Modelling the lactation curve of dairy cows using the differentials of growth functions

Abstract

SU MMARYDescriptions of entire lactations were investigated using six mathematical equations, comprising the differentials of four growth functions (logistic, Gompertz, Schumacher and Morgan) and two other equations (Wood and Dijkstra). The data contained monthly milk yield records from 70 first, 70 second and 75 third parity Iranian Holstein cows. Indicators of fit were model behaviour, statistical evaluation and biologically meaningful parameter estimates and lactation features. Analysis of variance with equation, parity and their interaction as factors and with cows as replicates was performed to compare goodness of fit of the equations. The interaction of equation and parity was not significant for any statistics, which showed that there was no tendency for one equation to fit a given parity better than other equations. Although model behaviour analysis showed better performance of growth functions than the Wood and Dijkstra equations in fitting the individual lactation curves, statistical evaluation revealed that there was no significant difference between the goodness of fit of the different equations. Evaluation of lactation features showed that the Dijkstra equation was able to estimate the initial milk yield and peak yield more accurately than the other equations. Overall evaluation of the different equations demonstrated the potential of the differentials of simple empirical growth functions used in the current study as equations for fitting monthly milk records of Holstein dairy cattle.

The effect of the calving season on the Wood’s model parameters and characteristics of the lactation curve in Czech Fleckvieh cows

“…Macciotta et al (2005), Třináctý et al (1990) and Dematawewa et al (2007) presented lower values of the parameters, while Gołębiewski et al (2011) found higher values (except for c). Fathi Nasri et al (2008) observed that the first-parity cows reached the peak yield of 33.6 kg 63 days post-partum, the second-parity cows achieve the climax of 39.5 kg 46 days post-partum and the third-parity cows produced a maximum of 41.8 kg of milk 42 days post-partum. Similarly to Fathi Nasri et al (2008), we also found that later-parity cows reached maximum sooner and produced more milk at peak than younger cows.…”

“…Fathi Nasri et al (2008) observed that the first-parity cows reached the peak yield of 33.6 kg 63 days post-partum, the second-parity cows achieve the climax of 39.5 kg 46 days post-partum and the third-parity cows produced a maximum of 41.8 kg of milk 42 days post-partum. Similarly to Fathi Nasri et al (2008), we also found that later-parity cows reached maximum sooner and produced more milk at peak than younger cows. In the study of Dematawewa et al (2007) cows produced a maximum of 33.35 kg milk 102 days post-partum.…”

“…Třináctý et al (1990) calculated the IP 2:1 between 74.2 and 77.2, regardless of the number of lactation, which is slightly lower than our values (Table 4). Fathi Nasri et al (2008) estimated the 305 days milk production at 8 068 kg (lactation 1), 9 233 kg (lactation 2) and 9 323 kg (lactation 3) in Holstein cattle population in Iran. The similar issue in population of Iranian Holstein was studied by Roshanfekr et al (2010).…”

“…Table 2 ( Fathi Nasri et al 2008) shows some parameters of the lactation curve: t-days at the peak yield, y m -peak milk yield, r-a coefficient describing the degree of declination between the peak and the end of the lactation, a, b, c-estimated parameters of the Wood's model. These parameters determined the shapes of lactation curves for the parity groups 1, 2 and 3, with respect to the calving season; the total and partial (305 days, 1-100 days and 100-200 days) milk yields were calculated.…”

Lactation curves of different cattle breeds under cooperative dairying conditions in Bangladesh

“…Several studies (e.g. Macciotta et al 2005;Fathi Nasri et al 2008), have shown that the differences in the general shape and the differences of model parameters are associated with yield at the beginning of lactation, the degree of incline and decline before and after peak yield, days in milk at peak and peak and lactation yields of the lactation curves.…”