Analysis of lactation shapes in extended lactations

Abstract

In order to describe the temporal evolution of milk yield (MY) and composition in extended lactations, 21 658 lactations of Italian Holstein cows were analyzed. Six empirical mathematical models currently used to fit 305 standard lactations (Wood, Wilmink, Legendre, Ali and Schaeffer, quadratic and cubic splines) and one function developed specifically for extended lactations (a modification of the Dijkstra model) were tested to identify a suitable function for describing patterns until 1000 days in milk (DIM).Comparison was performed on individual patterns and on average curves grouped according to parity (primiparous and multiparous) and lactation length (standard <305 days, and extended from 600 to 1000 days). For average patterns, polynomial models showed better fitting performances when compared with the three or four parameters models. However, LEG and spline regression, showed poor prediction ability at the extremes of the lactation trajectory. The Ali and Schaeffer polynomial and Dijkstra function were effective in modelling average curves for MY and protein percentage, whereas a reduced fitting ability was observed for fat percentage and somatic cell score. When individual patterns were fitted, polynomial models outperformed nonlinear functions. No detectable differences were observed between standard and extended patterns in the initial phase of lactation, with similar values of peak production and time at peak. A considerable difference in persistency was observed between 200 and 305 DIM. Such a difference resulted in an estimated difference between standard and extended cycle of about 7 and 9 kg/day for daily yield at 305 DIM and of 463 and 677 kg of cumulated milk production at 305 DIM for the first-and second-parity groups, respectively. For first and later lactation animals, peak yield estimates were nearly 31 and 38 kg, respectively, and occurred at around 65 and 40 days. The asymptotic level of production was around 9 kg for multiparous cows, whereas the estimate was negative for first parity.

On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions

“…Some of the models have been derived from a mechanistic approach (Dijkstra et al, 1997;Pollott, 2000) with the purpose of not only predicting milk yield at any DIM but also of representing physiological and cellular processes occurring in the mammary gland. The statistical performance and suitability of the different lactation equations available in the literature has been extensively studied (Rook et al, 1993;Sherchand et al, 1995;Scott et al, 1996;Olori et al, 1999;Rekik et al, 2003;Val-Arreola et al, 2004;Macciotta et al, 2005;Silvestre et al, 2006;Dematawewa et al, 2007;Dijkstra et al, 2010;Steri et al, 2012). The study described herein provides a novel insight into the modeling of lactation curves, proposing the use of classical growth functions to represent the cumulative milk production curve.…”

Effect of calving interval and parity on milk yield per feeding day in Danish commercial dairy herds

“…A lactation curve can be fitted with either empirical (e.g., Wood, 1967;Wilmink, 1987) or mechanistic (e.g., Dijkstra et al, 1997) mathematical functions. The ability of the model to describe the asymptotic phase occurring mid to late lactation is important to estimate daily yield during extended lactations (Macciotta et al, 2011;Steri et al, 2012). Legendre polynomials are useful because they can represent a greater number of lactation curvatures, and their mathematical properties cause them to have less correlation among parameters (Macciotta et al, 2005).…”

Comparison of non-linear models to describe the lactation curves for milk yield and composition in buffaloes (Bubalus bubalis)

“…Mathematical models of the lactation curve and, in general, of the mammary gland represent a valuable tool for basic research studies aimed at increasing the scientific knowledge of complex physiological mechanisms that underlie the milk secretion process (Dimauro et al, 2005). Lactation curves may be applied by physiologists, nutritionists and other researchers to mimic the lactation process and to study the relationships existing between secretory cells, hormones, energy supply and environmental effects affecting the milk production process (Steri et al, 2012). On a dairy farm scale, the pattern of milk yield (MY) across the year depicts the trend of the main farm income.…”

“…The aim of empirical mathematical models is to provide a basis for identifying the difference between regular component and stochastic one. In addition, interpretation of the parameters of the function used and identification of the mechanisms which control the process are important in empirical models (Steri et al, 2012). These empirical models have large application in different fields of animal science, basically due to their limited mathematical complexity.…”