Conditioning on the causal network prevents indirect response to selection

Multiple trait animal models (MTM) allow to estimate the breeding values (BV) of several traits simultaneously while accounting for genetic and environmental correlations among them. However, relationships among traits may not be reciprocal but rather causal in nature. In these cases, and given a causal network, structural equations models (SEM) arise as a more appropriate methodology. Although MTM and SEM have been shown to be parametrically equivalent, the estimated breeding value (EBV) obtained from either one or the other should be interpreted differently. In this study, we investigated the impact of using these estimates on the response to selection for a causal network comprising five different traits through a stochastic simulation experiment. Three different selection targets were assayed, involving traits located upstream, midstream and downstream this causal network. We first considered the case in which traits were causally related but not genetically correlated. The current results support our hypothesis that MTM will absorb causal relationships as genetic correlations and, consequently, change the response to selection achieved as compared with SEM. We found no differences on the response to selection when the target trait was located at the top of the causal network, but noticeable differences were detected on upstream traits when selection pressure was placed on midstream or downstream traits. We also assayed a scenario in which causal effects and genetic correlations act simultaneously and found that selection based on BVs estimated using SEM diminished the indirect response in traits upstream the causal network.