Fitting lactation data with two mathematical models and extension factors for milk, fat and protein of Belgian dairy goats

Data for 18 155 test day milk yields and fat and protein percentages recorded from 15 February 1988 to 1 September 1993 were obtained from the Office de promotion des petits élevages en Wallonie. Due to irregular test intervals and a variable number of tests per lactation, production was estimated at 25 day intervals (25, 50, ..., 250 days). A total of 13 773 test day records for Anglo-Nubian, Chamoisee, Saanen and crossbreds were available for analysis. Parities were classified into 1 and ≥ 2. The inverse polynomial and the incomplete gamma functions were fitted to test day milk yields in order to define the shape of the lactation curves for the various breeds and parities. Two data subsets were created by random selection of entire lactation data from the original data set, and both functions were fitted to test day milk yields within breed-parity classes. Parameters of equations estimated on a subset of the data were validated on the other subset. Estimates of peak yields were higher and times of peak yield later by the inverse polynomial method than by the incomplete gamma but remained within ranges found in the literature. Based on the coefficient of multiple determination (R2), both equations were equally accurate in fitting lactation data of a subset. Though average residual deviations were slightly higher with the inverse polynomial than with the incomplete gamma, the crossvalidation did not reveal any particular trend of residuals for any equation. For practical reasons, extension factors for milk, fat and protein yields were derived using the inverse polynomial and are presented.