Interaction effect under ammi model

Abstract

The study of interaction is one of the major objectives of most of agricultural experiments. Conceptually this is done based on regression technique. Among the interactions studied, two factor interaction derives its importance as it is the simplest of the interactions. The joint regression technique is employed to study the G x E interaction. The regression techniques are having the assumption of additivity of effects. When there is departure from these assumption the joint regression technique fails. Additive Main effects and Multiplicative Interaction studies have helped a lot at this juncture. Raju (2002) derived a more comprehensive measure of interaction based on AMMI model. This was achieved using the spectral decomposition of the relevant interaction matrix which enabled the study of interaction with the same precision as that of studying the main effects. Biplots formulations of interaction effects based on the PCA vector scores are the most simplest and explicit representation of interaction.

The study of interaction based on spectral decomposition has been illustrated using the secondary data on the biometric, chemical and qualitative characters from the projects “Development of a bimodal phasic management system to improve both quantity and quality in Kacholam (Kaempferia galanga)” and “Development of a bimodal phasic management system to improve both quantity and quality in Njavara (Oriza Sativa)”.

The DMRT tests for each level of the factors viz., calcium and source were carried out for the parameters viz., percentage content of phosphorus in rhizome, percentage content of potassium in rhizome and North – South foliage spread. In all these characters no specific interaction effect could be sorted out. These interactions when studied based on the factor analytical technique revealed that source II and second level of calcium had the highest positive interaction as regards the percentage content of phosphorus; source III and third level of calcium for percentage content of potassium and source II and third level of calcium for North – South foliage spread.

When the order of the interaction matrix was high as in the case of the second experiment, DMRT tests failed to highlight the appropriate interactive effect in the characters viz., grain yield, percentage content of nitrogen in grain, percentage content of phosphorus in grain, percentage content of phosphorus in straw and percentage content of potassium in straw. The study based on the factor analytical technique revealed that the treatments T15, T8, T3, T1 and T4 respectively had the highest interactive effect with Payyanur for the above said characters where as for Badagara they were T3, T14, T4, T5 and T8 .