Modeling the lactation curve of Holstein dairy cows using the Sine function and comparing it with Dijekstra and Wood’s functions in a herd of Holstein dairy cow

Document Type : Research Paper


1 PhD student, Department of Applied Mathematics, Faculty of Mathematics, University of Guilan, Rasht, Iran.

2 PhD student, Department of Animal Science, Faculty of Agriculture, Ferdowsi University of Mashhad, Mashhad, Iran.

3 Professor, Department of Applied Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.

4 Professor, Department of Animal Science, Faculty of Agriculture, University of Birjand, Birjand, Iran


Description of lactation curve were investigated using sine function, compare it with two functions (Dijekstra and Wood). The data contained 32233 dairy milk yield records from 93 first parity Iranian Holstein cows that had calving between Aug. 2008 and Jul. 2009. Actual milk production per day and subsequently the actual production of each animal were available in the first lactation. Lactation records of milk production per cow from 7 until the end of lactation was used for the study. The data was fitted by the Trust-Region method in MATLAB software. The models were tested for goodness of fit using sum of squares error (SSE), root mean square error (RMSE) and coefficient of determination (R-square). Also expression for the feautures of the lactation curve were calculated by using mathematical’s formulaes. Goodness of fit and lactation features of models was subjected to analysis using the MIXED procedure of SAS (2001) that the random effect was effect of cow. The results showed that Sine function can be fitted to daily milk production records. Statistical analysis showed that significant differences exist between the goodness of models (P< 0.01) and the best fitting was related to the Sine and Wood function. The random effect of cow was also significant (P< 0.01) that reflects the variable response of each animal to each model. Numerically, all the estimated features of the lactation curve given by the Sine function were similar to Dijkstra and Wood functions. The results showed simple Sine function has high competence and ability to fit the daily records of milk production. Also, Sine function could describe the persistency of lactation much better than the other models. Biologically, the parameters of Sin function were acceptable and showed some part of lactation curve but all three functions couldn’t fit the first 30 days of lactation in the best way.