Nonparametric measures of phenotypic stability. Part 2: Applications

Summary The three nonparametric measures of phenotypic stability S_i ⁽¹⁾, S_i ⁽²⁾ and S_i ⁽³⁾ introduced and discussed in Huehn (1990) and the classical parameters: environmental variance, ecovalence, regression coefficient, and sum of squared deviations from regression were computed for winter wheat grain yield data from the official registration trials (1974, 1975 and 1976) in the Federal Republic of Germany.The similarity of the resulting stability rank orders of the genotypes which are obtained by applying different stability parameters were compared using rank correlation coefficients. The correlations between each of S_i ⁽¹⁾, S_i ⁽²⁾ and S_i ⁽³⁾ and the classical stability parameters were different in sign and very low for regression coefficient and environmental variance, but positive and medium for ecovalence and sum of squared deviations from regression (except S_i ⁽³⁾ in 1976). The differences between the correlations for the 3 years were considerable.The parameters S_i ⁽¹⁾ and S_i ⁽²⁾ were very strong intercorrelated with each other with a good agreement of the correlations for the different years. The divergent property of S_i ⁽³⁾ can be explained by its modified definition (confounding of stability and yield level).The previous results and conclusions obtained from the stability analysis of the original uncorrected data x_ij are further strengthened if one uses corrected values % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiwamaaDa% aaleaacaqGPbGaaeOAaaqaaiaabQcaaaGccqGH9aqpcaqGybWaaSba% aSqaaiaabMgacaqGQbaabeaakiabgkHiTiaacIcaceqGybGbaebada% WgaaWcbaGaaeyAaaqabaGccqGHsislceqGybGbaebacaqGUaGaaeOl% aiaacMcaaaa!4724!\{\text{X}}_{{\text{ij}}}^{\text{*}} = {\text{X}}_{{\text{ij}}} - ({\text{\bar X}}_{\text{i}} - {\text{\bar X}}..)\]: The nonparametric stability measures were nearly perfectly associated (even with S_i ⁽³⁾ included) which, of course, implies no significant differences between the correlations of the different years.For the correlations between each of the S_i ⁽¹⁾, S_i ⁽²⁾ and S_i ⁽³⁾ and the classical parameters, very low values were obtained for regression coefficient and environmental variance, but relatively large values for ecovalence and sum of squared deviations from regression.The differences between the correlations for the different years are low for ecovalence and sum of squared deviations from regression with each of S_i ⁽¹⁾, S_i ⁽²⁾ and S_i ⁽³⁾, but these differences are large for regression coefficient and environmental variance. This transformation x_ijx_ij ^* reduced individual and global significances (stability of single genotypes and stability differences between all the tested genotypes) drastically. The significant results for the transformed data indicate a very reliable quantitative characterization of the stability of the genotypes independent from the yield level.