Supplementary information for. Genomic and metabolic prediction of complex heterotic traits in hybrid maize
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1 Supplementary information for Genomic and metabolic prediction of complex heterotic traits in hybrid maize Christian Riedelsheimer 1, Angelika Czedik-Eysenberg, Christoph Grieder 1, Jan Lisec, Frank Technow 1, Ronan Sulpice, Thomas Altmann 3, Mark Stitt, Lothar Willmitzer,4, & Albrecht E Melchinger 1 1 Institute of Plant Breeding, Seed Science, and Population Genetics, University of Hohenheim, Stuttgart, Germany Max-Planck Institute of Molecular Plant Physiology, Potsdam, Germany 3 Department Molecular Genetics, Leibniz Institute of Plant Genetics and Crop Plant Research (IPK), Gatersleben, Germany 4 King Abdulaziz University, Jeddah, Saudi Arabia Correspondence should be sent to: Prof. Dr. A.E. Melchinger University of Hohenheim Institut e of Plant Breeding, Seed Science, and Population Genetics Fruwirthstr Stuttgart Germany melchinger@uni-hohenheim.de Supplementary information, page 1
2 CONTENTS SUPPLEMENTARY FIGURES Supplementary Figure 1 Phenotypic variation of the predicted traits. Supplementary Figure Distribution of genetic distances. Supplementary Figure 3 Genealogy of the population with labeled leaves. Supplementary Figure 4 Distribution of repeatabilities of individual metabolites ( w ). Supplementary Figure 5 Results of a principal component analysis (PCA). Supplementary Figure 6 Comparison of genetic architecture of GCA for dry matter yield with the estimated SNP effects used for its prediction. Supplementary Figure 7 Manhattan plots showing the genetic architectures of the investigated traits. Supplementary Figure 8 Quantile-Quantile (QQ) plots of genome-wide association scans of the investigated traits. Supplementary Figure 9 Effects for metabolites ( û ) estimated with RR-BLUP for predicting GCA for dry matter yield. Supplementary Figure 10 Analysis of genetic distances within the core set of 14 lines. Supplementary Figure 11 Accuracy of whole-genome prediction of GCA for dry matter yield within the core set depending on number of SNPs. Supplementary Figure 1 Observed versus whole-genome predicted GCA for female flowering within the core set. M i SUPPLEMENTARY TABLES Supplementary Table 1 Summary information about the inbred lines. Supplementary Table List of measured metabolites. Supplementary Table 3 Summary of whole-genome and metabolic prediction within the core set. Supplementary Table 4 Predictive abilities of whole-genome and metabolic prediction within the core set using different subgroups as validation sets. SUPPLEMENTARY NOTE 1. Near-infrared spectroscopy (NIRS).. Statistical analysis of phenotypic data..1. Metabolites... General combining ability (GCA). References. Supplementary information, page
3 Supplementary Figure 1 Phenotypic variation of the predicted traits. Distribution of GCA for (a) dry matter yield, (b) plant height, (c) dry matter concentration, (d) female flowering, (e) starch content, (f) sugar content, and (g) lignin content. The distributions are shown for the breeding subgroups Stiff Stalk (SS), tropical lines (T), and non-stiff Stalk (NSS) as well as for the geographical origins Europe (EU) and North America (NA). Supplementary information, page 3
4 Supplementary Figure Distribution of genetic distances. Pairwise genetic distances were calculated as Euclidean distances scaled to lie within zero and one (modified Rogers distances). The mean value ( x ) is indicated as a red line. Supplementary information, page 4
5 Supplementary Figure 3 Genealogy of the population with labeled leaves. The tree was reconstructed from SNP data with the balanced minimum evolution (BME) algorithm on genetic distances. The breeding subgroups Stiff Stalk (SS), tropical lines (T) and non-stiff Stalk (NSS) are distinguished by their color. Supplementary information, page 5
