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

Published online by Cambridge University Press:  02 September 2010

P. C. N. Groenewald ,
A. V. Ferreira ,
H. J. van der Merwe  and
S. C. Slippers
P. C. N. Groenewald
Affiliation:
Department of Mathematical Statistics, University of the Orange Free State, Bloemfontein, South Africa
A. V. Ferreira
Affiliation:
Department of Animal Science, Faculty of Agriculture, University of the Orange Free State, PO Box 339, Bloemfontein 9300, South Africa
H. J. van der Merwe
Affiliation:
Department of Animal Science, Faculty of Agriculture, University of the Orange Free State, PO Box 339, Bloemfontein 9300, South Africa
S. C. Slippers
Affiliation:
Department of Agriculture, University of Zululand, Kwadlangezwa, South Africa
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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.

Keywords

eweslactation curvemathematical models
Type
Research Article
Information
Animal Science , Volume 61 , Issue 1 , August 1995 , pp. 95 - 101
Copyright
Copyright © British Society of Animal Science 1995

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