Reduced-rank random regression for improved yield prediction across the Australian wheatbelt

Predicting complex traits like yield in new environments is challenging due to genotype-by-environment interactions (GEI). Environmental covariates (ECs) can improve prediction by describing environmental variation relevant to GEI. However, approaches that model genotype-specific responses to one or multiple ECs can become highly parameterized and difficult to fit because of the need to estimate complex covariance structures. In addition, EC-based prediction methods typically assume that future environmental conditions are known. Building on recent work, we extended a reduced-rank factor-analytic random-regression (RR) framework to enable simultaneous fitting of multiple ECs and higher-order polynomial responses. We further incorporated uncertainty in estimated reaction norms together with historical multivariate variation in ECs, addressing a realistic breeding scenario in which future EC values are unavailable. We applied the models to eight years of grain-yield data from the Australian National Variety Trials network (935 trials), spanning a wide range of environmental conditions. Using leave-one-year-out cross-validation, multi-EC RR achieved median predictive ability >20% higher than standard compound-symmetry models (CS) and up to 30% higher than single-EC RR. Extending the models to borrow information across regions further increased median predictive ability by up to four percentage points. Moreover, standard errors of prediction relative to mean yield were reduced by up to four-fold relative to models without ECs. Thus, our extended RR framework provides an effective approach for modelling GEI, delivering accurate predictions and explicit uncertainty quantification using a small set of biologically informative ECs and offering an interpretable alternative or complement to large-scale enviromic and machine-learning approaches.