The mathematical description of lactation curves in dairy cattle

Abstract

This review gives an overview of the mathematical modelling of lactation curves in dairy cattle. Over the last ninety years, the development of this field of study has followed the main requirements of the dairy cattle industry. Non-linear parametric functions have represented the preferred tools for modelling average curves of homogeneous groups of animals, with the main aim of predicting yields for management purposes. The increased availability of records per individual lactations and the genetic evaluation based on test day records has shifted the interest of modellers towards more flexible and general linear functions, as polynomials or splines. Thus the main interest of modelling is no longer the reconstruction of the general pattern of the phenomenon but the fitting of individual deviations from an average curve. Other specific approaches based on the modelling of the correlation structure of test day records within lactation, such as mixed linear models or principal component analysis, have been used to test the statistical significance of fixed effects in dairy experiments or to create new variables expressing main lactation curve traits. The adequacy of a model is not an absolute requisite, because it has to be assessed according to the specific purpose it is used for. Occurrence of extended lactations and of new productive and functional traits to be described and the increase of records coming from automatic milking systems likely will represent some of the future challenges for the mathematical modelling of the lactation curve in dairy cattle

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

“…Modern milking systems in dairy farms record the individual yields at each milking, thus the novel approach can be easily implemented. The increased availability of records per individual lactation represents a challenge for the mathematical modeling of lactation curves in dairy cattle, shifting the emphasis of modelers toward more flexible functions (Macciotta et al, 2011). The number of measurements, milking intervals, time interval between 2 consecutive recordings, and the DIM at which milk yield was recorded (particularly in early lactation and around the peak) are critical for accurate determination of lactation traits using conventional lactation curves (Nielsen et al, 2010;Macciotta et al, 2011;Wasike et al, 2011).…”

“…The increased availability of records per individual lactation represents a challenge for the mathematical modeling of lactation curves in dairy cattle, shifting the emphasis of modelers toward more flexible functions (Macciotta et al, 2011). The number of measurements, milking intervals, time interval between 2 consecutive recordings, and the DIM at which milk yield was recorded (particularly in early lactation and around the peak) are critical for accurate determination of lactation traits using conventional lactation curves (Nielsen et al, 2010;Macciotta et al, 2011;Wasike et al, 2011). Missing milk recordings (especially in early lactation) are a major handicap with classical lactation equations (Wasike et al, 2011;Adediran et al, 2012), whereas the novel approach presented herein would be affected to a lesser extent if a few (sporadic) records are missed.…”

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).…”

Molecular and Morphological Characteristics of Aradi Goats with Prediction Equation of Growth Pattern

“…Linear equation with only two parameters was perfect fit to growth data on Aradi goat from birth to 24 weeks of age. The linear model y t =a +bt was convenient tendency of growth pattern, a biological mean of parameter (b) was average growth rate and (a) was initial body weight (Macciotta et al, 2011;Madalena et al, 1979;Kamidi, 2005). A total of 1533 records of Aradi kids growth weights were used to test the model.…”