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A partial adjustment model to describe the lactation curve of a dairy cow

Published online by Cambridge University Press:  02 September 2010

M. S. Dhanoa  and
Y. L. P. Le Du
M. S. Dhanoa
Affiliation:
Grassland Research Institute, Hurley, Maidenhead, Berkshire SL6 SLR
Y. L. P. Le Du
Affiliation:
Grassland Research Institute, Hurley, Maidenhead, Berkshire SL6 SLR
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Abstract

A new model is proposed to describe the lactation curve of a dairy cow. It uses the fact that milk yield at a given stage of lactation is largely determined by the yield in the preceding stage. The model is written as: yt = λ(m0 – m1t) + (1 – λ)yt–1. t ≥ 1, 0 ≤ λ ≤ 1, where y1, and yt–1 are the current and preceding milk yields in kg/week, and the constant × estimates the fraction (1–λ) by which milk yield adjusts to the level at the next stage. The fraction (1–λ) by which the milk yield persists at the preceding level is used to define a measure of persistency, P = (1–λ)m0/m1 weeks, where m1 is the rate of decline in kg/week and m0 is a constant.

Type
Research Article
Information
Animal Production , Volume 34 , Issue 3 , June 1982 , pp. 243 - 247
Copyright
Copyright © British Society of Animal Science 1982

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References

REFERENCES

Box, G. E. P. and Jenkins, G. M. 1976. Time Series Analysis: Forecasting and Control, pp. 174–186. Holden-Day, San Francisco.Google Scholar
Box, G. E. P. and Pierce, D. A. 1970. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J. Am. statist. Ass. 65: 1509–1526.CrossRefGoogle Scholar
Chatterjee, S. and Price, B. 1977. Regression Analysis by Example, pp. 181–192. John Wiley, New York.Google Scholar
Cobby, J. M. and Le Du, Y. L. P. 1978. On fitting curves to lactation data. Anim. Prod. 26: 127–133.Google Scholar
Dhanoa, M. S. 1981. A note on an alternative form of the lactation model of Wood. Anim. Prod. 32: 349–351.Google Scholar
Gaines, W. L. 1927. Persistency of lactation in dairy cows. Bull. III. agric. Exp. Stn, No. 288, pp. 355–424.Google Scholar
Griliches, Z. 1967. Distributed lags: a survey. Econometrica 35: 16–49.Google Scholar
Hoerl, A. E. and Kennard, R. W. 1970. Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12: 55–67.CrossRefGoogle Scholar
Jenkins, G. M. 1979. Modelling and Forecasting Time Series, pp. 88–94. Gwilym Jenkins and Partners (Overseas), Jersey.Google Scholar
Johnston, J. 1972. Econometric Methods, pp. 292–230. McGraw-Hill, Kogakusha, Tokyo.Google Scholar
Ludwick, T. M. and Petersen, W. E. 1943. A measure of persistency of lactation in dairy cattle. J. Dairy Sci. 26: 439–445.Google Scholar
Nelder, J. A. 1966. Inverse polynomials, a useful group of multi-factor response functions. Biometrics 22: 128–141.Google Scholar
Turner, C. W. 1926. A quantitative form of expressing persistency of milk or fat secretion. J. Dairy Sci. 9: 203–214.Google Scholar
Vinod, H. D. 1973. Generalization of the Durbin-Watson statistic for higher order autoregressive processes. Communs Statist. 2: 115–144.Google Scholar
Wood, P. D. P. 1967. Algebraic model of the lactation curve in cattle. Nature, Lond. 216: 164–165.Google Scholar
Wood, P. D. P. 1979. A simple model of lactation curves for milk yield, food requirement and body weight. Anim. Prod. 28: 55–63.Google Scholar