Mixed-Model Analysis of Crossover Genotype-Environment Interactions

Abstract

Genotype–environment interactions (GEI) are important in crop improvement if genotype ranks change across environments. Current tests for crossover (rank changing) interactions (COI) assume that effects are all fixed or all random. The objective of this study was to develop a new test for COI under the model with a mixture of fixed and random genotypic, environmental, and GEI effects. The key part of this new test is that the difference between a pair of genotypes at a random environment or the difference between a pair of environments for a random genotype involves the linear combinations (predictable functions) of both best linear unbiased estimates (BLUEs) of fixed effects and best linear unbiased predictors (BLUPs) of random effects. The predictable functions are used in the same way as the usual estimable functions for the fixed effects in hypothesis testing except that the BLUPs of random effects are adjusted by accounting for the uncertainty arising from the distributions of these effects. Strategies are proposed to implement the procedure using the SAS system. The procedure was used to analyze barley (Hordeum vulgare L.) and field pea (Pisum sativum L.) cultivar trials. The analyses show that treating random effects as fixed, as may happen with previous analysis procedures, results in detection of more COI than mixedߚ or random-effect models. Therefore, significant COI may be overemphasized when random GEI effects are treated as fixed.