A weighted AMMI algorithm to study genotype-by-environment interaction and QTL-by-environment interaction

Genotype-by-environment (G x E) interaction (GEI) and quantitative trait locus (QTL)-by-environment interaction (QEI) are common phenomena in multiple-environment trials and represent a major challenge to breeders. The additive main effects and multiplicative interaction (AMMI) model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of G x E means. For complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals, thereby implicitly assuming equal weights for all G x E means. However, multiple-environment data with strong GEI are often also characterized by strong heterogeneous error variation. To improve the performance of the AMMI model in the latter situation, we introduce a generalized estimation scheme, the weighted AMMI or W-AMMI algorithm. This algorithm is useful for studying GEI and QEI. For QEI, the W-AMMI algorithm can be used to create predicted values per environment that are subjected to QTL analysis. We compare the performance of this combined W-AMMI and QTL mapping strategy to direct QTL mapping on G x E means and to QTL mapping on AMMI-predicted values, again with QTL analyses for individual environments. Finally, we compare the W-AMMI QTL mapping strategy, with a multi-environment mixed model QTL mapping approach. Two data sets are used: (i) data from a simulated pepper (Capsicum annuum L.) back cross population using a crop growth model to relate genotypes to phenotypes in a nonlinear way, and (ii) the doubled-haploid Steptoe x Morex barley (Hordeum vulgare L.) population. The QTL analyses on the W-AMMI-predicted values outperformed the QTL analyses on the G x E means and on the AMMI-predicted values, and were very similar to the mixed model QTL mapping approach with regard to the number and location of the true positive QTLs detected, especially for QTLs associated with the interaction and for environments with higher error variance. W-AMMI analysis for GEI and QEI provides an easy-to-use and robust tool with wide applicability.