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

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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.