Two multiple regression models were used to estimate energetic efficiency of protein and fat gain for 84 grade British steers, predominantly Hereford, and 84 Charolais steers using data obtained from a comparative slaughter feeding trial. In Model One, metabolizable energy intake was regressed on energy gain as fat and protein; the intercept was an estimate of maintenance. For Model Two, maintenance requirements were estimated by regression of log heat production (kcal/kg.75) on metabolizable energy intake (kcal/kg.75) and iterating to the point at which heat production was equal to metabolizable energy intake. Energy intake above maintenance was then regressed on energy gained as fat and protein. Results from Model One showed the efficiencies of protein and fat gain to be 10 and 49%, while Model Two indicated these efficiencies were 11 and 58%. Breeds did not appear to differ significantly in the efficiency with which they used metabolizable energy for protein or fat deposition.

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Hereford and Charolais steers were fed at three levels of feed intake (low, medium or ad libitum) to similar weights within breed groups to evaluate effects of energy intake on energetic efficiency and body composition. Two methods were employed to partition metabolizable energy intake into use for maintenance and gain. Method one used an assumed daily fasting heat production of 77 kcal/weight (W).75; method two estimated fasting heat production from the regression of log daily heat production against metabolizable energy intake (kcal/W.75). Net energy for gain (NEg) was determined in method one by regressing retained energy (kcal/W.75) against feed intake (g/W.75). For method two, the estimated maintenance requirement of feed was subtracted from total feed intake and retained energy was regressed against feed intake above maintenance to estimate NEg. Conclusions regarding feed energy utilization for maintenance and gain were the same by either method of energy partitioning. Charolais steers used feed energy less efficiently for gain than Hereford steers, and ad libitum steers used feed energy less efficiently for gain than steers at lower intakes (P less than .05). Charolais steers made leaner (P less than .05) gains than Hereford steers. Although steers consuming the lowest level of feed made gains containing a lower percentage of fat and a higher percentage of protein (P less than .05) than steers at higher intakes, body composition within a breed was not altered by level of energy intake when animals, within breeds, were slaughtered at similar end weights.

The robustness of efficiency estimates depends on theoretical consistency of models from which those estimates are developed; functional forms of the variables must be globally consistent with theoretical properties regarding feed utilization for maintenance and gain in growing and finishing cattle. Model parameter estimates and their dimensions must be unique or estimates of feed utilization and gain will not reflect reality. A linear equation commonly used to estimate daily DMI by the th individual animal (ADFI), based on mean weight and gain during a feeding period, was evaluated to determine if that model was correctly specified and if the vector predicted ADFI differed from the vector observed ADFI. Three independently gathered data sets were evaluated using a multiple linear regression model; variability described by that model failed to capture observed variability in the data (lack of fit, < 0.10), and predicted ADFI differed from observed ( < 0.05); for 1 of the 3 data sets, residuals were not normally distributed ( < 0.001). Functional forms of the variables in the first model evaluated, characterizing ADFI required for maintenance ( × BW) and gain ( × ADG), were consistent with neither published empirical nor theoretical relationships among ADFI, BW, and ADG. Parameter estimates determined for that linear model were not BLUE. Better fits among final BW, initial BW, and ADFI were found for a first-order relationship, in which final BW was a function of initial BW and ADFI, as indicated by > 0.90. The linear model and, to a lesser degree, the first nonlinear model lacked theoretical and global consistency. A second nonlinear model, which described retained energy as a function of ME intake, best fit the data, and functional forms of variables describing ME intake at maintenance and the efficiency of ME utilization for gain were consistent with theoretical estimates found in the literature. Changes in feed intake and live BW in linear and nonlinear models failed to adequately describe efficiencies of metabolic processes, which are better characterized by changes in retained energy as a function of ME intake in nonlinear models.

Models of energy utilization used in livestock production predict input:output relationships well, for all the wrong reasons. Predictive accuracy in such models is not due to fidelity to biochemistry and laws of thermodynamics, but because they were developed to predict accurately, often with little regard to biochemical consistency. Relatively static linear statistical models limit thermodynamically relevant descriptions of energy utilization, especially maintenance, in growing beef cattle and are inadequate research tools, in either ordinary least squares (OLS) or Bayesian frameworks. Metabolizable energy intake (MEI) at recovered energy (RE) = 0 (MEm) and efficiencies of ME utilization for maintenance (km) and gain (kg) were estimated for 3 independent data sets using OLS or Bayesian frameworks. Estimates of MEm differed (P < 0.05) between OLS and Bayesian estimates and were not unique, indicating model misspecification. Bayesian estimates of MEm were monotonic, positive, and nonlinear f(MEI); the range was from 6.74 to 14.8 Mcal/d. Estimates of km, the ratio of heat energy (HE) at MEI = 0 to MEm, for the 3 data sets averaged 0.590 for OLS solutions, or 0.616 for the first derivative (km, dHE/dMEI for RE = 0) of a first-order function. The first derivative (dHE/dMEI) of the OLS function was > 1.0 for MEI > 22.1 Mcal/d, counter to the laws of thermodynamics and indicated model misspecification. The Bayesian estimate of km (0.420) differed (P < 0.05) from the OLS estimate and was consistent with the efficiency of ATP synthesis. Efficiency of ME use for gain for RE > 0 (kg, OLS solutions) averaged 0.397, solutions were nonunique and single-variable OLS models were misspecified (P < 0.050) for 2 of the 3 data sets. The OLS estimate of kg differed (P < 0.05) from the estimate of kg (0.676) determined in a Bayesian framework; the latter was calculated as dRE/dMEI for RE > 0. For OLS estimates km > kg; for estimates determined in a Bayesian framework km < kg, the former is inconsistent, while the latter is consistent with the thermodynamic favorability of reactions underlying maintenance and gain. Our results show that the use of relatively fixed coefficients of maintenance in current feeding standards, mathematical descriptions of metabolic processes and concepts regarding efficiencies of energy utilization in those systems need modification to be consistent with animal biology and the laws of thermodynamics.