sufficient for predicting heterosis. The genetic markers used here and in most other studies however are far from representing a complete coverage of the entire genome. On the other hand, in our study, individual genetic markers contain much information on the neighbouring regions, since we investigated a RIL population. Each line carries on average 1.86 recombinations per chromosome, and the average length of segments of a certain parental origin is 32.06 cM [23]. As illustrated by the slow decay of linkage disequilibrium among markers, the information carried by individual markers decreases only slowly with increasing distance. Consequently, strong individual gene effects, which are independent of other genes, should be reflected by our genetic markers, i.e. their effects should be recognised as effects of the marker alleles closely linked in coupling. However, in those cases where many genes are involved, genetic markers will not provide much information, especially if each gene contrib- utes only a minor effect, which, in addition is depending on other genes (i.e. when epistasis has a high influence). In this situation, more integrated markers, such as metabolite levels, will contribute a decisive part of information, since they reflect the combined effect of many genes. In our analysis, metabolic markers turned out to carry information on heterosis that is complementary to the genetic markers’ information. Therefore, one should assume that epistatic gene effects are actually involved in heterosis. This is consistent with recent analyses which indicate a strong role for epistasis in the manifestation of heterosis in Arabidopsis [24,25]. Heterosis Prediction Markers Concerning an effective genetic heterosis prediction model, the complex trait thus would require to be modelled via complex nonlinear interactions of the different genetic markers. Since we know little concerning gene-gene interactions in relation to their influence on the trait of our interest, too many possibilities exist for modelling such a nonlinear phenomenon. Thus, nonlinear gene interactions should be integrated indirectly by using metabolic markers. This is very simple to model, since this approach essentially follows a linear combination of genetic and metabolic markers (cf. Figure 5). Nevertheless, this simple combined model appears to cover at least some parts of the complex gene-gene interactions, which are not yet captured by linear combinations of the available genetic markers, indicated by its significantly increased predictive power. Parental biomass, as an even more integrated variable than metabolite levels, is a strong but not a steady predictor for heterosis Biomass is an integrated variable reflecting the action (and thus presence) of many, if not all, genes of the respective genotype. We therefore expected, following the argument used for metabolic markers, that the RILs’ biomass as additional predictor is even more valuable. Actually, just like metabolic markers (cf. Table 1), the RILs’ biomass alone holds some considerable information on heterosis. Namely, RILs with a low biomass tend to have a higher potential for heterosis effects and vice versa, which is indicated by a negative Figure 5. Simplified display of the idea behind the modelling for the different predictor sets. The chain of causality from genes to phenotype is displayed here. Since genes are at the starting point of the causal chain, one established way to model a phenotype Y is to use genetic markers X and combine them linearely (genetic model in red). Using instead predictor variables Z, which are close to the phenotype, such as metabolites, presents another promising way to predict a complex phenotype, since those variables integrate already parts of the complex gene interactions (represented by products Xi*Xj). The advantage is that we do not need to know, which genes actually interact in which way, and that the model can stay simple. It just linearely combines metabolite variables, thus integrating non-linear interactions indirectly (metabolite model in blue). In the end, one might use a combination of both approaches, i.e. combining different levels of the causal chain, to explain as much as possible of the complex phenotype. Hence one integrates linear relationships concerning the response as well as non-linear gene interactions, while sticking to the simple model ansatz of a linear combination of genetic predictors X and metabolite variables Z (combined model in violet). doi:10.1371/journal.pone.0005220.g005 PLoS ONE | www.plosone.org 7 April 2009 | Volume 4 | Issue 4 | e5220