6 Supplementary Figure 4 Distribution of repeatabilities of individual metabolites ( w value ( x ) is indicated as a red line. M i ).The mean Supplementary Figure 5 Results of a principal component analysis (PCA). Results are shown for (a) SNPs and (b) metabolites. Variables were centered and scaled. Only metabolites with a repeatability greater than 0.9 were used. The explained variance is given in brackets. The breeding subgroups Stiff Stalk (SS), tropical lines (T), and non-stiff Stalk (NSS) are distinguished by their color. The weak correspondence of the grouping pattern was also reflected by the low Mantel correlation of 0.31 between (i) genetic distances and (ii) Euclidean distances on standardized levels of metabolites. Supplementary information, page 6
7 Supplementary Figure 6 Comparison of genetic architecture of GCA for dry matter yield with the estimated SNP effects used for its prediction. (a) Manhattan plot showing the obtained P- values on a log 10 scale of a genome-wide association scan with correction for population structure and cryptic relatedness using a Q + K-model. (b) Estimated normally distributed SNP effects ( û ) obtained with RR-BLUP. Supplementary information, page 7
8 Supplementary Figure 7 Manhattan plots showing the genetic architectures of the investigated traits. Results are shown for GCA for (a) plant height, (b) dry matter concentration, (c) female flowering, (d) starch content, (e) sugar content, and (f) lignin content. The obtained P-values are shown on a log 10 scale and were obtained with genome-wide association scans with correction for population structure and cryptic relatedness using a Q + K-model. Supplementary information, page 8
9 Supplementary Figure 8 Quantile-Quantile (QQ) plots of genome-wide association scans of the investigated traits. Results are shown for GCA for (a) dry matter yield, (b) plant height, (c) dry matter concentration, (d) female flowering, (e) starch content, (f) sugar content, and (g) lignin content. Supplementary information, page 9
10 Supplementary Figure 9 Effects for metabolites ( û ) estimated with RR-BLUP for predicting GCA for dry matter yield. The model includes all metabolites M i with different individual Pearson correlations with GCA for dry matter yield ( r (M, y) ). i Supplementary information, page 10
11 Supplementary Figure 10 Analysis of genetic distances within the core set of 14 lines. (a) Distribution of genetic distances. The mean value ( x ) is indicated as a red line. (b) Heatmap of pairwise genetic distances. (c) Decay of within groups sum of squares depending on the number of k-means clusters estimated on genetic distances. Supplementary information, page 11
12 Supplementary Figure 11 Accuracy of whole-genome prediction of GCA for dry matter yield within the core set depending on number of SNPs. Accuracies ( r g,g ) averaged over all crossvalidation runs are shown for 15, 50, 500, 1,000,,500, 5,000 and 10,000 evenly spaced SNPs. The red line shows the accuracy obtained with the full model of 38,019 SNPs. ( ˆ ) Supplementary Figure 1 Observed versus whole-genome predicted GCA for female flowering within the core set. Results were averaged over all cross-validation runs and colored according to (a) the breeding subgroups Stiff Stalk (SS), tropical lines (T), and non-stiff Stalk (NSS), and (b) their geographical origins Europe (EU), North America (NA), and other regions. Supplementary information, page 1
