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

Published online by Cambridge University Press:  21 November 2008

M. H. FATHI NASRI ,
J. FRANCE ,
N. E. ODONGO ,
S. LOPEZ ,
A. BANNINK  and
E. KEBREAB
M. H. FATHI NASRI
Affiliation:
Department of Animal Science, Faculty of Agriculture, University of Birjand, Birjand, Iran
J. FRANCE
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON, N1G 2W1, Canada
N. E. ODONGO
Affiliation:
Agriculture and Agri-Food Canada, Lethbridge Research Centre, Lethbridge, AB, T1J 4B1, Canada
S. LOPEZ
Affiliation:
Departamento de Producción Animal, Facultad de Veterinaria, Universidad de León, 24007 León, Spain
A. BANNINK
Affiliation:
Animal Sciences Group, Wageningen University and Research Centre, Lelystad, The Netherlands
E. KEBREAB*
Affiliation:
Department of Animal Science, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada
*
*To whom all correspondence should be addressed. Email: Ermias_Kebreab@umanitoba.ca
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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.

Type
Modelling Animal Systems Paper
Information
The Journal of Agricultural Science , Volume 146 , Issue 6 , December 2008 , pp. 633 - 641
Copyright
Copyright © 2008 Cambridge University Press

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References

REFERENCES

Burnham, K. P. & Anderson, D. R. (2002). Model Selection and Multimodel Inference: a Practical–theoretic Approach, 2nd edn. Berlin, Germany: Springer-Verlag.Google Scholar
Dijkstra, J., France, J., Dhanoa, M. S., Maas, J. A., Hanigan, M. D., Rook, A. J. & Beever, D. E. (1997). A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science 80, 2340–2354.Google Scholar
Fathi Nasri, M. H., Danesh Mesgaran, M., France, J., Cant, J. P. & Kebreab, E. (2006). Evaluation of models to describe ruminal degradation kinetics from in situ ruminal incubation of whole soybeans. Journal of Dairy Science 89, 3087–3095.Google Scholar
Gipson, T. A. & Grossman, M. (1989). Diphasic analysis of lactation curves in dairy goats. Journal of Dairy Science 72, 1035–1044.CrossRefGoogle ScholarPubMed
Gipson, T. A. & Grossman, M. (1990). Lactation curves in dairy goats: a review. Small Ruminant Research 3, 383–396.CrossRefGoogle Scholar
Grossman, M. & Koops, W. J. (1988). Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71, 1598–1608.Google Scholar
Lopez, S., France, J., Gerrits, W. J., Dhanoa, M. S., Humphries, D. J. & Dijkstra, J. (2000). A generalised Michaelis–Menten equation for the analysis of growth. Journal of Animal Science 78, 1816–1828.Google Scholar
Lopez, S., Prieto, M., Dijkstra, J., Dhanoa, M. S. & France, J. (2004). Statistical evaluation of mathematical models for microbial growth. International Journal of Food Microbiology 96, 289–300.CrossRefGoogle ScholarPubMed
Motulsky, H. J. & Ransnas, L. A. (1987). Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB Journal 1, 365–374.Google Scholar
Pérochon, L., Coulon, J. B. & Lescourret, F. (1996). Modelling lactation curves of dairy cows with emphasis on individual variability. Animal Science 63, 189–200.Google Scholar
Pollott, G. E. (2000). A biological approach to lactation curve analysis for milk yield. Journal of Dairy Science 83, 2448–2458.Google Scholar
Rook, A. J., France, J. & Dhanoa, M. S. (1993). On the mathematical description of lactation curves. Journal of Agricultural Science, Cambridge 121, 97–102.Google Scholar
SAS Institute (1999). User's Guide: Statistics, 1999. Version 8.2. Cary, NC, USA: SAS Institute Inc.Google Scholar
Scott, T. A., Yandell, B., Zepeda, L., Shaver, R. D. & Smith, T. R. (1996). Use of lactation curves for analysis of milk production data. Journal of Dairy Science 79, 1885–1894.Google Scholar
Sherchand, L., McNew, R. W., Kellogg, D. W. & Johnson, Z. B. (1995). Selection of a mathematical model to generate lactation curves using daily milk yields of Holstein cows. Journal of Dairy Science 78, 2507–2513.Google Scholar
Stanton, T. L., Jones, L. R., Everett, R. W. & Kachman, S. D. (1992). Estimating milk, fat and protein lactation curves with a test day model. Journal of Dairy Science 75, 1691–1699.Google Scholar
Theil, H. (1966). Applied Economic Forecasting. Amsterdam, The Netherlands: North-Holland Publishing Co.Google Scholar
Thornley, J. H. M. & France, J. (2007). Mathematical Models in Agriculture, 2nd edn. Wallingford, UK: CABI Publishing.Google Scholar
Val-Arreola, D., Kebreab, E., Dijkstra, J. & France, J. (2004). Study of the lactation curve in dairy cattle on farms in central Mexico. Journal of Dairy Science 87, 3789–3799.Google Scholar
Vargas, B., Koops, W. J., Herrero, M. & Van Arendonk, J. A. M. (2000). Modeling extended lactations of dairy cows. Journal of Dairy Science 83, 1371–1380.Google Scholar
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature 216, 164–165.Google Scholar
Wood, P. D. P. (1969). Factors affecting the shape of the lactation curve in cattle. Animal Production 11, 307–316.Google Scholar