Bayesian modeling of heterogeneous error and genotype X environment interaction variances

An important assumption in the analysis of multienvironment cultivar trials is homogeneity of error and genotype X environment interaction variances. When variances are heterogeneous, the best estimators of performance are obtained by weighting inversely to variance components. However, because variances are almost never known and must be estimated, the additional error introduced into the model from estimating many variances may cause weighted estimators to perform poorly. Our objective was to test a Bayesian approach to estimating heterogeneous error and genotype X environment interaction variances. A Bayesian model for multienvironment yield trials that includes a linear model for error and genotype X environment interaction variances was applied to yield data from the Iowa State University Oat Variety Trial for the years 1997 to 2003. The Bayesian approach revealed that error variances were highly heterogeneous among environments and that genotype X environment interaction variances were heterogeneous among environments and genotypes. Incorporation of heterogeneity of variances significantly decreased estimates of marginal error, genotypic, and genotype X environment variance components, with the largest change being a reduction in the marginal genotype X environment interaction variance. Repeatabilities were higher in the heterogeneous variance model but not at a high level of statistical significance. Genotype-specific estimates of genotype X environment interaction variances were correlated with estimated genotypic yields and heading dates, providing biological validity to our estimates of genotype-specific estimators of genotype X environment interaction variances as stability estimators.