13 Supplementary Table 1 Summary information about the inbred lines. Inbred line Maturity group Geographical origin Breeding Used for Part of subgroup prediction core set Late USA NSS Yes Yes A148 Early USA NSS Yes Yes A188 Intermediate USA NSS Yes Yes A347 Late USA NSS Yes Yes A374 Early USA NSS Yes - A375 Intermediate USA NSS Yes Yes A619 Intermediate USA NSS Yes - A63 Late USA SS Yes - A654 Early USA NSS Yes Yes B100 Late USA NSS Yes - B101 Late USA SS Yes Yes B10 Late USA NSS Yes - B103 Early USA NSS Yes Yes B106 Late USA NSS Yes Yes B107 Late USA NSS Yes - B108 Intermediate USA NSS Yes Yes B109 Intermediate USA SS Yes - B110 Late USA SS Yes Yes B111 Late USA SS Yes Yes B11 Late USA NSS Yes Yes B113 Late USA NSS Yes Yes B14a Late USA SS Yes - B37 Late USA SS Yes Yes B68 Late USA SS Yes - B73 Intermediate USA SS Yes - B97 Late USA NSS Yes Yes B98 Late USA NSS Yes Yes B99 Intermediate USA NSS Yes Yes CG1 Intermediate Canada NSS Yes Yes CH39 Early Switzerland NSS Yes Yes CI187 Late USA NSS Yes Yes CL30 Early Canada NSS Yes Yes CM105 Intermediate Canada SS Yes - CM174 Early Canada SS Yes Yes CML103 Late Mexico T Yes - CML46 Late Mexico T Yes Yes CML3 Late Mexico T Yes Yes CML333 Late Mexico T Yes Yes CML91 Late Mexico T Yes Yes Co15 Early Canada NSS - - Co151 Early Canada NSS Yes Yes Co158 Early Canada NSS Yes Yes Co431 Early Canada NSS Yes Yes Supplementary information, page 13
14 Co43 Early Canada NSS Yes Yes Co441 Early Canada NSS Yes Yes CQ01 Early Canada NSS Yes Yes CQ50 Early Canada NSS Yes Yes D01 Early Germany NSS Yes - D06 Early Germany NSS Yes - D09 Early Germany NSS Yes Yes D17 Early Germany NSS Yes Yes D Late Germany NSS Yes - D3 Early Germany NSS Yes - D4 Early Germany NSS Yes - D3 Intermediate Germany NSS Yes - D403 Early Germany NSS - - D408 Early Germany NSS Yes Yes D46 Early Germany NSS Yes - D48 Late Germany NSS Yes - D51 Intermediate Germany NSS Yes - D60 Intermediate Germany NSS Yes - D61 Intermediate Germany NSS Yes - D63 Early Germany NSS Yes - D66 Intermediate Germany NSS Yes - D67 Intermediate Germany NSS - - D800 Early Germany NSS Yes Yes D83 Intermediate Germany NSS Yes - D851 Intermediate Germany NSS Yes Yes D95 Early Germany NSS Yes Yes De811 Late USA SS Yes Yes Dent_1 Intermediate Germany NSS - - Dent_ Early Germany NSS - - Dent_3 Late Germany NSS - - Dent_4 Intermediate Germany NSS - - Dent_5 Late Germany NSS - - Dent_6 Late Germany NSS - - Dent_7 Late Germany NSS - - Dent_8 Late Germany NSS - - Dent_9 Intermediate Germany NSS - - F5 Early France NSS Yes - F544 Early France NSS Yes - F7009 Intermediate France NSS Yes Yes F7019 Early France NSS Yes Yes F705 Early France SS Yes Yes F708 Intermediate France NSS Yes Yes F7038 Early France NSS Yes - F7057 Intermediate France NSS - - F7058 Intermediate France NSS Yes - F7059 Early France NSS Yes - F71 Late France NSS Yes - Supplementary information, page 14
15 F748 Late France SS Yes Yes F75 Late France SS Yes Yes F838 Late France NSS Yes Yes F888 Late France NSS Yes Yes F904 Intermediate France NSS Yes Yes F908 Early France NSS Yes Yes F91 Late France NSS Yes Yes F918 Late France SS Yes Yes FC185 Early France NSS Yes Yes FC1890 Early France NSS Yes - FV18 Early France NSS Yes Yes FV30 Early France NSS Yes Yes FV5 Early France NSS Yes - FV71 Early France NSS Yes Yes FV84 Early France NSS Yes Yes FV88 Early France NSS Yes Yes FV317 Early France NSS Yes Yes FV330 Early France NSS Yes Yes FV33 Intermediate France NSS Yes Yes FV335 Early France NSS Yes Yes FV353 Early France NSS Yes Yes FV354 Early France NSS Yes Yes FV356 Early France NSS Yes Yes GL7 Intermediate Canada NSS Yes Yes GL6 Late Canada NSS Yes - GY93 Late China NSS Yes Yes H95 Late USA NSS Yes Yes H99 Intermediate USA NSS Yes Yes Ia153 Early USA NSS Yes - M16W Late USA NSS Yes Yes M37W Late USA NSS Yes Yes M01 Early Germany NSS Yes - M016 Early Germany NSS Yes - Mo17 Late USA NSS Yes Yes Mo18W Late USA T Yes Yes Mo4W Late USA NSS Yes Yes Ms71 Late USA NSS Yes Yes Mt4 Early USA NSS Yes Yes N19 Early USA SS Yes Yes N Late USA SS Yes Yes N5 Late USA NSS Yes Yes N6 Late USA NSS Yes Yes NC50 Late USA SS Yes Yes NC58 Late USA NSS Yes - NC60 Late USA NSS Yes - NC6B Late USA NSS Yes - NC88 Late USA NSS Yes - Supplementary information, page 15
