each scenario, G with the lowest performance in the third year were deleted, one by one, from all sites to generate a scenario with missing G. Although we used different statistical procedures to obtain AMMI‐biplot and FA‐biplot, they showed the same interaction pattern in the case of up to 50% of G dropped from all E in the last year of the multiyear trials. We conclude that the FA‐biplot yields a robust G ordination even when with incomplete datasets.