Development of empirical models to describe the response in lactating dairy cattle to changes in nutrient intake as defined in terms of metabolisable energy intake

Abstract The aim of this study was to develop empirical models to describe the response in lactating dairy cattle to changes in nutrient intake using data taken from the literature covering the past 25 years of research. Two curvilinear models were developed where all data points played a role in determining a common intercept on the x axis (metabolisable energy intake (MEI)) (model CI) or y axis (milk energy output) (model CII) using the asymptotic relationship y = a + br x . In determining the goodness-of-fit of the applied models, model CI had an R 2 value of 0.99 for milk yield (MY), milk energy output, milk fat output and milk protein output, while model CII had respective R 2 values of 0.96, 0.96, 0.94 and 0.96. Although all these values indicated that both models fitted the data very well, model CI was considered to be more appropriate. The developed models CI and CII were validated using data independent of those used in model development. Validation of models CI and CII verified that the developed models could predict, with reasonable precision (MSPE: 2.63 and 2.72 for model CI ( y =0) and model CII ( x =0), respectively), the outcome of an in vivo situation. Based on model CI, when cows had a milk yield (MY) of 20, 30 and 40 kg/day and a MEI of 210 MJ/day, the incremental responses in yield were predicted to be 0.06, 0.08 and 0.11 kg milk/MJ additional MEI. Similarly, using model CI, predictions showed that for cows yielding 30 kg milk/day and receiving 160, 210 or 260 MJ MEI/day, concomitant responses in MY were 0.14, 0.08 and 0.06 kg/MJ additional MEI. The developed models can predict the marginal response in MY to increasing increments of MEI, and will aid in the evolution of an economic basis to feeding systems for dairy cows.