Principal Component Analysis, Population Structure (Q), and Kinship Matrix (K)

To better understand the dependencies among traits, Pearson correlation coefficients were computed in R (version 3.3.2). Principal component analysis (PCA) was performed using original phenotypic values of all genotypes for all root traits in R (version 3.3.2). Data were centered and scaled using the scale function, and then the prcomp function was used to conduct the PCA. The scores, or rotations, from principal components (PCs) 1 and 2 were selected as aggregate traits to be included in the GWAS.

For the 289 genotypes included in the GWAS analysis, single-nucleotide polymorphism (SNP) markers originated from the application of the Illumina Infinium SoySNP50K iSelect SNP Beadchip (Song et al., 2013). The SNP markers available for the 289 genotypes were filtered to ultimately include 31,708 polymorphic SNPs with a minor allele frequency (MAF) ≥5% in the GWAS analysis. The Bayesian model-based program STRUCTURE 2.3.4 (Pritchard et al., 2000) software was used to infer the population structure (Q) using the 31,708 SNPs. The burn-in iteration and Markov chain Monte Carlo (MCMC) replications after burn-in with an admixture and allele frequencies correlated model was used as described previously (Dhanapal et al., 2015a,b). The population structure analysis was performed with 10 independent iterations with the hypothetical number of subpopulations (k) ranging from 1 to 10. All soybean accessions were assigned to a subpopulation based on the optimum k (k = 8), and the population structure matrix (Q) was generated for further association analyses. TASSEL 5.2.3 software (Bradbury et al., 2007; Buckler et al., 2009) was used to generate the kinship matrix (K) based on “scaled Identity by State (IBS)” similarity matrix (Endelman and Jannink, 2012).