A meta-analysis of the relationship between milk protein production and absorbed amino acids and digested energy in dairy cattle

Milk protein production is the largest draw on AA supplies for lactating dairy cattle. Prior NRC predictions of milk protein production have been absorbed protein (MP)-based and used a first-limiting nutrient concept to integrate the effects of energy and protein, which yielded poor accuracy and precision (root mean squared error [RMSE] >21%). Using a meta-data set gathered, various alternative equation forms considering MP, absorbed total EAA, absorbed individual EAA, and digested energy (DE) supplies as additive drivers of production were evaluated, and all were found to be superior in statistical performance to the first limitation approach (RMSE = 14%-15%). Inclusion of DE intake and a quadratic term for MP or absorbed EAA supplies were found to be necessary to achieve intercept estimates (nonproductive protein use) that were similar to the factorial estimates of the National Academies of Sciences, Engineering, and Medicine (2021). The partial linear slope for MP was found to be 0.409, which is consistent with the observed slope bias of -0.34 g/g when a slope of 0.67 was used for MP efficiency in a first-limiting nutrient system. Replacement of MP with the supplies of individual absorbed EAA expressed in grams per day and a common quadratic across the EAA resulted in unbiased predictions with improved statistical performance as compared with MP-based models. Based on Akaike's information criterion and biological consistency, the best equations included absorbed His, Ile, Lys, Met, Thr, the NEAA, and individual DE intakes from fatty acids, NDF, residual OM, and starch. Several also contained a term for absorbed Leu. These equations generally had RMSE of 14.3% and a concordance correlation of 0.76. Based on the common quadratic and individual linear terms, milk protein response plateaus were predicted at approximately 320 g/d of absorbed His, Ile, and Lys; 395 g/d of absorbed Thr; 550 g/d of absorbed Met; and 70 g/d of absorbed Leu. Therefore, responses to each except Leu are almost linear throughout the normal in vivo range. De-aggregation of the quadratic term and parsing to individual absorbed EAA resulted in nonbiological estimates for several EAA indicating over-parameterization. Expression of the EAA as g/100 g total absorbed EAA or as ratios of DE intake and using linear and quadratic terms for each EAA resulted in similar statistical performance, but the solutions had identifiability problems and several nonbiological parameter estimates. The use of ratios also introduced nonlinearity in the independent variables which violates linear regression assumptions. Further screening of the global model using absorbed EAA expressed as grams per day with a common quadratic using an all-models approach, and exhaustive cross-evaluation indicated the parameter estimates for BW, all 4 DE terms, His, Ile, Lys, Met, and the common quadratic term were stable, whereas estimates for Leu and Thr were known with less certainty. Use of independent and additive terms and a quadratic expression in the equation results in variable efficiencies of conversion. The additivity also provides partial substitution among the nutrients. Both of these prevent establishment of fixed nutrient requirements in support of milk protein production.