Phenotypic stability via ammi model with bootstrap re-sampling

Abstract

Reliable evaluation of the stability of genotypes and environment is of prime concern to plant breeders, but the lack of a comprehensive analysis of the structure of the GE interaction has been a stumbling block to the recommendation of varieties. The Additive Main Effects and Multiplicative Interaction (AMMI) Model currently offers the good approach to interpretation and  understanding of the GE interaction but lacks a way of assessing the stability of its estimates. The present contribution proposes the use of bootstrap resampling
in the AMMI Model, and applies it to obtain both a graphical and a numerical analysis of the phenotypic
stability of 20 Eucalyptus grandis progenies from Australia that were planted in seven environments in the Southern and Southeastern regions of Brazil. The results showed distinct behaviors of genotypes and
environments and the genotype x environment interaction was significant (p value < 0.01). The bootstrap coefficient of stability based on the squared Mahalanobis distance of the scores showed that genotypes and environments can be differentiated in terms of their stabilities. Graphical analysis of the AMMI biplot provided a better understanding of the interpretation of phenotypic stability. The proposed AMMI bootstrap eliminated the uncertainties regarding the identification of low scores in traditional analyses.