Predicting milk protein responses and the requirement of metabolizable protein by lactating dairy cows

The objective of this study was to develop a modeling framework to predict milk protein yield responses to varying metabolizable protein (MP) supplies and to determine the requirement of MP by lactating dairy cows. The logistic curve was used to model milk protein yield while accounting for a variable efficiency of MP utilization and between-study variability. Models were developed with databases from 2 recently published meta-analyses and based on either total MP supply or MP supply available for milk production. All models provided reasonable fit to data, with root mean square prediction error ranging from 18 to 20% of the average milk protein yield. The estimated horizontal asymptotes were 1.17 (posterior SD = 0.02) and 1.55 (posterior SD = 0.06) in the 2 databases, suggesting that the limiting milk protein yield, as MP supply increases, converges to 1.17 or 1.55 kg/d in the environments determined by the 2 databases. The observed efficiencies ranged from 0.75 to 0.18 when total MP supply was used as the denominator and above 1 to 0.24 when the MP supply available for milk production was used as the denominator. The predicted efficiencies were in good agreement with the data, decreasing nonlinearly with the MP supply. The MP requirement was calculated with a function constructed with the inverse of the logistic model and modified at regions of maximum marginal efficiency and minimum second derivative. This strategy assumes that the MP solution, or the MP needed to predict a given protein yield in the fitted logistic curve, determines the MP requirement for maintenance and lactation. Requirements calculated with the independent variable as total MP supply refer to the total requirement of maintenance plus lactation, whereas the requirement from models based on MP supply available for milk production are referent to the MP required only for lactation. The requirements were, on average, slightly smaller than the ones predicted by the current Northern American feeding system for dairy cows at lower protein yields and greater than currently recommended at high yields.