Partitioning of feed intake into maintenance and gain in growing beef cattle: Evaluation of conventional and Bayesian analyses

Mathematical absurdities in the California net energy system

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 f (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 f (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.

BOARD-INVITED REVIEW: Efficiency of converting digestible energy to metabolizable energy and reevaluation of the California Net Energy System maintenance requirements and equations for predicting dietary net energy values for beef cattle

For the past several decades, nutrient requirement systems for beef cattle in North America have recommended that dietary ME can be calculated as dietary DE × 0.82, but considerable published data suggest a variable relationship between DE and ME. We reviewed the literature and tabulated the results of 23 respiration calorimetry studies (87 treatment mean data points), in which measurements of fecal, urinary, and gaseous energy were determined with beef cattle (bulls, steers, and heifers) and growing dairy cattle. Mixed-model regression analyses to adjust for the effects of the citation from which the data were obtained suggested a strong linear relationship between ME and DE (Mcal/kg of DM; ME = 0.9611 × DE - 0.2999; = 0.986, root mean square error [RMSE] = 0.048, < 0.001 for intercept, slope ≠ 0). Analysis of residuals from this simple linear regression equation indicated high correlations of residuals with other dietary components, and a slight increase in precision was obtained when dietary CP, ether extract, and starch (% of DM) concentrations were included in a multiple linear regression equation (citation-adjusted = 0.992, RMSE = 0.039). Using the simple linear relationship, we reevaluated the original data used to develop the California Net Energy System (CNES) for beef cattle by recalculating ME intake and heat production and regressing the logarithm of heat production on ME intake (both per BW, kg daily). The resulting intercept and slope of the recalculated data did not differ ( ≥ 0.34) from those reported for the original analyses of the CNES data, suggesting that use of the linear equation for calculating ME concentration was consistent with NEm and NEg values as derived in the CNES. Nonetheless, because the cubic equations recommended by the NRC to calculate dietary NEm and NEg from ME were based on conversion of DE to ME using 0.82, these equations were mathematically recalculated to account for the linear relationship between DE and ME. Overall, our review and analyses suggested that there is a strong linear relationship between DE and ME, which seems to be consistent across a wide range of dietary conditions, cattle types, and levels of intake. Applying this linear relationship to predict ME concentrations agreed with the original CNES calculations for NE requirements, thereby allowing the development of new equations for predicting dietary NEm and NEg values from ME.

Growth performance, feed digestibility, body composition, and feeding behavior of high- and low-residual feed intake fat-tailed lambs under moderate feed restriction

Two experiments were conducted to evaluate the effect of moderate feed restriction on productivity of lambs classified on the basis of phenotypic expression of residual feed intake (RFI). In Exp. 1, 58 fat-tailed Kurdi ram lambs (32.1 ± 4.2 kg BW) were individually fed, ad libitum, a pelleted diet (35% alfalfa hay and 65% concentrate). Feed intake and ADG were determined for a 6-wk period and 3 feed efficiency measures including RFI, G:F, and partial efficiency of maintenance (PEM) were calculated. The lambs were sorted based on RFI and the 16 highest RFI (RFI ≥ mean + 0.5 SD) and 16 lowest RFI (RFI ≤ mean - 0.5 SD) lambs were subjected to body composition (BC) and DM digestibility (DMD) analysis. Feeding behavior traits (FB) were also evaluated for 24 h using a regular 5-min interval observation method. The high- and low-RFI lambs (14 lambs/RFI group) so classified in Exp. 1 were used in Exp. 2. Half of the lambs in each RFI group were randomly selected to be fed ad libitum or 85% of ad libitum (restricted feeding), which resulted in 4 experimental groups: 1) ad libitum high-RFI, 2) feed restricted high-RFI, 3) ad libitum low-RFI, and 4) feed restricted low-RFI. The lambs were fed the same diet as Exp. 1, and growth efficiency during a 6-wk test period as well as BC, DMD, and FB were also determined in Exp. 2. In Exp. 1, the low-RFI lambs consumed 14% ( < 0.01) less feed than high-RFI lambs. Differences were also observed between high- and low-RFI groups for G:F ( = 0.01), RFI ( < 0.01), and PEM ( < 0.01) in Exp. 1, but no differences were detected between high- and low-RFI lambs for ADG ( = 0.79), DMD ( = 0.42), BC ( > 0.72), and FB ( > 0.24). In Exp.2, the restriction feeding regime negatively affected ADG ( < 0.01) and G:F ( = 0.02) in low-RFI lambs, whereas G:F ( = 0.02) and PEM ( < 0.01) were improved in high-RFI lambs under the feed restriction condition. No effects of feed restriction on DMD ( = 0.87) and BC ( > 0.05) were observed. The lambs fed at the restricted level of intake presented a greater time ( < 0.01) and rate ( = 0.01) of eating than those fed ad libitum. Although bunk visits and feeding events were decreased ( < 0.01) with feed restriction, no interaction ( > 0.05) was detected between RFI phenotype and feeding regime for FB. In summary, feeding high-RFI lambs at 85% of ad libitum level improved G:F with no effect on ADG, whereas growth performance was reduced by feeding low-RFI lambs at 85% of ad libitum. However, these changes in feed efficiency were not related to DMD, BC, or FB.