Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins

In order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin–Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second- and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second- and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first- and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second- and third- lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.