*3.3. Phenotypic Variation Explained by SNPs and QTL*

SNP heritability (*h* 2 *SNP*) for a trait is the total proportion of phenotypic variance explained by additive contributions from genome-wide SNPs. A method for estimating *h* 2 *SNP* for a complex trait was initially proposed in 2011 [60,61] and implemented in GCTA (Genome-wide Complex Trait Analysis) software [61]. Since then, the method has been applied to many quantitative traits largely in human and animal genetic studies [62,63]. The method was also used to estimate phenotypic variance explained by a subset of SNPs selected by *p*-values from GWAS in an independent sample [64]. However the estimate of variance explained by the SNP subsets ascertained by the *p*-values from GWAS in the same sample may be inflated due to positive correlation between true SNP effects and estimation errors (personal communication to the GCTA author, Jian Yang). However, as the GCTA-based heritability estimation method includes the population structure effect in the linear model and also considers heritability estimates to be irrelevant to the number of SNPs used [60,61], the accuracy of estimates should be higher than those obtained simply using the simple multivariate regression adopted in most GWAS of plant traits. In the current study, for the first time we applied this method to estimate *h* 2 *SNP* for 11 agronomic and seed quality traits in three bi-parental populations and a merged population. As the number of SNPs identified from a population depends on its genetic variation for the traits, the trait-associated *h* 2 *SNP* estimates vary across populations and traits. Overall, seed yield had a lower *h* 2 *SNP* than seed quality traits as expected considering the extent of genetic complexity of the former (Table 2). We also used the same method to estimate phenotypic variation explained by individual QTL (*h* 2 *QTL*) and by all QTL for a specific trait (*h* 2 *GWAS*). *h* 2 *GWAS* measures the extent of the phenotypic variation explained by QTL compared to that of all SNPs. This comparison led to the conclusion that many QTL for PLH, DTM and YLD were not detected in our study but the QTL for seed quality traits identified herein likely represent major genetic regions or genes controlling these traits.
