Exploring causal networks of bovine milk fatty acids in a multivariate mixed model context

Knowledge regarding causal relationships among traits is important to understand complex biological systems. Structural equation models (SEM) can be used to quantify the causal relations between traits, which allow prediction of outcomes to interventions applied to such a network. Such models are fitted conditionally on a causal structure among traits, represented by a directed acyclic graph and an Inductive Causation (IC) algorithm can be used to search for causal structures. The aim of this study was to explore the space of causal structures involving bovine milk fatty acids and to select a network supported by data as the structure of a SEM.

The IC algorithm adapted to mixed models settings was applied to study 14 correlated bovine milk fatty acids, resulting in an undirected network. The undirected pathway from C4:0 to C12:0 resembled the de novo synthesis pathway of short and medium chain saturated fatty acids. By using prior knowledge, directions were assigned to that part of the network and the resulting structure was used to fit a SEM that led to structural coefficients ranging from 0.85 to 1.05. The deviance information criterion indicated that the SEM was more plausible than the multi-trait model.

The IC algorithm output pointed towards causal relations between the studied traits. This changed the focus from marginal associations between traits to direct relationships, thus towards relationships that may result in changes when external interventions are applied. The causal structure can give more insight into underlying mechanisms and the SEM can predict conditional changes due to such interventions.