Capturing the Heterogeneity of the Error Variances of a Group of Genotypes in Crop Cultivar Trials

Appropriate experimental designs provide an efficient estimate of cultivar performance by allowing better control of experimental error. The standard approach assumes homogeneity of experimental error variances across plots. However, a given trial may involve genotypes having different scales of response and/or associated with plots with different error variances. This study on cereal and legume trials detected the heterogeneity of the error variances associated with genotypes or groups of genotypes. A hierarchical clustering method, using absolute plot residuals, was used to group the genotypes. The heterogeneity of the error variances was determined using the difference in the deviances resulting from models based on an assumed homogeneity and heterogeneity of the error variances and on an adjusted level of significance for the chosen threshold for cluster formation. The efficiency of pairwise genotype comparisons, based on heterogeneous error variances, ranged from 105 to 116% for the cereals and from 124 to 254% for the legumes. Variations in the estimates of heritability and genetic gain resulting from selection were substantial. Accounting for the heterogeneous error variances, on average, led to higher estimates of heritability and genetic gain in each of the crop trials examined. This study found that heterogeneous variance, varying with the groups of genotypes, was frequent. The approach presented here is recommended for the analysis of cultivar trials.