Fig 2. The effect of indirect effect size variance on the R² of PGS regression analyses from different study designs.

y-axis shows the ratio of R² from between family design (red) or sibling difference design (blue) vs. the proportion of phenotypic variance due to the direct effect in the population. The yellow box shows the ratio of R² from the sibling difference design based on PGS_mix vs. that in a sibling difference design based on PGS_dir. Each boxplot shows the simulation results of 200 repeats. In this figure, the variance of direct effect size and the variance of the environment effect size were fixed at 1 and 3, respectively. The correlation r_g between direct and indirect effect sizes and the correlation r_e between two sibling’s environments were fixed at 0 and 0.5, respectively. When the indirect effect is 0 (both ${\sigma }_{ind}^2$ and β_ind are 0), the sibling difference analyses become identical regardless of whether the PGS is computed based on (β_dir+β_ind) or β_dir, thus the yellow box is fixed at 1 when ${\sigma }_{ind}^2=0$ in this figure.