Heterogeneity of error variance and its influence on genotype comparison in multi-location trials

Multi-location trials play an important role when evaluating genotypes at many stages of plant-breeding programs, as well as when recommending varietal plant production. The most common procedure for analyzing these trials is based on the assumption that the residual error variance is homogenous across all considered locations. However, this may often be unrealistic, and therefore limit the accuracy of genotype evaluations or the reliability of varietal recommendations. The objectives of this study were to investigate how frequently and how seriously the problem of heterogeneous variances appears across locations in multi-location trials, and to evaluate the impact of the analytical procedure with different considerations about error variations when comparing genotype effects. A series of 16 multi-location trials from a corn-breeding program in the north of China were simultaneously analyzed from 2005 to 2008 using a randomized complete block design at each location; the analysis used models with homogeneous residual variances, as well as models with heterogeneous residual variances to take into account that different locations may have different levels of precision. The results showed that the residual error variances strongly varied across locations in all of the considered trials. The model with heterogeneous residual error variances was significantly (α < 0.001) more appropriate than the one with homogeneous error variances in all of the trials for both fixed and random locations, according to model fitting statistics. Ignoring error variance differences across locations in the analysis procedure of multi-location trials could result in a large Type I error rate for comparisons (F-test) of the main effect of genotypes, especially in case of random location main effects and genotype-location interactions, locations, and genotype-location interactions, as well as an inflation or deflation of statistical Type I error rates for comparisons (t-test) of simple genotype effects depending on specific locations.