Use of some mathematical models to study the lactation curve of Murrah buffaloes and their crossbreeds under a semi-extensive system in the state of Sao Paulo

Abstract

In the present study, five mathematical models, two of which were linear: linear hyperbolic (FLH) and quadratic logarithmic (FQL); and three non linear: parabolic exponential (FPE), incomplete gamma (FIG), and inverse polynomial (FIP), were used to determine which of them gave best fit to the mean lactation curve, using data from three buffalo herds of the Murrah breed and its crossbreds, under a semi-extensive production system employing twice daily milking. Information was obtained on 3267 lactations, including 27600 test day milk weights. Milk testing was done at 30-day intervals over the period from 1990 to 2001. Lactations utilized in the analysis were based on a minimum of four and maximum of nine test days. Criteria used to verify the goodness of fit of the curve generated by each model were: adjusted coefficient of determination (R2A), lack of fit test (LDF), and graphs of the distribution of residuals and of residual lag. The highest R2A 86.29%, was obtained with both FQL and FLH, which also yielded the lowest residuals and not significant results (P>.05) in the LOF test.