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

Abstract

SUMMARY Descriptions 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.