Higher Order AMMI (HO-AMMI) analysis: A novel stability model to study genotype-location interactions

Additive main effects and multiplicative interaction (AMMI) model is most widely used to analyse genotype*environment interactions (GEI) wherein interaction effects of location is masked by year effect. Hence, presently available models are not able to estimate interaction effects of genotype*location (GLI) and genotype*year (GYI) separately. Moreover, genotype ranking differs as number of years of evaluation vary making selection of genotype for target location difficult. In the present study we propose a novel stability model i.e Higher-order-AMMI (HO-AMMI) analysis which is capable of calculating GLI without the confounding effect of GYI and GLYI. GEI of AMMI model and all 2-way interactions of HO-AMMI model follow χ2 distribution, whereas 3-way interaction (GLYI) of HO-AMMI follow noncentral χ2 distribution. With increase in number of years of evaluation contribution of GLI towards total variation increased whereas in AMMI model contribution of GEI towards total variation decreased. Variation explained by multiplicative components is higher in HO-AMMI compared to AMMI model. Genotypes were ranked using GL, GY and GL+GY+GLY interactions of HO-AMMI and GEI of AMMI for stability and yield and compared their ranks with field ranking. Correlation and linear regression analysis have indicated high association of GLI (HO-AMMI) with field ranking with high R2 values. Further, HO-AMMI model was able to remove the confounding effect of GYI and GLYI on GLI for accurate identification of genotype for target location irrespective of number of years of evaluation. Hence, HO-AMMI model can be used under multi-environment trials (MET) for selecting genotypes efficiently. Availability and Information Source code implemented in R is available from corresponding author. ### Competing Interest Statement The authors have declared no competing interest. * AMMI : Additive main effects and multiplicative interaction HO-AMMI : Higher-order Additive main effects and multiplicative interaction GEI : Genotype*environment interactions GLI : Genotype*location interaction GYI : Genotype*year interaction GLYI : Genotype\*location\*year interaction LYI : Location*year interaction MET : Multi-environment trials