Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T03:05:48.810Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aguillar, J. A., Aparicio, J. J., Fernandez-Rivera, S. and Tovar, I. 1989. Lactation curves and milk yield of Corriedale, Rambouillet and Suffolk ewes. Journal of Dairy Science 72:426–427.Google Scholar
Cappio-Borlino, A., Pulina, G., Cannas, A. and Rossi, G. 1989. The theoretical lactation curve of Sardinian ewes. Zootecnicae Nutrizione Animate 15:59–63.Google Scholar
Cobby, J. M. and Le Du, Y. L. P. 1978. On fitting curves to lactation data. Animal Production 26:127–133.Google Scholar
Congleton, W. R. 1984. Dynamic model for combined simulation of dairy management strategies. Journal of Dairy Science 67:644–660.CrossRefGoogle Scholar
Doney, J. M., Peart, J. N., Smith, W. F. and Louda, F. 1979. A consideration of the techniques for estimation of milk yield by suckled sheep and a comparison of estimates obtained by two methods in relation to the effect of breed, level of production and stage of lactation. Journal of Agricultural Science, Cambridge 92:123–132.CrossRefGoogle Scholar
Doyle, C. J. 1983. Evaluating feeding strategies for dairy cows: a modelling approach. Animal Production 36:47–57.Google Scholar
Gipson, T. A. 1989. Lactation curves in dairy goats. Ph.D. thesis, University of Illinois, Urbana, USA.CrossRefGoogle Scholar
Gipson, T. A. and Grossman, M. 1989. Diphasic analysis of lactation curves in dairy goats. Journal of Dairy Science 72:1035–1044.CrossRefGoogle ScholarPubMed
Goodall, E. A. 1986. Prediction of milk and milk solids production. Agricultural Systems 21:189–200.CrossRefGoogle Scholar
Goodall, E. A. and Sprevak, D. 1984. A not e on a stochastic model to describe the milk yield of a dairy cow. Animal Production 38:133–136.Google Scholar
Grossman, M. and Koops, W. J. 1988. Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71:1598–1608.CrossRefGoogle Scholar
Lennox, S. D., Goodall, E. A. and Mayne, C. S. 1992. A mathematical model of the lactation curve of the dairy cow to incorporate metabolizable energy intake. The Statistician 41:285–293.CrossRefGoogle Scholar
McCane, I. 1959. The determination of milk yield in the Merino ewe. Australian Journal of Agricultural Research 10:839–853.CrossRefGoogle Scholar
Morant, S. V. and Gnanasakthy, A. 1989. A new approach to the mathematical formulation of lactation curves. Animal Production 49:151–162.Google Scholar
National Research Council. 1985. Nutrient requirements of sheep. National Academy of Sciences, Washington, DC.Google Scholar
Neal, H. D. St C. and Thornley, J. H. M. 1983. The lactation curve in cattle: a mathematical model of the mammary gland, journal of Agricultural Science, Cambridge 101:389–400.CrossRefGoogle Scholar
Rook, A. J., France, J. and Dhanoa, M. S. 1993. On the mathematical description of lactation curves. Journal of Agricultural Science, Cambridge 121:97–102.CrossRefGoogle Scholar
Sakul, H. and Boylan, W. J. 1992. Lactation curves for several US sheep breeds. Animal Production 54:229–233.Google Scholar
Torres-Hernandez, G. and Hohenboken, W. D. 1980. Biometric properties of lactation in ewes raising single or twin lambs. Animal Production 30:431–436.Google Scholar
Williams, J. C. 1993. An empirical model for the lactation curve of white British dairy goats. Animal Production 57:91–97.Google Scholar
Wood, P. D. P. 1967. Algebraic model of the lactation curve in cattle. Nature, London 216:164–165.CrossRefGoogle Scholar
Wood, P. D. P. 1974. A note on the estimation of total lactation yield from production on a single day. Animal Production 19:393.Google Scholar
Wood, P. D. P. 1977. The biometry of lactation. Journal of Agricultural Science, Cambridge 88:333–339.CrossRefGoogle Scholar