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.