Colloquium Biometricum (Online)

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Vol: 33 Page: 147

Authors:

Title:
An empirical comparison of some estimators for stability measures in mixed Shukla’s model and E-R-S joint regression model

Language: English

Keywords:
Summary:
The aim of the paper is: 1) to present theoretical backgrounds for a mixed Shukla’s model and a joint regression model with unequal residual variances called model of Eberhart-Russell–Shukla (E-R-S model), 2) to give the MINQUE estimator of stability variance in Shukla’s model and estimators of regression coefficients, residual variances and determination coefficients obtained by ordinary approximate least squares method (OALS) in E-R-S model for balanced (complete) data of two-way genotype*environment classification, 3) to give the newest concepts of practical using REML method to estimate the above stability measures in both models, as well as 4) to compare and evaluate agreement between estimates of the presented stability measures calculated when using considered estimators for grain yield of spring wheat genotypes grown in three complete multi-location series of variety trials. Estimates of the environmental variance σ_e² were larger 3.8 to 20.6 times than estimates of the interaction variance σ_ge² and larger 30.9 to 75.7 times than mean error variance σ². Accordingly to given by Piepho (1993) some results [presented in this paper in (4.6)], the above relation of variance estimates and a relatively large numbers of genotypes (20 to 25) could guarantee good properties of OALS estimators for stability measures in E-R-S model (4.2). It was proved good agreement between MINQUE and REML estimates of stability variance σ_i² in Shukla’s model for genotypes studied in series 1, 2 and 3. Similarly, there was good agreement between OALS and REML estimates of regression coefficients and other stability measures based on E-R-S model. REML estimators for stability measures in E-R-S model could have as good properties as OALS estimators in a case of a series of variety trials when environmental variance would be larger than residual variances and the number of genotypes would be large (at least about 20), even when the number of environments would not be large (however not less than about 10).