metabolic markers, i.e. relative levels of particular metabolic compounds, with regard to their predictive power for biomass heterosis in the plant model organism Arabidopsis thaliana. The reason for choosing these predictors is that metabolite levels are the result of more genes than those represented by genetic markers, and as a rule they are also influenced by several genes and/or their products. As shown in the Results section, the predictive power of genetic data for heterosis is significantly improved by combining it with metabolic measurements of one parent, suggesting complex mechanisms underlying heterosis. Finally, when analyzing the minimal set of metabolic and genetic markers needed for heterosis prediction in the two different testcross populations used, three classes can be identified. Firstly, there are markers highly predictive in both kinds of testcross combinations, secondly, we find markers specifically predictive for one kind of testcross combination, and there are also markers negligible in any of our prediction models. Results Design of the experiment and analysis As described in the Introduction, heterosis levels are a function of the two parental lines used to produce the offspring. Classical heterosis experiments are performed between two completely different parental lines, which have been inbred to a high degree and are essentially homozygous, resulting in a highly heterozygous F1 offspring. We here deliberately chose a different and genetically simpler experimental set-up as a first step towards investigation of the information carried by metabolic markers in comparison to, or in combination with, molecular genetic markers. To this end, a recombinant inbred line (RIL) population consisting of 359 lines derived from a cross between the two Arabidopsis thaliana accessions C24 and Col-0 [17] was used. The mean frequency of C24 alleles and Col-0 alleles per RIL was 48% and 50%, respectively. The remaining fraction comprised heterozygous regions and a few missing values (cf. Methods section for details). The 359 RILs served as one parental population. They were backcrossed with both, the C24 and the Col-0 accessions, resulting in a total of 718 testcross-progeny. Heterosis Prediction Markers The analysis of a full or half diallele involves crosses among numerous lines with different degrees of relatedness, and in each cross only a subset of the genetic factors responsible for heterosis might be shared with any other cross. In contrast to that, in our much simpler experimental design one parent was kept constant (C24 and Col-0 respectively, cf. Figure 1). Consequently, we were able to use prediction models which consider just the metabolic/ genetic markers of the particular RIL parent, since those of the second parent are constants. We merely had to distinguish the two different response effects C24-heterosis and Col-heterosis, i.e. the relative biomass gain when a RIL is backcrossed to C24 and Col- 0, respectively. In that way, we were able to detect not only markers for heterosis prediction, but also factors which are involved in heterosis in only one particular testcross setting, for instance in Col-0 testcrosses. Such Col-heterosis specific markers hold the potential to reveal loci with dominance for C24 or overdominance effects, whereas C24-heterosis specific markers indicate dominance for Col-0 or overdominance. To determine the degree of heterosis displayed in the two different testcross set-ups, biomass was measured in the testcross- progeny and compared to the mean of the biomasses of the two corresponding parental lines (cf. Figure 1). Thus the relative mid parent heterosis was observed to vary from approximately 236 per cent to 99 per cent depending on the parental lines used. Analyses of the genetic markers and the metabolic profile of the RIL population have been described previously [17–19]. For training and evaluating the prediction models, we applied a partial least squares (PLS) approach [20], using a leave-one-out validation (LOOV) test (cf. Methods section for details). Using all available genetic or metabolic markers for heterosis prediction leads to an overfitting problem In a first approach we compared the whole set of available genetic versus metabolic markers according to their suitability for heterosis prediction. Applying PLS-modelling on all 110 genetic markers, the Pearson correlation between observed and in cross- validation predicted heterosis was 0.39 for the C24 crosses and 0.35 for the Col-0 crosses. Using, on the other hand, all available Figure 1. Rationale of the experimental outline. The experimental set-up comprised the two Arabidopsis thaliana accessions C24 and Col-0, which served one at a time as the first parent of the testcrosses. One of 359 recombinant inbred lines derived from the two original accessions acted as the second parent. The analysis implicated the metabolic profile and genetic markers of the RILs, which were then used to predict the relative mid- parent heterosis rMPH in biomass. The latter is defined as the relative biomass gain of the testcross as compared to the mean biomass of its parents (cf. Methods section for details) and therefore manifests itself not until the next generation. P1 describes the shoot biomass of the first parent, RIL the shoot biomass of the particular recombinant inbred line and TC_RIL the shoot biomass of the corresponding testcross. The function mean(N, N) refers to the arithmetic mean of the respective values. doi:10.1371/journal.pone.0005220.g001 PLoS ONE | www.plosone.org 2 April 2009 | Volume 4 | Issue 4 | e5220