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, C.K. Reynolds

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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 (MEm), 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, MEm 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 MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 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 BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.
Original languageEnglish
Pages (from-to)2904-2913
JournalJournal of Dairy Science
Issue number9
Publication statusPublished - 2003


  • whole-crop wheat
  • nutrient utilization
  • feeding systems
  • milk-production
  • genetic merit
  • cattle
  • grass
  • nitrogen
  • silage
  • fermentation

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    Kebreab, E., France, J., Agnew, R. E., Yan, T., Dhanoa, M. S., Dijkstra, J., Beever, D. E., & Reynolds, C. K. (2003). Alternatives to linear analysis of energy balance data from lactating dairy cows. Journal of Dairy Science, 86(9), 2904-2913.