A new method to estimate residual feed intake in dairy cattle using time series data

In dairy, the usual way to measure feed efficiency is through the residual feed intake (RFI) method. However, this method is, in its classical form, a linear regression, which, by construction, does not take into account the evolution of the RFI components across time, inducing approximations in the results. We present here a new approach that incorporates the dynamic dimension of the data. Using a multitrait random regression model, the correlations between milk, live weight, DM intake (DMI) and body condition score (BCS) were investigated across the lactation. In addition, at each time point, by a matrix regression on the variance–covariance matrix and on the animal effects from the three predictor traits, a predicted animal effect for intake was estimated, which, by difference with the actual animal effect for intake, gave a RFI estimation. This model was tested on historical data from the Aarhus University experimental farm (1 469 lactations out of 740 cows). Correlations between animal effects were positive and high for milk and DMI and for weight and DMI, with a maximum mid-lactation, stable across time at around 0.4 for weight and BCS, and slowly decreasing along the lactation for milk and weight, DMI and BCS, and milk and BCS. At the Legendre polynomial coefficient scale, the correlations were estimated with a high accuracy (averaged SE of 0.04, min = 0.02, max = 0.05). The predicted animal effect for intake was always extremely highly correlated with the milk production and highly correlated with BW for the most part of the lactation, but only slightly correlated with BCS, with the correlation becoming negative in the second half of the lactation. The estimated RFI possessed all the characteristics of a classical RFI, with a mean at zero at each time point and a phenotypic independence from its predictors. The correlation between the averaged RFI over the lactation and RFI at each time point was always positive and above 0.5, and maximum mid-lactation (>0.9). The model performed reasonably well in the presence of missing data. This approach allows a dynamic estimation of the traits, free from all time-related issues inherent to the traditional RFI methodology, and can easily be adapted and used in a genetic or genomic selection context.