Comparative BLUP-GGE Biplots from Linear Mixed Model and Factor-Analytic LMM for Grain Yield in Unbalanced Multi-Environment Wheat Trials

Data imbalance is common in multi-environment trials (METs) and complicates genotype and environment evaluations. To address this, linear mixed models (LMMs) and factor-analytic linear mixed models (FA-LMMs) were employed to estimate best linear unbiased predictions (BLUPs) for genotype effects. The highly unbalanced wheat grain yield data from the 2021–2025 national regional trials in the Northern Winter Wheat Region (NWWR) served as our case study. These BLUP values were then integrated into the genotype plus genotype-by-environment interaction (GGE) biplot framework to construct BLUP-GGE biplots. Subsequently, these biplots were systematically compared in terms of genotype evaluation, environment evaluation, and mega-environment delineation. Based on Akaike Information Criterion (AIC) and cross-validation, FA2 was chosen as the representative FA-LMM for comparison with LMM. For genotype evaluation, the two biplots produced highly consistent rankings. Based on the FA-LMM output, the top five genotypes were BH5318, BH2605, BH7868, JD39, and ZM8729. For mega-environment delineation, both approaches consistently identified one major and one minor mega-environment, with eight and three environments, respectively. The FA-LMM-based biplot provided clearer separation between them. For environment evaluation, the two biplots showed highly significant correlations for discriminating ability, representativeness, and desirability index. Luannan ranked first, followed by Zunhua, Baodi, Gu’an, Changping, and Shunyi, Xushui and Wuqing were intermediate, while Taiyuan, Tunliu, and Qixian performed relatively poorly. In summary, both methods are effective and reliable for analyzing highly unbalanced MET data, and show high consistency in genotype and environment evaluation. However, the FA-LMM-based BLUP-GGE biplot provides superior goodness-of-fit and more precise mega-environment delineation.