Inferring causal structures and comparing the causal effects among calving difficulty, gestation length and calf size in Japanese Black cattle

The objectives of this study were to infer phenotypic causal networks involving gestation length (GL) and calving difficulty (CD) for the primiparity of 1850 Japanese Black heifers, and the birth weight (BWT), withers height (WH) and chest girth (CHG) of their full blood calves, and to compare the causal effects among them. The inductive causation (IC) algorithm was employed to search for causal links among these traits; it was applied to the posterior distribution of the residual (co)variance matrix of a multiple-trait sire-maternal grand sire (MGS) model. The IC algorithm implemented with 95% and 90% highest posterior density intervals detected only one structure with links between GL and BWT (WH or CHG) and between BWT (WH or CHG) and CD, although their directions were not resolved. Therefore, a possible causal structure based on the networks obtained from the IC algorithm [GLBWT (WH or CHG)CD] was fitted using a structural equation model to infer causal structure coefficients between the traits. The structural coefficients of GL on BWT and of BWT on GL on the observable scale showed that an extra day of GL led to a 270-g gain in BWT, and a 1-kg increase in BWT increased the risk for dystocia by 1.1%, in the causal structure. Similarly, an increase in GL by 1 day resulted in a 2.1 (2.0)-mm growth in WH (CHG), and a 1-cm increase in WH (CHG) increased the risk of dystocia by 1.2% (0.9%). The structural equation model was also fitted to alternative causal structures, which involved the addition of a directed link from GL to CD, or GLCD to the structures described above. The inferred structural coefficients with the alternative structures were almost the same as the corresponding ones that had GLBWT (WH or CHG)CD. However, the direct causal effect of the extra link from GL on CD was similar to the indirect causal effect of GL through the mediating effect of BWT (WH or CHG) on CD and significant (P<0.05). This suggest that maternal genetic effects might not be removed completely from the residual variance components in the sire-MGS model, and the application of the IC algorithm to the variances from the model could detect an incorrect structure. Nonetheless, fitting the structural equation model to the causal structure provided useful information such as the magnitude of the causal effects between the traits.