Review: Improving residual feed intake modelling in the context of nutritional- and genetic studies for dairy cattle.

The residual feed intake (RFI) model has recently gained popularity for ranking dairy cows for feed efficiency. The RFI model ranks the cows based on their expected feed intake compared to the observed feed intake, where a negative phenotype (eating less than expected) is favourable. Yet interpreting the biological implications of the regression coefficients derived from RFI models has proven challenging. In addition, multitrait modelling of RFI has been proposed as an alternative to the least square RFI in nutrition and genetic studies. To solve the challenge with the biological interpretation of RFI regression coefficients and suggest ways to improve the modelling of RFI, an interdisciplinary effort was required between nutritionists and geneticists. Therefore, this paper aimed to explore the challenges with the traditional least square RFI model and propose solutions to improve the modelling of RFI. In the traditional least square RFI model, one set of fixed effects is used to solve systematic effects (e.g., seasonal effects and age at calving) for traits with different means and variances. Thereby, measurement and model fitting errors can accumulate in the phenotype, resulting in undesirable effects. A multivariate RFI model will likely reduce this problem, as trait-specific fixed effects are used. In addition, regression coefficients for DM intake on milk energy tend to have more biologically meaningful estimates in multitrait RFI models, which indicates a confounding effect between the fixed effects and regression coefficients in the least square RFI model. However, defining precise expectations for regression coefficients from RFI models or sourcing for accurate feed norm coefficients seems difficult, especially if the coefficients are applied to a wide cattle population with varying diets or management systems, for example. To improve multitrait modelling of RFI, we suggest improving the modelling of changes in energy status. Furthermore, a novel method to derive the energy density of the diet and individual digestive efficiency is proposed. Digestive efficiency is defined as the part of the efficiency associated with digestive processes, which primarily reflects the conversion from gross energy to metabolisable energy. We show the model was insensitive to prior values of energy density in feed and that there was individual variation in digestive efficiency. The proposed method needs further development and validation. In summary, using multitrait RFI can improve the accuracy of the ranking of dairy cows' feed efficiency, consequently improving economic and environmental sustainability on dairy farms.