16 NC90 Intermediate USA NSS Yes Yes NC96 Late USA T Yes Yes NC98 Late USA T Yes - NC30 Late USA T Yes Yes NC348 Late USA T Yes Yes NC350 Late USA T Yes Yes NC358 Late USA T Yes Yes ND11 Early USA NSS Yes Yes ND46 Early USA NSS Yes Yes NDB8 Early USA NSS Yes Yes Oh0 Late USA NSS Yes Yes Oh33 Late USA NSS Yes Yes Oh40B Late USA NSS Yes Yes OH43 Late USA NSS Yes Yes Oh7B Late USA NSS Yes Yes Os46 Late USA NSS Yes Yes P001 Late Germany NSS Yes - P006 Early Germany NSS Yes - P009 Intermediate Germany NSS Yes - P017 Early Germany NSS Yes - P0 Intermediate Germany NSS Yes - P07 Late Germany NSS Yes - P09 Intermediate Germany NSS Yes - P031 Early Germany NSS Yes - P033 Early Germany NSS Yes - P034 Intermediate Germany NSS Yes - P036 Early Germany NSS Yes - P038 Intermediate Germany NSS Yes - P040 Intermediate Germany NSS Yes - P04 Intermediate Germany NSS Yes - P043 Early Germany NSS Yes - P045 Early Germany NSS Yes - P046 Early Germany NSS Yes - P047 Early Germany NSS - - P053 Intermediate Germany NSS Yes - P054 Early Germany NSS Yes - P057 Early Germany NSS Yes - P060 Intermediate Germany NSS Yes Yes P063 Intermediate Germany NSS Yes - P064 Late Germany NSS Yes - P065 Late Germany NSS Yes - P066 Intermediate Germany NSS Yes - P068 Late Germany NSS Yes - P070 Late Germany NSS Yes - P071 Intermediate Germany NSS Yes - P074 Intermediate Germany NSS Yes - P075 Intermediate Germany NSS Yes - Supplementary information, page 16
17 P079 Intermediate Germany NSS Yes - P080 Intermediate Germany NSS Yes - P081 Intermediate Germany NSS Yes - P083 Intermediate Germany NSS Yes - P084 Intermediate Germany NSS Yes Yes P086 Intermediate Germany NSS Yes - P087 Intermediate Germany NSS Yes - P089 Late Germany NSS Yes Yes P091 Late Germany NSS Yes - P09 Intermediate Germany NSS Yes - P094 Intermediate Germany NSS Yes - P095 Early Germany NSS Yes - P096 Early Germany NSS Yes - P097 Early Germany NSS Yes - P100 Intermediate Germany NSS Yes - P101 Intermediate Germany NSS Yes - P103 Intermediate Germany NSS Yes - P104 Intermediate Germany NSS Yes - P105 Early Germany NSS Yes - P106 Intermediate Germany NSS Yes - P107 Late Germany NSS Yes - P110 Early Germany NSS Yes - P111 Intermediate Germany NSS Yes - P11 Early Germany NSS Yes - P114 Late Germany NSS Yes - P115 Intermediate Germany NSS Yes - P118 Intermediate Germany NSS Yes - P119 Late Germany NSS Yes - P10 Late Germany NSS Yes - P1 Intermediate Germany NSS Yes - P16 Intermediate Germany NSS Yes - P17 Late Germany NSS Yes - P18 Late Germany NSS Yes - P19 Intermediate Germany NSS Yes - P130 Early Germany NSS Yes - P131 Intermediate Germany NSS Yes - P133 Intermediate Germany NSS Yes - P135 Intermediate Germany NSS Yes Yes P136 Intermediate Germany NSS Yes - P137 Early Germany NSS Yes - P14 Intermediate Germany NSS Yes - P144 Intermediate Germany NSS Yes - P145 Early Germany NSS Yes - P146 Early Germany NSS Yes - P148 Early Germany NSS Yes - P39 Late USA NSS Yes Yes Pa31 Early USA SS Yes Yes Supplementary information, page 17
