Exploring opportunities for reducing complexity of genotype-by-environment interaction models

Heterogeneity in genetic effects among environments (G x E) is a common phenomenon in crop plants and can arise from heterogeneity in variance (scale effects) and/or crossover interaction. Here, a study of yield of macadamia progeny in 15 trials established at 9 locations and assessed for yield at 7 years is used to explore the impact on prediction of clonal values (additive + dominance effects) from (i) scaling observations by phenotypic standard deviation of each trial, and (ii) reducing complexity of the pattern of genotype-by-environment interaction. The initial fit of an unconstrained G x E model to unscaled observations indicated significant G x E, which was supported by the fit of the same model to scaled data. Scaling observations reduced heterogeneity of genetic parameter estimates among locations. Clustering of the additive and dominance genetic-by-environment covariance matrices from the fit of G x E models to scaled observations and log-likelihood testing was used to identify reduced models where locations with apparent homogeneous genetic effects (genetic variance not significantly different, and genetic correlations not significantly different from 1) were grouped into single environments. Complexity reduction condensed the additive genetic-by-environment covariance matrix to 3 environments, and 4 environments for the dominance matrix, and the accuracy of parameters estimates increased, although accuracy of prediction as assessed by generalised heritability only improved for a few locations. On the other hand, accuracies of clonal values predicted from a main effects only G + E model were lower. Nevertheless, correlations of the averages of predicted clonal values across locations from different models were very high suggesting models are robust to parameter estimates. These results support the use of scaling by the phenotypic standard deviation to reduce heterogeneity in parameter estimates, and complexity reduction to improve accuracy of estimating parameters required to predict genetic effects.