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Alternatives to Linear Analysis of Energy Balance Data from Lactating Dairy Cows

E. Kebreab^*, J. France^*, R. E. Agnew, T. Yan, M. S. Dhanoa, J. Dijkstra, D. E. Beever^* and C. K. Reynolds^*,1

^* School of Agriculture, Policy and Development, The University of Reading, Earley Gate, Reading RG6 6AR, United Kingdom
The Agricultural Research Institute of Northern Ireland, Hillsborough, Co. Down, Northern Ireland BT26 6DR, United Kingdom
Institute of Grassland and Environmental Research, Plas Gogerddan, Aberystwyth, Dyfed SY23 3EB, United Kingdom
Animal Nutrition Group, Wageningen Institute of Animal Sciences, Wageningen University, Marijkeweg 40,6709 PG Wageningen, The Netherlands

Corresponding author: E. Kebreab; e-mail: e.kebreab{at}reading.ac.uk.

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (ME_m), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k_l), 3) growth (k_g), and the efficiency of utilization of body stores for milk production (k_t). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k_g and k_t. Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k_g and k_t using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k_g and 0.82 to 0.84 for k_t. Using the estimated values of k_g and k_t, the data were corrected to allow for body tissue changes. Based on the definition of k_l as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, ME_m and k_l were determined. Meta-analysis of the pooled data showed that the average k_l ranged from 0.50 to 0.58 and ME_m ranged between 0.34 and 0.64 MJ/kg of BW^0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW^0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Key Words: energy metabolism • dairy cow • lactation

Abbreviation key: BIC = Bayesian information criteria, E_l = energy in milk (MJ/d), k_g = the marginal efficiency of utilization of MEI for growth, k_l = the marginal efficiency of utilization of MEI for milk production, k_m = the marginal efficiency of utilization of MEI for maintenance, k_t = the marginal efficiency of utilization of body stores for milk production, MBW = metabolic body weight (kg^0.75), ME = metabolizable energy, MEI = ME intake (MJ/kg^0.75/d), ME_m = ME requirement for maintenance (MJ/kg^0.75/d), T_g = tissue gain (MJ/kg^0.75/d), T_l = tissue loss (MJ/kg^0.75/d)

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