Abstract
Among milk traits, fat-to-protein ratio (FPR) is considered a potential measure of a cow’s energy status and is one of the selection criteria necessary to improve metabolic stability. Further genetic analyses require an appropriate model that describes the pattern of FPR changes throughout lactation. The objective of the study was to examine five mathematical functions to describe the lactation curve for FPR in the first three lactations of Polish Holstein-Friesians. The dataset contained FPR records for 5690 cows in the first lactation, 4081 cows in the second, and 2636 cows in the third lactation based on 48908, 34706, and 22097 test-day (TD) records, respectively. Using the MIXED procedure of SAS statistical analytics software, ten linear models (five with fixed effects only, and five with the additional random effect of cow) were fitted to the TD records. The goodness of fit was tested with Akaike's information criterion, residual variances and the correlation coefficient between the actual and estimated values. The model proposed by Ali and Schaeffer (1987) had the best fit to FPR in the first three parities, and the model of Wilmink (1987) provided the worst fit. The correlation coefficient between the actual and the estimated values of FPR was higher for models that included the random cow effect compared with models without this effect.
Highlights
Modelling lactation curves for dairy cows has been under development from the first half of the twentieth century (Brody et al, 1924; Grossman & Koops, 1988; Tozer & Huffaker, 1999; Tekerli et al, 2000; Macciotta et al, 2005; Silvestre et al, 2006; Torshizi et al, 2011)
The mean TD milk yield was lowest in the first lactation (26.70) and highest in the third lactation (31.15), whereas the mean test-day fat-to-protein ratio (FPR) remained at the same level in all three lactations (0.15 - 0.16) (Table 2)
Five mathematical functions were tested for modelling the lactation curve for FPR in the first three lactations of Polish Holstein-Friesian cows
Summary
Modelling lactation curves for dairy cows has been under development from the first half of the twentieth century (Brody et al, 1924; Grossman & Koops, 1988; Tozer & Huffaker, 1999; Tekerli et al, 2000; Macciotta et al, 2005; Silvestre et al, 2006; Torshizi et al, 2011). The suitability of mathematical functions for modelling lactation curves for other species (dairy goats, sheep, beef cows) was investigated (Hohenboken et al, 1992; Carta et al, 1995; Groenewald et al, 1995). Researchers began to use more general mathematical functions such as splines and Legendre polynomials (White et al, 1999; Schaeffer, 2004; Macciotta et al, 2005; Silvestre et al, 2005; Silvestre et al, 2006). Higher-order Legendre polynomials were required to fit the lactation curve correctly. Splines seemed to be a good replacement for Legendre polynomials because of their flexibility in fitting lactation curves. Problems occurred with choosing an optimal number and placement of knots (Silvestre et al, 2005; Bohmanova et al, 2008; Macciotta et al, 2010)
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