18 Pa405 Early USA NSS Yes Yes Pa91 Late USA NSS Yes Yes S015 Late Germany NSS Yes - S016 Intermediate Germany NSS Yes - S018 Late Germany NSS Yes - S00 Intermediate Germany NSS Yes Yes S01 Late Germany NSS Yes - S05 Intermediate Germany NSS Yes Yes S033 Late Germany NSS Yes - S034 Late Germany NSS Yes - S035 Intermediate Germany NSS Yes - S036 Intermediate Germany NSS Yes - S037 Intermediate Germany NSS Yes - S040 Intermediate Germany NSS Yes - S044 Intermediate Germany NSS Yes - S046 Early Germany NSS Yes - S048 Intermediate Germany NSS Yes - S049 Intermediate Germany NSS Yes - S050 Late Germany NSS Yes - S051 Intermediate Germany NSS Yes - S05 Intermediate Germany NSS Yes - S053 Intermediate Germany NSS Yes - S054 Late Germany NSS Yes - S055 Early Germany NSS Yes - S058 Early Germany NSS Yes - S060 Early Germany NSS Yes - S065 Intermediate Germany NSS Yes - S066 Intermediate Germany NSS Yes - S067 Intermediate Germany NSS Yes - S069 Intermediate Germany NSS Yes Yes S070 Early Germany NSS Yes - S073 Early Germany NSS Yes - SDp54 Early USA NSS Yes - T3 Late USA NSS Yes Yes T8 Late USA NSS Yes Yes UH00 Intermediate Germany NSS Yes - UH50 Intermediate Germany NSS Yes - UH301 Intermediate Germany NSS Yes Yes UH303 Intermediate Germany NSS Yes Yes UH304 Intermediate Germany NSS Yes Yes W117 Early USA NSS Yes - W117HT Early USA NSS Yes - W153R Intermediate USA NSS Yes Yes W18B Early USA NSS Yes - W18E Intermediate USA NSS Yes Yes W3 Late USA NSS Yes Yes W401 Early USA NSS Yes Yes Supplementary information, page 18
19 W60S Late USA NSS Yes Yes W604S Intermediate USA NSS Yes Yes W64A Late USA NSS Yes Yes W79A Early USA NSS Yes Yes W9 Early USA NSS Yes Yes WH Early USA NSS Yes Yes WJ Early USA NSS Yes Yes Supplementary information, page 19
20 Supplementary Table List of measured metabolites. Metabolite 1,3-Diaminopropane -Aminobutyric acid -oxo-glutaric acid 6-alpha-Mannobiose β-alanine γ-aminobutyric acid p-coumaric acid Adenosine Alanine Amino acids Ascorbic acid Asparagine Aspartic acid Benzoic acid Caffeic acid Chlorogenic acid Chlorophyll A Chlorophyll B Citramalic acid Dopamine Ethanolaminie Ferulic acid Fructose Fumerate Galactinol dihydrate Gentiobiose Glucopyranose Glucose Glucose-6-phosphate Glutamic acid Glyceric acid Glyceric acid-3-phosphat Glycerol Glycine Homoserine Hydroxypyridine Isoleucine Itaconic acid Leucine Lysine MaLate Maltose Methionin Myo-Inositol Nitrate O-Acetylserine Octacosanoic acid Oxaloacetate Palmitic acid Phenylalanine Phenylpyruvic acid Phosophoric acid Phosphoric acid monomethyl ester Supplementary information, page 0
21 Proline Protein (total) Putrescine Pyruvic acid Quinic acid Raffinose Rhamnose Ribitol Serine Spermidine Starch Succinic acid Sucrose Threonic acid-1,4-lactone Threonine Triacontanoic acid Tyramine Tyrosine Valine Xylose 57 metabolites with unknown chemical structure Supplementary Table 3 Summary of whole-genome and metabolic prediction within the core set. GCA h GCA w M r( y,y ˆ ) SNPs r g,g s.d. ˆ ( ˆ ) r( y,y ) Metabolites Dry matter yield Plant height Dry matter concentration Female flowering Starch content Sugar content Lignin content Prediction accuracies ( r g,g ) averaged over all cross-validation runs and their standard deviations ( ˆ ) (s.d.) are shown for models using either SNPs or metabolites within the core set of 14 lines only. Repeatabilities of the used metabolic profile ( w ) were calculated as the weighted sum of the repeatabilities of the individual metabolites (Methods). Heritabilites of the predicted traits ( h ) were calculated using raw data of the core set only. M r( g,g ˆ ) s.d. GCA Supplementary information, page 1
22 Supplementary Table 4 Predictive abilities of whole-genome and metabolic prediction within the core set using different subgroups as validation sets. r( y,y ˆ ) (s.d.) GCA SNPs Metabolites SS NSS EU NA SS NSS EU NA Dry matter yield 0.40 (0.34) 0.68 (0.11) 0.6 (0.0) 0.76 (0.10) 0.74 (0.14) 0.39 (0.18) 0.41 (0.36) 0.44 (0.0) Plant height 0.45 (0.8) 0.64 (0.11) 0.41 (0.33) 0.74 (0.10) 0.6 (0.34) 0.45 (0.16) 0.34 (0.31) 0.49 (0.17) Dry matter concentration 0.89 (0.1) 0.60 (0.13) 0.7 (0.37) 0.68 (0.11) 0.74 (0.8) 0.51 (0.15) 0.37 (0.35) 0.53 (0.16) Female flowering 0.91 (0.14) 0.69 (0.10) 0.4 (0.34) 0.80 (0.08) 0.49 (0.41) 0.55 (0.13) 0.5 (0.34) 0.58 (0.15) Starch content 