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NONPARAMETRIC METHODS IN COMBINED HETEROSCEDASTIC EXPERIMENTS FOR ASSESSING STABILITY OF WHEAT GENOTYPES IN PAKISTAN

SYED HAIDER SHAH¹, SYED MUNAWAR SHAH², M. INAYAT KHAN³, MAQSOOD AHMED⁴, IMDAD HUSSAIN⁵ AND K. M. ESKRIDGE⁶

Abstract: Genotype performance in multienvironment trials (METs) are usually analyzed by parametric analysis of variance (ANOVA) and stability models. The results of these models can give misleading inferences when some sensitive assumptions are not satisfied. In this paper, assumptions of combined ANOVA are scrutinized in detail to justify the validity of use of 5 nonparametric stability methods (S_i⁽¹⁾, S_i⁽²⁾, S_i⁽³⁾, S_i⁽⁶⁾ and YS_i⁽¹⁾, YS_i⁽²⁾) applied to 20 genotypes grown in 40 hetroscedastic and nonnormal  environments in Pakistan for the year 2004-05. There is a severe heterogeneity problem in the data because the ratio of the largest estimated mean squares error (MSE) for individual environments randomized complete block design (RCBD) to the smallest MSE is approximately (1.00/0.02=50). Out of 40 environments individual coefficients of determination (R²), 27 are less than 0.70. This leads to violation of linearity assumption in the model. Standardized residual plots vs. individual environments plots and normal probability plot are indicators of the violation of homogeneity, normality assumptions and absence of outliers. No linear relationship was established between the natural logs of the error variance and the natural log of environments’ mean, which again violates coefficient of variation (CV) assumption. Remedial transformations as suggested in literature were not successful to stabilize environments MSEs and could not normalize the data, so as a last resort in this regard nonparametric stability methods seem to justify the analysis of genotype x environment interactions (GEI). The low values of modified rank-sum statistics YS_i⁽¹⁾ and YS_i⁽²⁾ were positively and significantly associated with mean yield but the other nonparametric methods were not correlated with mean yield. The results of principal component analysis and correlation analysis of nonparametric stability methods indicate that the use of modified rank-sum method would be justifiable for simultaneous selection for high yield and stability. Using modified rank-sum method, the genotypes G7, G3, G15, G5 and G12 were found to be the most stable with yield, whereas G14 and G19 were the least stable genotypes.

¹Department of Statistics, University of Balochistan, Quetta, Pakistan

²Department of Economics, Balochistan University of Information Technology, Engineering and Management Sciences, Quetta, Pakistan

³Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan

⁴Department of Environmental Management and Policy, BUITEMS, Quetta, Pakistan

⁵Department of Business administration, Iqra University, Karachi, Pakistan

⁶ Department of Statistics, University of Nebraska, Lincoln, USA