An alternative Interpretation of residual feed intake by phenotypic recursive relationships in dairy cattle

There has been an increasing interest in residual feed intake (RFI) as a measure of net feed efficiency in dairy cattle. RFI phenotypes are obtained as residuals from linear regression encompassing relevant factors (i.e., energy sinks) to account for body tissue mobilization. However, fitting energy sink phenotypes as regression variables in standard linear regression was criticized because phenotypes are subject to measurement errors. Multiple-trait models have been proposed which derive RFI by follow-up partial regression. By re-arranging the single-trait linear regression, we showed a causal RFI interpretation underlying the linear regression for RFI. It postulates recursive effects in energy allocation from energy sinks on dry matter intake, but the feedback or simultaneous effects are assumed to be nonexistent. A Bayesian recursive structural equation model was proposed for directly predicting RFI and energy sinks and estimating relevant genetic parameters simultaneously. A simplified Markov chain Monte Carlo algorithm that implemented the Bayesian recursive model was described. The recursive model is asymptotically equivalent to one-step linear regression for RFI, yet extends the analytical capacity to multiple-trait analysis. It is equivalent to Bayesian-implemented, multiple-trait model reparameterized based on Cholesky decomposition of phenotypic (co)variance matrix for evaluating RFI, but varied in assumptions about relationships between energy sinks.