A Comparison of Different Functions for the Description of Lactation Curve in Different Periods of Lactation of Holstein Cows using Test Day Records

Test day milk records of a Holstein dairy farm collected during years 2004 to 2006 on 142 cows in the 1st lactation vs. 140 cows in the 2nd lactation were used in this research. There were real milk yields of cows available in each part of lactation in this farm making it possible to compare functions based on the new criteria (squared error of estimation). Five functions were compared to estimate production records during each month of lactation, using test day records. These functions were incompelete gama, polynomial regression, inverse polynomial, Wilmink and mixed log function. These functions were compared with third order legender polynomial function for an estimation of total lactation milk yield (305 day milk yield). The criterion for comparing these six functions was the squared error of estimation. Functions were ranked through Quad test on squared error. The first rank in the 1st lactation belonged to incomplete gama function in the 1st, 2nd, 4th, 5th, 8th, and 9th month, polynomial regression function in the 3rd, and 6th month, mixed log function in the 7th month while Wilmink function in the 10th month of lactation. The first rank in the 2nd lactation belonged to incomplete gama function in the 1st, 4th, 5th, 6th, and 9th month, mixed log function in the 7th, and 8th month, while Wilmink function in the the 3rd, and 10th month and polynomial regression function in the 2nd month of lactation. Incomplete gama function won the first rank for estimation of total milk yield (305 day milk yield) in the 1st, 2nd lactation. In the 1st lactation, difference between Incomplete gama function and polynomial regression, third order legender polynomial function and in the 2nd lactation the difference between incomplete gama function and polynomial regression functions were significant.