to the respective response in the different models. The darker the bar, the higher the VIP of the corresponding marker in the particular model. Panel A shows that, when training on the whole set of markers, the contribution to C24-heterosis prediction is more diffused on many different markers, whereas it is strongly concentrated on top of chromosome 4 in the case of Col-heterosis. Panel B shows the VIP when trained on those selected genetic markers, which turned out to be essential predictors in the respective models. Each of the five chromo- somes is represented by at least one marker in both minimal models, which overlap on the chromosome 1, 3 and 4. The two markers at the bottom of chromosome 3 only selected as predictors in the minimal Col-heterosis model were confirmed to be Col-heterosis specific markers by the combined genetic- metabolic model (cf. Methods section for details and Figure 3). This holds also true for at least one marker on each chromosome in the case of C24-heterosis. Found at: doi:10.1371/journal.pone.0005220.s002 (0.11 MB TIF) Figure S3 Histograms of allele frequencies. The figure shows how the allele frequencies are distributed in the RIL population. The panels A and B deal with the frequency of C24 alleles and Col-0 alleles, respectively. For each RIL there are 110 genetic markers featuring C24, Col-0 or heterozygosity. The x-axis represents the number of the corresponding alleles per RIL. The y-axis presents how many of the 359 RILs show the corresponding allele frequency. The mean frequency of C24 alleles and Col-0 alleles per RIL is 48% and 50%, respectively. In average, 2% of the markers are heterozygous. The minimal frequencies for C24 and Col-0 alleles are 11% and 10%, respectively, while the maximal frequencies are 89% and 85%. The standard deviation was about 15.4 and 15.1, respectively. Using a Mantel test (P,0.001) to estimate association between marker matrices, we did not find significant differences in marker distribution between the two sub-populations [22]. Distorted segregation ratios were detected at the bottom of chromosomes I and V, at the top of chromosomes III and IV and in the lower region of chromosome III [23]. Found at: doi:10.1371/journal.pone.0005220.s003 (0.00 MB PDF) Figure S4 Feature selection process in metabolite model for C24-heterosis. Panel A shows the crude optimization of predictive power according to the number of predictors in the model with increment 10. It determines the breakpoint for the refined version (panel B) to reduce the computational costs (cf. Methods section for details). In the end, the in panel B determined optimal number Opt of variables is used to estimate a confidence interval for the corresponding maximal predictive power. This can be seen in panel C, where black dots represent the predictive power of the optimal variable selection when models were trained on jackknife resamplings of the data. Their range determines the estimate of the confidence interval, which is represented by gray lines. Min is the smallest number of variables, whose predictive power is still within the estimated confidence interval of the maximal predictive power. Found at: doi:10.1371/journal.pone.0005220.s004 (0.03 MB PDF) Table S1 Estimated confidence intervals of the optimal predictive power in leave-one-out validation. References Heterosis Prediction Markers Found at: doi:10.1371/journal.pone.0005220.s005 (0.03 DOC) MB Table S2 Number of variables in the optimal and minimal predictor sets, in comparison to the number of all available predictors in the corresponding set. Abbreviations: Het, heterosis; Gen, genetic marker set; Met, metabolic marker set; Bio, biomass marker; Gen-Met, combined genetic-metabolic marker set etc. Found at: doi:10.1371/journal.pone.0005220.s006 (0.04 MB DOC) Table S3 List of metabolic markers that turned out to be relevant neither for C24- nor for Col-heterosis prediction in our analysis, i.e. omission of those markers did not significantly deplete the predictive power in the metabolic models or in the combined genetic-metabolic models. Found at: doi:10.1371/journal.pone.0005220.s007 (0.03 MB DOC) Table S4 List of the 40 metabolic markers highly ranked in C24- heterosis prediction, sorted according to the sum of their VIP in the minimal metabolic (met) and in the minimal combined genetic-metabolic (gen-met) model. Interestingly, the three highest ranked metabolic markers are distinct from those most important for biomass per se prediction [17]. Found at: doi:10.1371/journal.pone.0005220.s008 (0.02 MB XLS) Table S5 List of the 40 metabolic markers highly ranked in Col- heterosis prediction, sorted according to the sum of their VIP in the minimal metabolic (met) and in the minimal combined genetic-metabolic (gen-met) model. Interestingly, again the three highest ranked metabolic markers are distinct from those most important for biomass per se prediction [17]. Found at: doi:10.1371/journal.pone.0005220.s009 (0.03 MB XLS) Table S6 Dry weight (DW) and rMPH values for the 359 investigated RILs and the corresponding testcrosses (TC-C24 and TC-Col), including the standard deviation (sd) and the arithmetic mean (mean) for each column. Found at: doi:10.1371/journal.pone.0005220.s010 (0.10 MB XLS) Acknowledgments We thank Hannelore Liero and Henning La¨uter for their suggestions and advice concerning mathematical statistics and for helpful discussions and encouragement. We thank Detlef Groth, Jan Hummel and Manuela Hische for support with databases. We thank Stefanie Hartmann for proof- reading the manuscript. We also thank all partners within the DFG Priority Programme SPP 1149 ‘‘Heterosis in Plants’’. Author Contributions Conceived and designed the experiments: RCM TA LW. Performed the experiments: JL RCM. Analyzed the data: TG. Contributed reagents/ materials/analysis tools: MS. Wrote the paper: TG. Supervised the whole project: JS. Wrote the computer programmes: TG. Provided support in the analysis: JL SA MS. Proofread the manuscript: TA JL SA MS. Provided support in interpreting the results: TA LW RCM. Revised the manuscript: LW RCM JS. 1. Shull GH (1948) What is heterosis? Genetics 33: 439–446. 2. Duvick DN (2001) Biotechnology in the 1930s: the development of hybrid maize. Nat Rev Genet 2: 69–74. 3. Miedaner T, Gey A-K, Sperling U, Geiger HH (2002) Quantitative-genetic analysis of leaf-rust resistance in seedling and adult-plant stage of inbred lines and their testcrosses in winter rye. Plant Breed 121: 475–479. PLoS ONE | www.plosone.org 11 April 2009 | Volume 4 | Issue 4 | e5220