A mathematical model for describing and predicting the lactation curve of Merino ewes

Abstract

The milk production of 63 5-year-old Merino ewes was measured over a 16-week period after lambing. The purpose was to find a suitable mathematical model to represent the lactation curve of Merino sheep and to estimate the parameters of the model for an individual ewe from a single data point in early lactation. Three models were considered, the three-parameter Wood model, yn = nb exp(a + en), the four-parameter Morant model, yn = exp(a + bn + en2 + d/n and the six-parameter Grossman model, yn = a1b1 - [tanh2 (b1n - c1))] + a2b2[1 – tanh2 (b2(n -c2,))].The Grossman model was found to be inappropriate for the available data, while there seems to be little difference in the suitability of the other two models. The Wood and Morant models both seem adequate to represent the lactation curve. A pattern in the estimated residuals suggests possible autocorrelations in the errors, but this is inconclusive due to the limited number of data points per animal.The correlation between the estimated parameters of the model and the daily yield measured during the 1st week of lactation enabled us to use linear regression to estimate the lactation curve of an individual animal based on the 1st week's yield. Confidence and prediction intervals for the yield during the rest of the lactation period may then also be constructed. This makes it possible to extend incomplete milk records for use in genetic evaluation, formulation of rations and economic evaluations.

Accurate mathematical models to describe the lactation curve of Lacaune dairy sheep under intensive management

“…The primary advantage of FP over other functions is the ease of calculation. The Grossman model showed good results, similar to the study by Groenewald et al (1995) on sheep, but with a more complex function.…”

“…Few studies have examined the complete lactation of sheep. Most of them deal with ewes under experimental conditions (Groenewald et al, 1995;Portolano et al, 1996) or management conditions with suckling periods (Ruiz et al, 2000;Oravcová et al, 2006). Not many studies have been conducted under intensive farm conditions (Pollott andGootwine, 2000 and2004).…”

Application of two models to the lactation curve of Massese ewes

“…Though estimated values with other sheep breeds in other studies may not be strictly comparable, it should be noted that the time of peak yield obtained here by the W model (average 9.3 days) was earlier than that reported for Comisana sheep (14.3 days) by Portolano et al (1996a), for various crossbreeds (16.5 days) by Torres-Hernandez and Hohenboken (1980), for Merinos (3 weeks) by Groenewald et al (1995), and for Sarda sheep (4.6 weeks) by Cappio-Borlino et al (1989), and that generally actual peak yield is higher than the estimates for those sheep breeds. It therefore seems that the milk yield of Massese ewes exhibits a more sudden and rapid increase than that of other sheep breeds, and it may be for this reason that the W model does not ®t this yield so well in the initial phase.…”

“…To study the lactation curve of dairy sheep, several papers dealt speci®cally with the application of Wood's model (W model) to various sheep breeds (Torres-Hernandez and Hohenboken, 1980;CappioBorlino et al, 1989;Sakul and Boylan, 1992;Groenewald et al, 1995Groenewald et al, , 1996Portolano et al (1996a). Cappio-Borlino et al (1995), however, proposed a non-linear modi®cation of Wood's equation (a biexponential function) for the lactation curve of Sarda ewes in order to make it ®t better the rising phase of lactation which is often not adequately described by the b parameter of the W model because of the very early occurrence of peak yield.…”

Modelling the lactation curve of rabbit does: Towards a model including fit suitability and biological interpretation

“…(Groenewald et al, 1995). The most well-known and commonly used model to describe lactation curves, especially applied to cattle, is the incomplete gamma function or Wood's model (Wood, 1967), which is defined by three parameters related to the shape of the lactation curve.…”