Stability Analysis: Where Do We Stand?¹

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 X 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.

Nonparametric stability methods for interpreting genotype by environment interaction of bread wheat genotypes (Triticum aestivum L.)

“…In fact, there are several reasons to prefer nonparametric stability models, one being that outlier bias is avoided and no assumptions are needed about the distribution of the data and the second is that nonparametric statistics are easy to use and to interpret. Based on these considerations, it appears that the estimation of stability is an appropriate approach for GEI analysis, this view being supported by the fact that a variety of parametric and nonparametric stability measures have been compared in the literature (Lin et al, 1986;Flores et al, 1998;Sabaghnia et al, 2006).…”

A parsimonious statistical design and breeding procedure for evaluating and selecting desirable characteristics over environments

“…Likewise, its variance in yield over all environments is small. S 11 however, has zero slope and zero variance, which under several proposed stability measures (see Lin et al, 1986) would be optimal. S 2 would also rate high in stability under these measures.…”

“…The standard pedigree and bulk methods (Allard, 1960) would fall somewhere in between. The pedigree method is perhaps more desirable than the bulk method because individual plant selections in the early generations could be focused on parameter traits other than stability (in the sense of Lin et al, 1986). In later generations when family selection is practiced, stability response would be included as a criterion.…”

“…From the literature, it appears that the concept and definition of stability needs considerably more discussion and quantification (Lin et a/., 1986;Verma et a/., 1978). We shall attempt to make our use of this concept more consistent with the objectives of the grower rather than a statistical criterion.…”

Modelo de regressão não-linear aplicado ao estudo da estabilidade fenotípica de genótipos de feijão no Estado do Paraná

“…Para conhecê-la, muitas alternativas foram e têm sido propostas, sendo as mais empregadas as análises de estabilidade fenotípica que fazem uso dos modelos de regressão linear, nos parâmetros (FINLAY e WILKINSON, 1963;EBERHART e RUSSELL, 1966;VERMA et al, 1978;SILVA e BARRETO, 1985;CRUZ et al, 1989;STORCK, 1989). Embora bastante difundidos, esses modelos são passíveis de críticas por incorrerem em alguns inconvenientes de cunho estatístico (EBERHART e RUSSELL, 1966;FREE-MAN e PERKINS, 1971;LIN et al, 1986).…”