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Evaluation of a mechanistic lactation model using cow, goat and sheep data

Published online by Cambridge University Press:  15 January 2010

J. DIJKSTRA
Affiliation:
Animal Nutrition Group, Wageningen University, PO Box 338, 6700AH Wageningen, The Netherlands
S. LOPEZ*
Affiliation:
Instituto de Ganadería de Montaña, Universidad de León – Consejo Superior de Investigaciones Científicas, Departamento de Producción Animal, Universidad de León, E-24071León, Spain
A. BANNINK
Affiliation:
Livestock Research, Animal Sciences Group, Wageningen University Research Centre, PO Box 65, 8200 AB, Lelystad, The Netherlands
M. S. DHANOA
Affiliation:
North Wyke Research, Okehampton, Devon, EX20 2SB, UK
E. KEBREAB
Affiliation:
Department of Animal Science, University of California, Davis, CA 95616, USA
N. E. ODONGO
Affiliation:
Animal Production and Health Section, Department of Nuclear Sciences and Applications, International Atomic Energy Agency, Wagramer Strasse 5, A-1400Vienna, Austria
M. H. FATHI NASRI
Affiliation:
Department of Animal Science, Faculty of Agriculture, University of Birjand, Birjand, Iran
U. K. BEHERA
Affiliation:
Division of Agronomy, Indian Agricultural Research Institute, New Delhi110012, India
D. HERNANDEZ-FERRER
Affiliation:
Departamento de Mejora Genética Animal, Instituto Nacional de Investigaciones Agrarias, Ctra. de la Coruña km 7, 28040Madrid, Spain
J. FRANCE
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON, N1G 2W1, Canada
*
*To whom all correspondence should be addressed. Email: [email protected]

Summary

A mechanistic lactation model, based on a theory of mammary cell proliferation and cell death, was studied and compared to the equation of Wood (1967). Lactation curves of British Holstein Friesian cows (176 curves), Spanish Churra sheep (40 curves) and Spanish Murciano–Granadina goats (30 curves) were used for model evaluation. Both models were fitted in their original form using non-linear least squares estimation. The parameters were compared among species and among parity groups within species.

In general, both models provided highly significant fits to lactation data and described the data accurately. The mechanistic model performed well against Wood's 1967 equation (hereafter referred to as Wood's equation), resulting in smaller residual mean square values in more than two-thirds of the datasets investigated, and producing parameter estimates that allowed appropriate comparisons and noticeable trends attributed to shape. Using Akaike or Bayesian information criteria, goodness-of-fit with the mechanistic model was superior to that with Wood's equation for the cow lactation curves, with no significant differences between models when fitted to goat or sheep lactation curves. The rate parameters of the mechanistic model, representing specific proliferation rate of mammary secretory cells at parturition, decay associated with reduction in cell proliferation capacity with time and specific death rate of mammary secretory cells, were smaller for primiparous than for multiparous cows. Greater lactation persistency of cows compared to goats and sheep, and decrease in persistency with parity, were shown to be represented by different values of the specific secretory cell death rate parameter in the mechanistic model. The plausible biological interpretation and fitting properties of the mechanistic model enable it to be used in complex models of whole-cow digestion and metabolism and as a tool in selection programmes and by dairy producers for management decisions.

