Pleiotropic effect of SNP on plant height and seed weight
GWAS summary statistic data for both traits were obtained from above GWAS analysis and were used for common factor analysis. Pleiotropic effect of each SNP on plant height and seed weight were estimated with a common factor model (Grotzinger et al. 2019). The common factor model included the two traits plant height and seed weight, assuming each SNP assert effect on both traits. The effect of each SNP on each trait was estimated within a genomic structural equation modelling framework (Grotzinger et al., 2019). The estimate of the SNP effect and model test was implemented with GenomicSEM (Grotzinger et al., 2019). As the experimental data currently are not compatible with the hypothesis that every mutation (or gene) affects every trait (Wagner & Zhang 2011), and large data size (e.g. >10,000 in this case) could, meanwhile, cause spurious correlation (Lin et al., 2013; Kaplan et al. 2014), we identified the outliers that are deviated from the general pattern of relationship between the SNP effects on plant height and that on seed seeds as pleiotropic SNPs. A bivariate linear regression between the SNP effects on plant height and that on seeds weight was implemented, and residues of the regression were then obtained. The SNPs with residues of the regression beyond the 95% confident zone as outliers using a Z-score method (Z-score >1.96, or Z-score < - 1.96).
Basic summary statistics were carried out using PAST v3 (Hammer et al., 2011). The R package ggplot2 (Wickham, 2016) was used to plot model results including the kolmogorov-smirnov plots. Regression slopes were compared using estimated marginal means with the R package “emmeans (Lenth et al., 2017). Genomic diversity (π, nucleotide diversity) was calculated using TASSEL v5 (Bradbury et al., 2007). Significance was taken at p < 0.05 for the null hypothesis.