Heterosis Prediction Markers Figure 2. Predictive power of genetic (A, B), metabolic (C, D) and combined (E, F) marker sets for C24- and Col-heterosis. The diagrams shown here demonstrate the trade-off between overfitting and loss of information in the different models. The x-axis represents the number of predictors used to train the respective model. Red dots display the predictive power of the particular model in leave-one-out validation (LOOV). Panel A, C and E correspond to C24-heterosis, the remaining ones to Col-heterosis. The number of predictors, which maximizes the predictive power, is referred to as Opt, and it differs in the various models. In each case, the predictive power decreases by incorporating too many predictors in the corresponding model. This effect is due to overfitting. On the other hand, loss of information occurs, if too few predictors are selected in the model. Min refers to the minimal number of predictors that does not yet imply a significant loss of predictive power. The corresponding predictive power is still within the estimated confidence interval (gray lines) of the maximal predictive power. Black dots demonstrate the estimation of these confidence intervals. They represent the predictive power of the optimal predictor set when using jackknife resampled data (cf. Methods section for details). doi:10.1371/journal.pone.0005220.g002 specific importance with respect to Col-heterosis prediction (cf. Table 2). On the other hand, fourteen metabolic markers were identified as important for heterosis prediction irrespective of the parent (cf. Table 2). Five of the latter display metabolic QTL again at top of chromosome 4, including cellobiose and propanoic acid [22]. When comparing different metabolic markers concerning the distribution of their levels among the 359 RILs, it becomes obvious that the highly predictive markers tend to deviate from normal distributions (cf. Figure 4). The distribution is bimodal in the case of the most important metabolic markers, in other cases it is just too broad at the basis to pass for a single normal distribution. The deviation from a normal distribution seems to abate with decreasing importance of the metabolite in the prediction models (cf. Figure S1). Discussion Combination of genetic markers with metabolite markers leads to a significant improvement of heterosis prediction, which implies the existence of epistatic gene effects As shown in the Results section, the combined use of selected genetic and metabolic variables of the RIL population leads to a significant improvement of the predictive power for the heterosis effect observed in the progeny of both test parents, i.e. the C24 and the Col-0 testcrosses. The cause of this can at least partially be rationalised. It can be assumed that heterosis is primarily, if not exclusively, dependent on the match of the two alleles (or sets of alleles) derived from both parents, suggesting that complete genetic information should be Figure 3. Discrete VIP of genetic markers for Col-heterosis and C24-heterosis prediction, including overlap with QTL. Each of the 110 genetic markers and its position on a Chromosome (Chr) is represented by two circles. The circle size indicates high (large circles), medium and low (small circles) VIP in the genetic model for Col-heterosis (circle left of chromosome) and C24-heterosis prediction (circle right of chromosome). We refer to the VIP as high and medium, if the corresponding marker is contained in the minimal genetic model and in the optimal genetic model, respectively. Markers specific for Col-heterosis prediction and those specific for C24-heterosis prediction are coloured in dark blue and in light blue, respectively. To allow positional comparison, support intervals of biomass QTL and three kinds of heterosis related QTL detected by Meyer et al. (2008, submitted) are plotted as coloured boxes along the chromosomes (grey: biomass, green: Z2 [40], dark blue: absolute mid-parent heterosis concerning Col-0, referred to as aMPH_Col, light blue: absolute mid-parent heterosis concerning C24, referred to as aMPH_C24). Horizontal lines represent the position of genes directly involved in reactions including metabolites, which are contained in the respective minimal metabolite model and the combined genetic-metabolic model (Col: left of chromosomes, C24: right of chromosomes). For specific metabolites genes were coloured accordingly. doi:10.1371/journal.pone.0005220.g003 PLoS ONE | www.plosone.org 5 April 2009 | Volume 4 | Issue 4 | e5220