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Linear and Non-Linear Estimates of the Efficiency Of Metabolizable Energy Use for Maintenance and Gain in Beef Cattle

**Abstract Text:**

Efficiencies of metabolizable energy (ME) utilization for maintenance (k_{m}) and gain (k_{g}) have historically been determined using ordinary least squares (OLS); these differ from efficiencies determined from known biochemical pathways. We evaluated the relationship between retained energy (RE) and ME intake using OLS and non-linear (NL) regressions using the data set from which the California Net Energy System (CNES) was developed. Parameter estimates from OLS regression were similar to classical estimates. In the non-linear estimate, ME required for maintenance (ME_{m}) was a first order function of ME intake; efficiency of ME used for maintenance was calculated as the first derivative of that function. Efficiency of ME use for gain was linear and was calculated as (ME intake - ME_{m}) x k_{g}. Parameter stability was evaluated using Markov Chain Monte Carlo (MCMC) simulation for both linear and non-linear estimates. Linear and non-linear estimates of ME_{m}, k_{m} and k_{g} were different (P < 0.05); the non-linear equation fit the data better (R^{2} = 0.850) than the linear equation (R^{2} =0.777). Linear estimates of ME_{m}, k_{m} and k_{g} were 0.133BW^{0.75 }(a static estimate), 0.588 and 0.432, respectively. A lack of fit F test indicated that the OLS model was correctly specified. However, parameter estimates for OLS solutions, determined by MCMC simulation, were highly unstable, an indication that the model is incorrectly specified. Non-linear estimates of ME_{m}were dynamic and were, on the average, greater than OLS estimates. Efficiency of ME use for maintenance was 0.382, a value similar to the efficiency of ATP synthesis. Efficiency of ME use for gain was 0.614; theoretical estimates of gain for growing beef cattle are from 0.70 to 0.75. A lack of fit F test indicated that the NL model was correctly specified. Non-linear parameter estimates were stable, indicating that the model is correctly specified. While it was possible to describe the NL relationship used in this study in the 1960s, the solution of that equation was extremely difficult to perform due to the lack of computing power at that time. This analysis indicates that, while OLS models are adequate to the task for which they were developed, prediction of animal output from feed input, and vice-versa, efficiencies calculated for these models are not in concert with animal biology. Efficiencies determined for NL models are similar to those calculated for biochemical pathways and may improve prediction of animal performance.

**Keywords: **efficiency, metabolizable energy, non-linear