Figure 1.

(a) Path coefficient diagram or acyclic mixed graph of DGE. (b) Path coefficient diagram or acyclic mixed graph of ISGE. y_i, y_i′ = phenotypes of two related individuals; aD, a_D′ = Direct Breeding Values for animals i and i’; aS, a_S′ = Social Breeding Values for animals i and i’; ${\phi }_{D_i},{\phi }_{D_{i^{\prime }}}$ = Mendelian residual for animals i and i’; G_i,i߰ = genomic relationship between animals i and i’; r_DS = correlation between direct and social effects; h_D = square root of direct heritability; h_S= square root of $h_S^2$, where $h_S^2=\frac{{\widehat{\sigma }}_S^2}{{\widehat{\sigma }}_S^2+{\widehat{\sigma }}_e^2+{\widehat{\sigma }}_{pen}^2}$; $r_{A_{DS}}$= correlation between genetic direct and social breeding values; $Z_{S_{i,i^{\prime }}}$ = square root of the direct heritability; $Z_{S_{i^{\prime },i}}$, = intensity of social interaction between animals i and i’.