0.51 (0.9) 0.56 (0.15) 0.1 (0.37) 0.70 (0.11) 0.67 (0.1) 0.48 (0.16) 0.16 (0.34) 0.54 (0.16) Sugar content 0.51 (0.33) 0.51 (0.16) 0.11 (0.40) 0.70 (0.10) 0.33 (0.34) 0.37 (0.17) 0.14 (0.38) 0.47 (0.17) Lignin content 0.54 (0.3) 0.66 (0.1) 0.49 (0.30) 0.78 (0.09) 0.47 (0.34) 0.4 (0.18) 0.36 (0.9) 0.48 (0.19) Predictive abilities ( r y,y ) averaged over all cross-validation runs and their standard deviations ( ˆ ) (s.d.) are shown for models using either SNPs or metabolites within the core set of 14 lines only. For each validation population, predictive abilities were calculated separately for four subgroups of lines. The division was based on either breeding subgroups (Stiff Stalk, SS; Non-Stiff Stalk, NSS) or geographical origin (Europe, EU; North America, NA). The average numbers of lines in the validation populations were 6 for SS, 0 for NSS, 8 for EU, and 16 for NA. Supplementary information, page
23 Supplementary Note 1. Near-infrared spectroscopy (NIRS). A set of 55 maize genotypes served as the reference set to build the NIRS calibrations. The reference set was randomized as a randomized complete block design with two field replications and grown in the same environments as the testcrosses. Reference samples of 1.5 kg chopped whole plant material were collected from 66 plots in 008 (the second field replication was missing in some cases) and from 18 genotypes from one field replication in 009. Each field-plot sample was dried to constant weight at 55 C and ground with a Retsch mill to pass through a 1 mm grit. Starch and sugar contents in the reference samples were determined following the procedures prescribed by the European Commission. Lignin was determined as acid detergent lignin (ADL) following Goering and van Soest 1. Near infrared spectra were collected from the reference samples and from plant samples of one field replication of all field trials of all testcrosses. The spectra were measured using a laboratory NIRSystems 6500 spectrometer (FOSS NIRSystems, Inc. Silver Spring, MD, USA), equipped with sample cups having 3.5-cm diameter for measuring ground material. Spectra were collected in the nm spectral range at an interval of nm. For each field-plot sample, one sample cup was filled with sample material and measured in duplicate. Spectra were averaged over all technical and field replications. Partial least squares regression (PLSR) was used to develop calibration models. The first derivative of the spectra was used. Additionally, spectra were subjected to smoothing over a gap of four wavelengths and multiplicative scatter correction. For calibration development, the spectra were scaled to unit variance and centered to mean zero. From the complete spectral range, wavelengths at 8 nm intervals were included in the calibrations. The following validation scheme was applied: A set of 60 samples from a random draw of 18 genotypes was chosen as a prediction set whereas the remaining samples were used for developing the PLSR models. The model parameters were estimated in a 500 times repeated cross-validation using three quarters for calibration and one quarter for validation. The minimum root mean square error of prediction from cross-validation was used as the criterion for choosing the optimum number of components to be used for predicting. An upper limit was set to 15 components. In each cross-validation run, the developed model with the optimum number of components was applied to the prediction set to get appropriate performance statistics. The average coefficients of determination (R ) in the prediction set was 0.90 for starch content, 0.95 for sugar content, and 0.77 for lignin content. The final calibration models were applied on NIR spectra collected from all field trials of all testcrosses to predict phenotypic values per field plot. These were further analyzed to estimate GCA values of the lines (see section.). Supplementary information, page 3
