*4.6. Genome-Wide Association Study*

GWAS was performed with the GLM and compressed MLM [80,81] implemented in TASSEL (v5.2) [82], which employs the EMMA and P3D algorithms to reduce computing time. For MLM, the kinship matrices for the merged population and the three single populations were calculated using TASSEL (v5.2) [82]. Manhattan plots and quantile-quantile (Q-Q) plots of GWAS were obtained using the R package "qqman" [83].

SNP markers for candidate QTL were determined based on the *p*-value for each marker estimated in the GLM or MLM analysis. The *p*-values were adjusted by the Bonferroni correction, being α (0.05)/No. of SNPs used in the analyses. Allele effects of significant markers were calculated as the difference between the average phenotypic values of homozygous alleles which were obtained directly from the TASSEL outputs. Candidate QTL were defined based on peaks of SNPs exceeded the significance threshold for the trait. The genomic region for a QTL was defined as a genome block spanning all significant SNPs.

The amount of phenotypic variation explained by significant QTL was estimated for all SNP markers within the QTL regions using the same method as described above [61], denoted as *h* 2 *QTL*. We similarly estimated phenotypic variation explained by all significant QTL for a single trait and denoted it *h* 2 *GWAS*.
