It was adopted in this work a methodology to estimate the optimal level of concentrate food for dairy cows on tropical pastures based on the theory of marginal analysis. An empiric model was developed and validated for application of the methodology using a database composed of 62 means of treatments from 32 studies in which milk production was evaluated regarded to the levels of concentrate feeding. Milk production (MP) showed quadratic behavior in response to concentrate intake (CI): MP (kg/cow/day) = 10.554 + 1.5855CI - 0.0552CI². Evaluation of the MP values observed over the predicted ones pointed the non-rejection of the null hypothesis, indicating that the model can be applied on the prediction of milk production, and consequently, on the optimal level of supplementation. However, evaluation of the partition of mean square error of prediction indicated the need for adjustments. The marginal production response (MPR) presented decreasing linear effect at CI level: MPR (kg milk/kg concentrate added) = 1.5855 - 0.1104CI. The intake of concentrate that maximizes profit per animal (CIoptimum) is estimated by the following equation: CIoptimum (kg/cow/day, as fed basis) = (1.5855 - (Px/Py))/0.1104; in which Px and Py are, respectively, the prices of concentrate feeds ($/kg, as fed basis) and of the milk at farmgate ($/kg). It is suggested the realization of new studies to include in the model, indicators of reproductive performance and other factors that affect the productive response to supplementation with concentrate feeds. Recommendations on levels of concentrate feeding for bovines should be based on presuppotions of marginal response theory, in order to avoid irrational use of nutrients.
marginal production response; milk production; modeling; optimization
