Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

The objective of this study was to evaluate four mathematical models with regards to their fit to lactation curves of Holstein cows from herds raised in the southwestern region of the state of Parana, Brazil. Initially, 42,281 milk production records from 2005 to 2011 were obtained from "Associação Paranaense de Criadores de Bovinos da Raça Holandesa (APCBRH)". Data lacking dates of drying and total milk production at 305 days of lactation were excluded, resulting in a remaining 15,142 records corresponding to 2,441 Holstein cows. Data were sorted according to the parity order (ranging from one to six), and within each parity order the animals were divided into quartiles (Q25%, Q50%, Q75% and Q100%) corresponding to 305-day lactation yield. Within each parity order, for each quartile, four mathematical models were adjusted, two of which were predominantly empirical (Brody and Wood) whereas the other two presented more mechanistic characteristics (models Dijkstra and Pollott). The quality of fit was evaluated by the corrected Akaike information criterion. The Wood model showed the best fit in almost all evaluated situations and, therefore, may be considered as the most suitable model to describe, at least empirically, the lactation curves of Holstein cows raised in Southwestern Parana.

dairy cattle; milk yield; mathematical models selection; non-linear models