Multi-environment trials data analysis: linear mixed model-based approaches using spatial and factor analytic models

The analysis of multi-environment trials (MET) data in plant breeding and agricultural research is inherently challenging, with conventional ANOVA-based methods exhibiting limitations as the complexity of MET experiments grows. This study presents linear mixed model-based approaches for MET data analysis. Ten MET grain yield datasets from national variety trials in Ethiopia were used. Randomized complete block (RCB) design analysis, spatial analysis, and spatial+genotype-by-environment (G × E) analysis were compared under linear mixed model framework. Spatial analysis detected significant local, global, and extraneous spatial variations, with positive spatial correlations. For the spatial + G × E analysis, increasing the order of the factor analytic (FA) models improved the explanation of G × E variance, though the optimal FA model order was dataset-dependent. Integrating spatial variability through the spatial + G × E modeling approach substantially improved genetic parameter estimates and minimized residual variability. This improvement was particularly notable in larger datasets, where the number of trials and the size of each trial played a crucial role for presence of spatial variability and strong GxE effects. Additionally, the genetic correlation heat maps and dendrograms provided intuitive insights into trial relationships, revealing patterns of strong positive, negative, and weak correlations, as well as distinct trial clusters. The results clearly demonstrate that linear mixed model-based approaches, especially the spatial + G × E analysis excel in capturing complex spatial plot variation and G × E effects in MET data by effectively integrating spatial and FA models. These insights have important implications for improving the efficiency and accuracy of MET data analysis, which is crucial for improving genetic gain estimation in plant breeding and agricultural research, ultimately accelerating the delivery of high-performing crop varieties to farmers and consumers.