Selection of a mathematical model to generate lactation curves using daily milk yields of Holstein cows

Mathematical descriptions of early stages of lactation were investigated using daily milk yields of 117 first, 78 second, 57 third, and 36 fourth lactations of 120 Holstein cows fitted by 10 models. The measure of fit was the error mean squares, which were replaced by ranks to perform an analysis of variance with lactation number, model, and period as factors and with cows as replicates. The interaction of model and lactation number was significant for the fit of the entire lactation. A significant interaction of model and period was obtained for the fit of three 30-d intervals. For the entire lactation, the best fit for all four lactations occurred from the diphasic logistic function, y = d1(1-tanh2(b1(nk-c1))) + d2(1-tanh2(b2(n-c2))). For the first 30 d, a modified gamma function gave the best fit for the first lactation, the inverse polynomial function for the second lactation, and the quadratic log function for the third lactation. The diphasic logistic function gave the best fit for the remaining two periods and was not significantly different from the best fitting models for the first 30-d period. Hence, this function may be useful to describe the lactation curve of Holstein cows for dairy herds in which the daily milk yield of individual cows is constantly monitored with a computer.