A methodological approach to estimate the lactation curve and net energy and protein requirements of beef cows using nonlinear mixed-effects modeling

The objective of this study was to evaluate methods to predict the secretion of milk and net energy and protein requirements of beef cows (Bos indicus and B. taurus) after approximately 1 mo postpartum using nonlinear mixed-effect modeling (NLME). Twenty Caracu × Nellore (CN) and 10 Nellore (NL) cows were inseminated to Red Angus bulls, and 10 Angus × Nellore (AN) were bred to Canchim bulls. Cows were evaluated from just after calving (25 ± 11 d) to weaning (220 d). Milk yield was estimated by weighing calves before and after suckling (WSW) and by machine milking (MM) methods at 25, 52, 80, 109, 136, 164, 193, and 220 ± 11 d of lactation. Brody and simple linear equations were consecutively fitted to the data and compared using information criteria. For the Brody equation, a NLME model was used to estimate all lactation profiles incorporating different sources of variation (calf sex and breed of cow, cow as a nested random effect, and within-cow auto-correlation). The CV for the MM method (29%) was less than WSW (45%). Consequently, the WSW method was responsible for reducing the variance about 1.5 times among individuals, which minimized the ability to detect differences among cows. As a result, only milk yield MM data were used in the NLME models. The Brody equation provided the best fit to this dataset, and inclusion of a continuous autoregressive process improved fit (P < 0.01). Milk, energy and protein yield at the beginning of lactation were affected by cow genotype and calf sex (P < 0.001). The exponential decay of the lactation curves was affected only by genotype (P < 0.001). Angus × Nellore cows produced 15 and 48% more milk than CN and NL during the trial, respectively (P < 0.05). Caracu × Nellore cows produced 29% more milk than NL (P < 0.05). The net energy and net protein requirements for milk yield followed a similar ranking. Male calves stimulated their dams to produce 11.7, 11.4, and 11.9% more milk, energy and protein, respectively (P < 0.05). The MM method is better than the WSW technique to detect genetic or environmental differences in milk yield among beef cows. The data obtained by the MM method and analyzed by NLME models allows the inclusion of fixed effects, random effects and an auto-regressive process in lactation equations to describe lactation curves and net energy and protein requirements. The NLME is a powerful tool to describe differences in the secretion of milk due to heterosis and cell mammary external stimulus in beef c