Factor Analytic Mixed Model Analysis for Multi-Environmental Trials Data

Abstract

The analysis of multi-environment trials (MET) data is a critical component of plant breeding and agricultural research, providing essential insights into genotype-by-environment (GxE) interactions. However, as the complexity of MET experiments grows, conversional analysis of variance (ANOVA)-based methods can exhibit limitations in accurately capturing the underlying variance-covariance structure of genetic and non-genetic effects. This study presents a factor analytic mixed model (FAMM) approach to the analysis of MET data, using a dataset of grain yield from ten common bean variety trials conducted in Ethiopia. This study investigated the modeling of variance-covariance structure for genotype-by-environment (GxE) effects and residual error in a multi-environment field trial. The inclusion of a model with heterogeneous error variance resulted in a significant improvement in model fit compared to a base GxE model with heterogeneous genetic variance and constant error variance. Factor Analytic (FA) models of increasing order were then fitted, and the first three orders (FA1, FA2, and FA3) showed remarkable improvements in the percentage of variance explained and statistical significance. The FA3 model, which explained 78.12% of the total variance, was determined to provide the best fit between model complexity and explanatory power. Across the ten trial environments, the estimates of genetic variance, error variance, and heritability ranged widely, from 0.008 to 0.984, 0.053 to 0.695, and 65.40 to 89.86, respectively. This highlighted the substantial variability in the underlying genetic and environmental factors influencing the traits of interest. The genetic correlations between environments also varied from negative to positive values, indicating differing levels of consistency in the genetic factors across experimental conditions. These results demonstrate the importance of properly modeling the variance-covariance structure and considering the complex genotype-by-environment interactions when analyzing multi-environment trial data. It is strongly recommended to scale up the utilization of this efficient analysis method to enhance varietal evaluation across diverse environments, and  facilitating the identification of superior varieties.