ABSTRACT
Net energy systems, such as the California Net Energy System (CNES), are useful for prediction of input:output relationships not because of fidelity to the laws of thermodynamics, but because they were designed to predict well. Unless model descriptions of input:output relationships are consistent with the laws of thermodynamics, conclusions regarding those relationships may be incorrect. Heat energy (HE) + recovered energy (RE) = ME intake (MEI) is basic to descriptions of energy utilization found in the CNES and is consistent with the laws of thermodynamics; it may be the only relationship described in the CNES consistent with the first law of thermodynamics. In the CNES, efficiencies of ME utilization for maintenance (km) and gain (kg) were estimated using ordinary least squares (OLS) equations. Efficiencies thus estimated using static linear models are often inconsistent with the biochemistry of processes underlying maintenance and gain. Reactions in support of oxidative mitochondrial metabolism are thermodynamically favorable and irreversible; these reactions yield ATP, or other high-energy phosphate bonds, used for what is generally termed maintenance. Synthesis of biomass (gain) is less thermodynamically favorable; reactions do not proceed unless coupled with hydrolysis of high-energy phosphate bonds and lie closer to equilibrium than those in support of oxidative mitochondrial metabolism. The opposite is described in the CNES (k m > k g) due to failure of partitioning of HE; insufficient HE is accounted for in maintenance. Efficiencies of ME utilization (k m and k g) as described in the CNES are variable. Further neither k m nor k g are uniformly monotonic fâ(ME, Mcal/kg); for ME (Mcal/kg) <0.512 or >4.26, k m are inconsistent with thermodynamically allowed values for efficiencies (>1.0); k g are a monotonically positive fâ(ME) concentration (Mcal/kg) for ME <3.27 Mcal/kg. For ME <1.42 Mcal/kg, k g are not in the range of thermodynamically allowed values for efficiencies (0 to 1.0). Variable efficiencies of ME utilization require that the first law may not be observed in all cases. The CNES is an excellent empirical tool for prediction of input:output relationship, but many CNES parameter estimates evaluated in this study lack consistency with biology and the laws of thermodynamics.
ABSTRACT
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.
