Cross‐Validation in AMMI and GGE Models: A Comparison of Methods

Abstract

In plant breeding, the interaction of genotypes and environments is of major interest for breeders to develop genotypes that are well adapted to target environments. To investigate this interaction, multi‐environmental trials, which are typically laid out as randomized complete block designs (RCBD) or as resolvable incomplete block designs (rIBD) within each environment, are conducted. The analysis of multi‐environmental trials may be done by the AMMI (additive main effects and multiplicative interaction) or by the GGE (genotype and genotype × environment interaction) model. The objectives in the application of these models are (i) to determine the true number of multiplicative terms underlying the data, which is needed to obtain reliable biplots and (ii) to estimate the true genotype–environment means as precisely as possible. Here, the performances of nine different cross‐validation (CV) schemes, some of which represent expectation maximization algorithms, were investigated in terms of the two objectives using simulated RCBD or rIBD data. In some of the CV schemes, one replication of each genotype–environment combination was used for validation, whereas in the other schemes, the validation data consisted of one estimated genotype–environment mean. The performance of the FR test was also investigated for the RCBD data. The results indicate that the CV schemes that sample one replication of each genotype–environment combination outperform the other CV schemes with regard to the two objectives in most scenarios considered. For the RCBD data, the FR test performed similar to the best performing CV schemes.