Increasing Selection Response by Bayesian Modeling of Heterogeneous Environmental Variances

Heterogeneity of nongenetic variances among genotypes reduces selection response because high‐variance genotypes are more likely to have means in the tail of the distribution and thus more likely to be selected than low‐variance genotypes. The bias towards high‐variance genotypes is difficult to correct in selection programs because nongenetic variances must be estimated for each genotype with small sample size per genotype. We have tested a Bayesian approach to modeling heterogeneous variances among genotypes to test whether the Bayesian approach provides sufficient correction for variance heterogeneity to improve selection response. Data were simulated using a broad range of parameters and analyzed with a heterogeneous‐variance model and homogeneous‐variance model using Bayesian estimation. Selection was performed at intensities of 3.125 and 12.5% on the basis of Bayesian estimates of genotypic values with simulated data. Parameter values for heterogeneity of variances were chosen from previously published analyses of cultivar trials in maize ( Zea mays L.) and oat ( Avena sativa L.) in Iowa. With four to eight replications (i.e., four to eight environments with one replicate per environment) and intense selection, we estimated that modeling of heterogeneous variances with Bayesian estimation could increase selection response by up to 15%.