Bayesian Recursive and Structural Equation Models to Infer Causal Links Among Gait Visual Scores on Campolina Horses

Gait visual scores are widely applied to horse breeding because they are a fast and easy phenotyping strategy, allowing the numeric interpretation of a complex biological process such as gait quality. However, they may suffer from subjectivity or high environmental influence. We aimed to investigate potential causal relationships among six visual gait scores in Campolina horses. The data included 5475 horses with records for at least one of the following traits: Dissociation (Di), Comfort (C), Style (S), Regularity (R), Development (De), and Gait total Scores (GtS). The pedigree comprised three generations with 14,079 horses in the additive relationship matrix. Under a Bayesian framework, (co)variance components were estimated through a multitrait animal model (MTM). Then, the inductive causation algorithm (IC) was applied to the residual (co)variance matrix samples. The resulting undirected graph from IC was directed in 6 possible causal structures, each fitted by a structural equation model. The final causal structure was chosen based on deviance information criteria (DIC). It was found that S significantly impacts the causal network of gait, directly and indirectly affecting C. The indirect causal effect of S on C was through the direct effect of S on De, then the direct effect of De on R, and finally, the direct effect of R on C. Di was caused by S, which is the reason for the genetic correlation between Di and GtS, due to causal effects being added to the model, they absorb the genetic correlation between Di and GtS. Those paths have biological meaning to horse movements and can help breeders and researchers better understand horses' complex causal network of gait.