Type
Modelling Animal Systems Paper
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Anderson, R. R. & Sheffield, L. G. (1983). Growth of guinea pig mammary glands through their first six lactations. Journal of Dairy Science 66, 2934.CrossRefGoogle ScholarPubMed
Baldwin, R. L., France, J. & Gill, M. (1987). Metabolism of the lactating cow. I. Animal elements of a mechanistic model. Journal of Dairy Research 54, 77–105.CrossRefGoogle ScholarPubMed
Burnham, K. P. & Anderson, D. R. (2002). Model Selection and Multimodel Inference – A Practical Information–Theoretic Approach. New York: Springer.Google Scholar
Capuco, A. V., Wood, D. L., Baldwin, R., McLeod, K. & Paape, M. J. (2001). Mammary cell number, proliferation, and apoptosis during a bovine lactation: relation to milk production and effect of bST. Journal of Dairy Science 84, 21772187.CrossRefGoogle ScholarPubMed
Cobby, J. M. & Le Du, Y. L. P. (1978). On fitting curves to lactation data. Animal Production 26, 127133.Google Scholar
Dekkers, J. C. M., Hag, J. H. T. & Weersink, A. (1998). Economic aspects of persistency of lactation in dairy cattle. Livestock Production Science 53, 237252.CrossRefGoogle Scholar
Dematawewa, C. M. B., Pearson, R. E. & VanRaden, P. M. (2007). Modeling extended lactations of Holsteins. Journal of Dairy Science 90, 39243936.CrossRefGoogle ScholarPubMed
Dhanoa, M. S., Siddons, R. C., France, J. & Gale, D. L. (1985). A multicompartmental model to describe marker excretion patterns in ruminant faeces. British Journal of Nutrition 53, 663671.CrossRefGoogle ScholarPubMed
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, 23402354.CrossRefGoogle Scholar
Dijkstra, J., Kebreab, E., Mills, J. A. N., Pellikaan, W. F., López, S., Bannink, A. & France, J. (2007). Predicting the profile of nutrients available for absorption: from nutrient requirement to animal response and environmental impact. Animal 1, 99–111.CrossRefGoogle ScholarPubMed
Emmans, G. C. & Fisher, C. (1986). Problems in nutritional theory. In Nutrient Requirements of Poultry and Nutritional Research (Eds Fisher, C. & Boorman, K. N.), pp. 9–39. London: Butterworths.Google Scholar
Fathi Nasri, M. H., France, J., Odongo, N. E., Lopez, S., Bannink, A. & Kebreab, E. (2008). Modelling the lactation curve of dairy cows using the differentials of growth functions. Journal of Agricultural Science, Cambridge 146, 633641.CrossRefGoogle Scholar
Fernández, C., Sánchez, A. & Garcés, C. (2002). Modeling the lactation curve for test-day milk yield in Murciano–Granadina goats. Small Ruminant Research 46, 2941.CrossRefGoogle Scholar
Fowler, P. A., Knight, C. H., Cameron, G. G. & Foster, M. A. (1990). In-vivo studies of mammary development in the goat using magnetic resonance imaging (MRI). Journal of Reproduction and Fertility 89, 367375.CrossRefGoogle ScholarPubMed
France, J., Thornley, J. H. M., Dhanoa, M. S. & Siddons, R. C. (1985). On the mathematics of digesta flow kinetics. Journal of Theoretical Biology 113, 743758.CrossRefGoogle ScholarPubMed
Friggens, N. C., Emmans, G. C. & Veerkamp, R. F. (1999). On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production. Livestock Production Science 62, 113.CrossRefGoogle Scholar
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions Royal Society 115, 513585.Google Scholar
Goodwill, M. G., Jessop, N. S. & Oldham, J. D. (1996). Mammary sensitivity to protein restriction and re-alimentation. British Journal of Nutrition 76, 423434.CrossRefGoogle ScholarPubMed
Groenewald, P. C. N. & Viljoen, C. S. (2003). A Bayesian model for the analysis of lactation curves of dairy goats. Journal of Agricultural Biological and Environmental Statistics 8, 7583.CrossRefGoogle Scholar
Hanigan, M. D., Rius, A. G., Kolver, E. S. & Palliser, C. C. (2007). A redefinition of the representation of mammary cells and enzyme activities in a lactating dairy cow model. Journal of Dairy Science 90, 38163830.CrossRefGoogle Scholar
Hansen, J. V., Friggens, N. C. & Højsgaard, S. (2006). The influence of breed and parity on milk yield, and milk yield acceleration curves. Livestock Science 104, 5362.CrossRefGoogle Scholar
