Segmented regression to describe cumulative milk production of grazing dual-purpose Holstein-Zebu cows

Abstract

The objective of this study was to compare the fit of seven functions to cumulative daily milk yield records of grazing F1 (Holstein × Zebu) cows in a dual-purpose cattle production unit of the Mexican tropics. Fifty-seven lactations from cows that calved from 1998 to 2001 were used. The functions were quadratic without intercept, three with two segments (both segments linear, the first segment quadratic and the second linear, and both segments quadratic), and three classical growth functions (Gompertz, logistic, and Richards). The Akaike information criterion corrected (AIC_C) was used as criterion of fit, being the function with the best fit the one with the lowest AIC_C value. The best fit was for the segmented function with both segments quadratic, followed closely by the Richards function. The derivatives of these functions give the daily milk yield curve (kg/cow/day), so the former results in a straight line per segment and the latter in the usual shape of the typical lactation. However, as cumulative records produce a monotonic increasing line, neither function can distinguish a priori the presence of a lactation peak. For this reason, it is advisable to examine the common dispersion plot of daily milk yield of each cow, and if a peak is not evident, then proceed to fit the segmented function; otherwise, the function of Richards should be used. The need to study the causes for the absence of a lactation peak in tropical dual-purpose cows is highlighted.