A hierarchical Bayesian model for dynamic phenotypes in multi-environment trials with genotype by environment interaction

New phenotyping tools produce longitudinal phenotypes that describe plant growth and development. Estimates for the parameters that describe the dynamics of such longitudinal phenotypes can be incorporated as predictors in models for static target traits like yield and biomass. Within a hierarchical Bayesian context, we present a differential equation (DE) model for log-logistic growth in longitudinal traits for sets of genotypes across multiple environments. The DE parameters coincide with a midpoint, a slope, and an asymptote at the end of growth and development, i.e., final biomass. Each DE parameter in our hierarchical model results from contributions of genotype, environment, and G × E. This formulation allows one to assess and quantify the genotype-specificity of the DE parameters. When none of the DE parameters in our model requires a G × E term, the dynamic parameters characterizing the particular trait will be useful features for inclusion in prediction models for yield or biomass. We fitted a DE model to APSIM-simulated longitudinal wheat biomass data and quantified the contribution of genotype, environment and G × E to the phenotypic variation in the DE parameters. Only the upper asymptote showed clear G × E. Estimates for genotypic and G × E parameters within the DE parameters were used to characterize genotypes. Estimates for environmental and G × E effects formed inputs for environmental characterization.