Inferring causal phenotype networks using structural equation models

In animal breeding and quantitative genetics, relationships among phenotypic traits are traditionally studied via probabilistic relationships between them, using standard Multiple Trait Models (MTM) - see, for example, [1,2]. Although such models can be used satisfactorily to infer how probable events are, they are not stable enough to predict how probabilities would change as a result of external interventions [3,4]. In biological systems, phenotypic traits may exert causal effects between them. For example, on the one hand, high yield in dairy cows may increase the liability to certain diseases and, on the other hand, the incidence of a disease may affect yield negatively. Likewise, the transcriptome may be a function of the reproductive status in mammals and the latter may depend on other physiological variables. Such phenotypic relationships can be studied using statistical models that account for recursiveness and feedback between traits.Information regarding phenotype networks describing such interrelationships can be used to predict the behavior of complex systems, e.g. biological pathways underlying complex traits such as diseases, growth and reproduction, and ultimately it can be used to optimize management practices and multi-trait selection strategies in livestock. For instance, a correlation between traits y1 and y2 can be due to a direct effect of y1 on y2 (or y2 on y1) or to extraneous variables that jointly affect y1 and y2. Knowledge about the causal structure underlying phenotypic relationships is necessary to predict the effect of interventions (e.g., management practices) applied to trait y1 or y2. For example, if trait y1 affects y2, and y2 has no effect on y1, an intervention on y1 will cause changes on y2, but the reverse would not hold true.Similar situations can be considered from a genetic improvement standpoint. Conventionally, genetic correlation is defined as the proportion of variance that two traits share due to genetic causes, and it i