Models for multi-environment yield trials with fixed and random block effects and homogeneous and heterogeneous residual variances

Abstract

Multi-Environment Trials (METs) are used to make recommendations about genotypes at many stages of plant breeding programs. Because of the genotype-environment interaction, METs are usually conducted in various environments (locations and/or years), using designs which involve several repetitions (plots) for each genotype at each environment. The stratification or blocking of plots within each environment enables one to consider part of the variability due to differences between plots. The objective of this study was to see how frequently the problem of heterogeneous variances across environments appears in Peanut Breeding Program METs, and to evaluate the effects of diverse spatial modeling strategies on the comparison of genotype means in each environment. A series of 18 METs in a peanut breeding program with randomized complete block design in each environment were simultaneously adjusted by using 1) classic analysis of variance models (fixed and random block effects); 2) mixed models adjusted with homogenous and heterogeneous residual variances to take into account that experiments conducted in different environments may vary in precision (residual variances). The results suggest that the analysis of variance models with a block design and heteroscedastic errors between locations are more appropriate than their homogeneous residual variance versions.