Stability Analysis: Where Do We Stand?¹

TLDR

Stability statistics are categorized into four groups based on whether they rely on deviations from average genotype effect or genotype×environment terms, and whether they include a regression on an environmental index, while similarity measures define complete similarity in three distinct ways. The study investigates the interrelationships among nine stability statistics and nine similarity measures to clarify confusion about their diversity and linkage to genotype clustering for environmental response similarity. The authors examined the interrelationships among nine stability statistics and nine similarity measures through analytical investigation. The study demonstrates that stability can be characterized by among‑environment variance, parallel response to the mean genotype response, or small residual mean square from a regression on an environmental index, yet these concepts differ and do not always provide a complete picture, while the nonparametric cluster approach enables qualitative assessment of cultivar response without mathematical modeling.

Abstract

To clarify the apparent confusion arising from the diversity of published stability statistics, and the relationship of these with the clustering of genotypes for similarity of response to environments, the interrelationship of nine stability statistics and nine similarity measures are investigated. The stability statistics fall into four groups depending on whether they are based on the deviations from the average genotype effect or on the genotype ✕ environment (GE) term, and whether or not they incorporate a regression model on an environmental index. These groups of stability statistics are shown to be related to three concepts: A genotype may be considered to be stable (i) if its among‐environment variance is small, (ii) if its response to environments is parallel to the mean response of all genotypes in the trial, or (iii) if the residual mean square from a regression model on the environmental index is small. Unfortunately, these three concepts represent different aspects of stability and do not always provide a complete picture of the response. In the alternative approach of cluster analysis, the similarity measures define complete similarity in three different ways: i) equality of genotype's response across locations, ii) equality of all within location differences, and iii) equality of all within location ratios. The advantage of the nonparametric approach is that a cultivar's response characteristics can be assessed qualitatively, without the need for a mathematical characterization.