Deducing hybrid performance from parental metabolic profiles of young primary roots of maize by using a multivariate diallel approach

Abstract

Heterosis, the greater vigor of hybrids compared to their parents, has been exploited in maize breeding for more than 100 years to produce ever better performing elite hybrids of increased yield. Despite extensive research, the underlying mechanisms shaping the extent of heterosis are not well understood, rendering the process of selecting an optimal set of parental lines tedious. This study is based on a dataset consisting of 112 metabolite levels in young roots of four parental maize inbred lines and their corresponding twelve hybrids, along with the roots' biomass as a heterotic trait. Because the parental biomass is a poor predictor for hybrid biomass, we established a model framework to deduce the biomass of the hybrid from metabolite profiles of its parental lines. In the proposed framework, the hybrid metabolite levels are expressed relative to the parental levels by incorporating the standard concept of additivity/dominance, which we name the Combined Relative Level (CRL). Our modeling strategy includes a feature selection step on the parental levels which are demonstrated to be predictive of CRL across many hybrid metabolites. We demonstrate that these selected parental metabolites are further predictive of hybrid biomass. Our approach directly employs the diallel structure in a multivariate fashion, whereby we attempt to not only predict macroscopic phenotype (biomass), but also molecular phenotype (metabolite profiles). Therefore, our study provides the first steps for further investigations of the genetic determinants to metabolism and, ultimately, growth. Finally, our success on the small-scale experiments implies a valid strategy for large-scale experiments, where parental metabolite profiles may be used together with profiles of selected hybrids as a training set to predict biomass of all possible hybrids.

Figure 1. Hybrid class label matrix.

The hybrid class label matrix is established using moderated t-statistics (cf. Methods). It shows the observed metabolite heterosis mode of action in all hybrids. Metabolites with unbalanced class labels (e.g. predominantly showing similar class, upper 53 rows) were excluded before conducting classification methods. Various classification methods were used on parental metabolite data to investigate which parental metabolites allow to predict the observed classes within hybrids.

Figure 2. Ranking of the parental features.

Parental metabolite levels (224 features in total) are used to predict the observed class labels of 54 hybrid metabolites. In each prediction model all features can be ranked according to their weights. The ranks are scaled between 0 and 1 by dividing by the total feature number. The scaled median rank distribution of a feature, i.e. the individual boxes in the plot, then gives an estimate regarding the importance of the absolute parental level of the respective metabolite on the heterosis pattern of all hybrid metabolites.

Figure 3. Prediction evaluation.

The correlation between observed and predicted HP in models incorporating 5 metabolites. The metabolites have been selected based on a previous ranking (cf. Figure 2). It can be seen that good prediction accuracies are only obtained for high ranked metabolites and not for low ranked metabolites, which perform comparable to permuted data sets. Metabolite input matrices X_pp were established as described in Methods.