Modelling of the first lactation milk yield of Frieswal cows using different mathematical functions

Abstract

A study was conducted to find the most appropriate mathematical model that describes the first lactation milk yield of Frieswal cattle. Data on 42,368 individual first lactation test day yields of 1,072 Frieswal cows calved during 2005 to 2014 in Ambala and Meerut Military dairy farms were utilized for the study. The first test day milk yield was recorded on 6thday after calving while the subsequent records were collected at seven days interval and so the average 43 test day yields were taken for fitting the lactation curve models. Five different mathematical models, viz. Exponential decline function (EDF), Parabolic exponential function (PEF), Inverse polynomial function (IPF), Gamma function (GF) and Mixed log function (MLF) were fitted.The accuracy of fitting (R2 value) the models revealed that the MLF (96.14) was more appropriate followed by IPF (95.57), GF (93.85), PEF (83.68) and EDF (69.09). The RMSE estimate of MLF was lowest (0.3483) as expected while the EDF had the highest RMSE value of 0.9858.The AIC criterion was lowest for IPF (5.7175) and highest for GF (8.0212). The BIC values of five functions ranged between –83.6262 for MLF to 3.1809 for EDF. All the DW estimates were positive and ranged between 0.3656 for EDF to 0.7106 for GF indicating positive autocorrelation between the residuals. Based on the results obtained in the present study, it may be inferred that the first lactation yield was explained accurately by the mixed log function (MLF) in Frieswal cattle. As the inverse polynomial (IPF) and gamma function (GF) also had satisfactory results, these two functions can also be used for fitting the lactation curve models in Frieswal cattle. On the other hand, exponential decline function and parabolic exponential functions least explain the first lactation curve in Frieswal cattle.