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Adrian Wade
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1 Supplementary material Journal Name: Theoretical and Applied Genetics Evaluation of the utility of gene expression and metabolic information for genomic prediction in maize Zhigang Guo* 1, Michael M. Magwire*, Christopher J. Basten*, Zhanyou Xu**, Daolong Wang* Address: *Syngenta Crop Protection, LLC, 3054 E Cornwallis Rd., Research Triangle Park, NC 7709, US ** Syngenta Crop Protection, LLC, th street, Slater, IA 5044, US 1 Corresponding Author: Syngenta Crop Protection, LLC, 3054 E Cornwallis Rd., Research Triangle Park, NC 7709, USA. zhigang.guo@syngenta.com - 1 -

2 Supplementary Method 1 The mixed model used for analyzing data from each metabolite Based on the measurements collected for each metabolite in the current study, BLUPs for each inbred line across three locations can be obtained for each metabolite using the following model Y G L, (1) ij i j ij where Y ij is the metabolic data of line i (i = 1,,.., n) in location j (j = 1,, 3); μ is the overall mean; G i is the genetic value of genotype i; L j is the effect of location j; and ε ij is a model residual following a normal distribution N(0, σ e ). It is assumed that G i, and L j are random effects following the normal distribution with zero means and variances σ G and σ L respectively. The estimates of these variance components along with the residual variance σ e were obtained from a restricted maximum likelihood (REML) analysis. Given REML estimates of the variances, phenotypic BLUPs for each inbred line were predicted by solving the Henderson mixed model equation (Henderson 1984). Broad sense heritability is defined as the proportion of the phenotypic variance of all the individuals in a population due to genetic effects (Falconer and Mackay 1996). Given the estimates of the variance components from model (1), the broad sense heritability on the line mean basis, H, may be estimated based on the data set for each metabolite (Holland et al. 003) by G H, () e G r where r is the number of locations used for testing the metabolite - -

3 Supplementary Figure S1 Frequency distribution of broad sense heritabilities H for 33 metabolites - 3 -

4 Supplementary Figure S Comparision of predicted values obtained from different models in the subpopulatin NSS. a comparison between G-BLUP, T-BLUP, and M-BLUP; b comparison between G-BLUP and other combined models. b comparison between G-BLUP and other combined models. c comparison between GT-BLUP, GM-BLUP, GTM-BLUP and their counterpart models with interactions. Standard deviation of correlations of predicted values is indicated for each bar over the 500 replicates - 4 -

5 Supplementary Figure S3 Comparision of predicted values obtained from different models in subpopulation Mixed. a comparison between G-BLUP, T-BLUP, and M-BLUP; b comparison between G-BLUP and other combined models. b comparison between G-BLUP and other combined models. c comparison between GT-BLUP, GM-BLUP, GTM-BLUP and their counterpart models with interactions. Standard deviation of correlations of predicted values is indicated for each bar over the 500 replicates - 5 -

6 Supplementary Figure S4 Predictive abilities evaluated in the subpopulation NSS for 11 traits using different numbers of SNPs, trnascripts, and metabolites. Standard error is indicated for each point over the 50 runs of sampling SNPs, transcripts, and metabolites. On the labels of x- axis, the first number in the parenthesis is the number of SNPs, the second one is the nubmer of gene transcripts, and the third one the number of metabolites - 6 -

7 Supplementary Figure S5 Predictive abilities evaluated in the subpopulation Mixed for 11 traits using different numbers of SNPs, trnascripts, and metabolites. Standard error is indicated for each point over the 50 runs of sampling SNPs, transcripts, and metabolites. On the labels of x- axis, the first number in the parenthesis is the number of SNPs, the second one is the nubmer of gene transcripts, and the third one the number of metabolites - 7 -

8 Supplementary Table S1 Estimates of broad sense heritabilities (H ) for 11 traits within each of the four subpopulations TST, NSS, SS, and Mixed Trait TST NSS SS Mixed DS 0.79 (0.03) 0.79 (0.03) 0.5 (0.14) 0.76 (0.04) DA 0.8 (0.0) 0.77 (0.04) 0.69 (0.10) 0.8 (0.03) DH 0.81 (0.03) 0.59 (0.1) 0.80 (0.04) KW 0.81 (0.03) 0.85 (0.03) 0.77 (0.09) 0.89 (0.03) GW 0.66 (0.05) 0.6 (0.07) 0.40 (0.9) 0.63 (0.08) CW 0.84 (0.00) 0.79 (0.00) 0.81 (0.00) 0.79 (0.00) CD 0.89 (0.0) 0.85 (0.03) 0.65 (0.1) 0.86 (0.03) ED 0.83 (0.0) 0.87 (0.0) 0.34 (0.0) 0.83 (0.03) EL 0.81 (0.03) 0.85 (0.03) 0.49 (0.17) 0.78 (0.04) EH 0.91 (0.01) 0.93 (0.01) 0.81 (0.06) 0.91 (0.0) PH 0.9 (0.01) 0.9 (0.01) 0.85 (0.05) 0.91 (0.0) In parentheses is the standard error for the estimate of broad sense heritability. Note that the estimation for varaince components for DH trait in TST subpopulation failed with REML due to the limited replicates within each environment

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