A weighted AMMI algorithm for nonreplicated data

The objective of this work was to propose a weighting scheme for the additive main effects and multiplicative interactions (AMMI) model, as well as to assess the usefulness of this W-AMMI model in the study of genotype x environment interaction (GxE) and quantitative trait locus x environment interaction (QxE) for nonreplicated data. Data from the 'Harrington' x TR306 barley (Hordeum vulgare) mapping population, with 141 genotypes evaluated in 25 environments, were used to compare the results from the AMMI model with those of two proposed versions of the W-AMMI model: equal weights per row and equal weights per column. The proposed W-AMMI columns algorithm is viable to analyze data with heterogeneous variance, when there are no replicates available. The use of the AMMI and W-AMMI models, in the indicated cases, improves QTL detection, besides providing a sound interpretation of GxE and a better understanding of QxE, which allows obtaining valuable information on increasing productivities in different environments.