24 . Statistical analysis of phenotypic data..1. Metabolites. Estimates of metabolite levels on a genotype-mean basis were obtained using the following linear mixed model in the notation of Patterson and Piepho:,3 G + M + M R + M R A + M R A N : M R A B with effects genotype (G), trial of maturity group (M) captured with the common checks, field replication (R), block (B), batch (A), and technical replication (N). Fixed and random effects are separated by a colon and random effects follow fixed effects. To achieve homoscedasticity of the residuals, a Box-Cox power transformation was applied to all metabolic traits with the optimum transformation parameter estimated by the maximum likelihood method described by Piepho 4 using a grid search between 0 and 1 with 100 steps. The 1.1 % missing values in the metabolite matrix were imputed using a Bayesian PCA 5. Estimates of variance components σ (genotypic variance) and g σ e (error variance) were estimated with REML, considering their corresponding effects as random. Repeatability of metabolite i was obtained as w σ g M = i σ e σ g + r where r is the number of field replications... General combining ability (GCA). GCA values of the inbred lines were obtained in a joint linear mixed model analysis of both testcross populations over all six environments: GCA + T + SCA : GCA E + T E + SCA E + E + E M +E M R + E M R B with factors GCA of inbred lines, tester (T), specific combining abilitity (SCA) being the interaction between inbred lines and testers. Factors M, R, and B are the same as for the model for the metabolites. Block variances and error variances were allowed to be independent in every maturity group trial in each environment. Estimates of variance components variance), σ GCA E (GCA-by-environment interaction variance), σ SCA (SCA variance), σ GCA (GCA σ SCA E (SCA-by-environment interaction variance), and σ e (pooled error variance) were estimated with REML, considering their corresponding effects as random. Dummy variables were used to estimate these variance components only for the investigated testcrosses in order to eliminate the inflation of these variance components due to the superior performing commercial check hybrids 6. Supplementary information, page 4
25 Heritability of GCA values was obtained as h GCA GCA = σgca E σsca σsca E σe σ GCA σ e t te ter Where e is the number of environments, t is the number of testers, and r is the number of field replications. Mixed model calculations were performed using ASReml-R References. 1. Goering, H.K. & Van Soest, P.J. Forage Fiber Analysis. In: Agr. Handbook No. 379 (USDA-ARS, Washington D.C., USA, 1970).. Patterson, H.D. Analysis of series of variety trials. In: Kempton, R.A., Fox, P.N. (eds.) Statistical methods for plant variety evaluation (Chapman & Hall, London, UK, 1997). 3. Piepho, H.P., Büchse, A. & Emrich, K. A Hitchhiker s Guide to Mixed Models for Randomized Experiments. J. Agronomy & Crop Sci. 189, 10-3 (003). 4. Piepho, H.-P. Data transformation in statistical analysis of field trials with changing treatment variance. Agronomy J. 101, (009). 5. Oba, S. et al. A Bayesian missing value estimation method for gene expression profile data. Bioinformatics 19, (003). 6. Piepho, H.P., Williams, E.R., & Fleck, M. A Note on the Analysis of Designed Experiments with Complex Treatment Structure. HortScience 41, (006). 7. Butler, D.G., Cullis, B.R., Gilmour, A.R., & Gogel, B.J. ASReml-R reference manual. Version 3 (Queensland Department of Primary Industries and Fisheries, Australia, 009). Supplementary information, page 5
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