Comparative evaluation of some mathematical fuctions in describing the lactation curve of Iranian dairy cattle

The objective of this study was to compare some nonlinear functions (Wood, Dhanoa, Wilmink, Ali-Schaeffer, Cappio Borlino, Cobby – Le Du, Dijkstra, Rook, Gous and Nelder) to describe the milk production curve of Iranian Holstein cattle. A dataset consisted of 6079976, 4879486 and 3312416 test-day milk yield records related to first, second and third three lactation periods, respectively, from 3550 herds collecting by the Animal Breeding Center of Iran from 1983 to 2017, were used. The average of test day milk records for three lactation was 31.17, 34.08 and 33.83 kg, respectively. The nlme package of R software (version 3.4.3) was used for fitting nonlinear functions. The nonlinear functions were compared using four goodness of fit criteria, including Akaike’s information criterion (AIC), Bayesian information criterion (BIC), Root mean square error (RMSE) and Durbin-Watson index (DW). The Rook function showed the best fit for the milk production curve shape for three lactations in Iranian Holstein cattle when compared to other functions. The Gous and Rook functions showed the highest accuracy in predicting peak time, peak yield and persistency of milk production parameters in different lactations, but in general, the Rook function has a high predictive value in estimating the milk curve parameter descriptors.Therefore, Rook function is recommended for describing the milk production curve of Iranian Holstein cattle.