Knight, C. H. & Wilde, C. J. (1993). Mammary cell changes during pregnancy and lactation. Livestock Production Science 35, 3–19.CrossRefGoogle Scholar
Knight, C. H., Fowler, P. A. & Wilde, C. J. (1990). Galactopoietic and mammogenic effects of long-term treatment with bovine growth hormone and thrice daily milking in goats. Journal of Endocrinology 127, 129138.CrossRefGoogle ScholarPubMed
Knight, C. H., Peaker, M. & Wilde, C. J. (1998). Local control of mammary development and function. Reviews of Reproduction 3, 104112.CrossRefGoogle Scholar
Leonard, T. & Hsu, J. S. J. (2001). Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers. Cambridge, UK: Cambridge University Press.Google Scholar
Leon-Velarde, C. U., McMillan, I., Gentry, R. D. & Wilton, J. W. (1995). Models for estimating typical lactation curves in dairy cattle. Journal of Animal Breeding and Genetics 112, 333340.CrossRefGoogle Scholar
López, S. (2008). Non-linear functions in animal nutrition. In Mathematical Modelling in Animal Nutrition (Eds France, J. & Kebreab, E.), pp. 4788. Wallingford, UK: CAB International.CrossRefGoogle Scholar
Motulsky, H. J. & Christopoulos, A. (2003). Fitting Models to Biological Data using Linear and Nonlinear Regression. A Practical Guide to Curve Fitting. San Diego, CA: GraphPad Software Inc.Google Scholar
Nostrand, S. D., Galton, D. M., Erb, H. N. & Bauman, D. E. (1991). Effects of daily exogenous oxytocin on lactation milk yield and composition. Journal of Dairy Science 74, 21192127.CrossRefGoogle ScholarPubMed
Pollott, G. E. (2000). A biological approach to lactation curve analysis for milk yield. Journal of Dairy Science 83, 24482458.CrossRefGoogle ScholarPubMed
Portolano, B., Spatafora, F., Bono, G., Margiotta, S., Todaro, M., Ortoleva, V. & Leto, G. (1997). Application of the Wood model to lactation curves of Comisana sheep. Small Ruminant Research 24, 7–13.CrossRefGoogle 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.CrossRefGoogle Scholar
Rowlands, G. J., Lucey, S. & Russell, A. M. (1982). A comparison of different models of the lactation curve in dairy cattle. Animal Production 35, 135144.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, 18851894.CrossRefGoogle ScholarPubMed
Shanks, R. D., Berger, P. J., Freeman, A. E. & Dickinson, F. N. (1981). Genetic aspects of lactation curves. Journal of Dairy Science 64, 18521860.CrossRefGoogle ScholarPubMed
Sorensen, M. T., Nørgaard, J. V., Theil, P. K., Vestergaard, M. & Sejrsen, K. (2006). Cell turnover and activity in mammary tissue during lactation and the dry period in dairy cows. Journal of Dairy Science 89, 46324639.CrossRefGoogle ScholarPubMed
SAS Institute Inc. (1999). SAS/STAT® User's Guide, Version 8. Cary, NC: SAS Institute Inc.Google Scholar
Thornley, J. H. M. & France, J. (2007). Mathematical Models in Agriculture, Revised 2nd edn.Wallingford, UK: CAB International.Google Scholar
Tucker, H. A. (1987). Quantitative estimates of mammary growth during various physiological states: a review. Journal of Dairy Science 70, 19581966.CrossRefGoogle ScholarPubMed
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, 37893799.CrossRefGoogle ScholarPubMed
Van Knegsel, A. T. M., Van den Brand, H., Dijkstra, J., Tamminga, S. & Kemp, B. (2005). Effect of dietary energy source on energy balance, production, metabolic disorders and reproduction in lactating dairy cattle. Reproduction Nutrition Development 45, 665688.CrossRefGoogle ScholarPubMed
Wilde, C. J., Henderson, A. J., Knight, C. H., Blatchford, D. R., Faulkner, A. & Vernon, R. G. (1987). Effect of long-term thrice-daily milking on mammary enzyme activity, cell population and milk yield in the goat. Journal of Animal Science 64, 533539.CrossRefGoogle ScholarPubMed
Williams, J. C. (1993). An empirical model for the lactation curve of white British dairy goats. Animal Production 57, 9197.Google Scholar
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature 216, 164165.CrossRefGoogle Scholar
Wood, P. D. P. (1969). Factors affecting the shape of the lactation curve in cattle. Animal Production 11, 307316.Google Scholar
Wood, P. D. P. (1977). The biometry of lactation. Journal of Agricultural Science, Cambridge 88, 333339.CrossRefGoogle Scholar