A proposed new empirical model for the lactation curve of the cow and its use with a milking database for farm management

On a dairy cattle farm in Basilicata over a three-year period, for cows milked twice per day, milking data were collected using an automatic system based on electronic individual identification of cows and their related milk yields. Using collected data a new empirical model of the cow lactation curve was tested in order to verify its predictive capacity in comparison with other existing models. The model proposed uses the cubic b-spline function as an approximating function on 6 variable knots sequence. The models considered were: spline3-6 (6 variable knots), spline3-5 (5 variable knots), lognormal4 (a general peak approximating function), Guo95, Wilmink87, Ali87, Emmans86, Wood67, Nelder66, Brody45. The cubic b-spline with 6 variable knots achieved the best score (S). A possible use of the model with respect to the lactation curve database involves the definition of the "mean productivity index after 305 days from calving" (IPM305): this is defined as the average value of the lactation curve over the specified 305-day period. Two useful guideline applications are proposed and discussed: the first involves the positioning of the daily milk yield onto the herd lactation curve model; the second concerns the comparison of IPM305 of each cow with respect to the IPM305 of the herd averaged over all the cows (HIPM305).