Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T00:58:51.777Z Has data issue: false hasContentIssue false
  • English
  • Français

Appropriate mathematical models for describing the complete lactation of dairy sheep

Published online by Cambridge University Press:  18 August 2016

G. E. Pollott  and
E. Gootwine
G. E. Pollott
Affiliation:
Wye College – University of London, Ashford, Kent TN25 5AH, UK
E. Gootwine
Affiliation:
Department of Animal Reproduction, Agricultural Research Organisation, The Volcani Centre, PO Box 6, Bet Dagan 50250, Israel
Get access

Abstract

Despite milk being an important product from sheep, there are very few reports of milk production from the complete lactation of dairy sheep. The Improved Awassi in Israel is kept under an intensive system of management with lambs being weaned soon after birth. Records from one such flock were analysed to investigate the suitability of various mathematical functions for describing milk yield from the complete lactations of dairy sheep. This included a consideration of whether the functions could cope with short lactations, a characteristic of dairy sheep, and a limited number of test-day records per lactation.

Four non-linear mathematical functions were investigated (Wood, Morant, Grossman and Pollott), two of which could also be fitted in a linear and a linear weighted form (Wood and Morant). These functions were fitted to weekly data from a ‘typical Awassi lactation curve’, represented by least squares means of daily milk yield from each week of a 40-week lactation derived from an analysis of 25605 test day records. Characteristics of the lactation were calculated from the functions, such as total milk yield, day and level of peak yield and persistency. These functions were also fitted to 1416 individual lactation records of up to 10 test-day records per lactation. The value of the functions was investigated using the residual mean square (RMS) of the fitted curve as an indicator of how well each function described the lactation. Forms of these functions with a reduced number of parameters were also investigated.

The non-linear functions always fitted the data with a lower RMS than their linear equivalent and the weighted form of the linear functions always had a lower RMS than the unweighted form. Of the linear functions, Morant fitted better than Wood. Of the non-linear functions Grossman, Morant and Pollott (additive and multiplicative) fitted the data equally as well but better than Wood. The various functions predicted characteristics of the lactation curve differently; the Wood functions tended to overestimate yield in early lactation and the Morant functions underestimated peak yield.

No function was better suited to short lactations than another. However the three-parameter function of Morant, Pollott multiplicative and Pollott additive were considered to be the most suitable for describing the complete lactation of dairy sheep.

Keywords

Awassidairy sheeplactation curvemilk recording
Type
Breeding and genetics
Information
Animal Science , Volume 71 , Issue 2 , October 2000 , pp. 197 - 207
Copyright
Copyright © British Society of Animal Science 2000

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

Ali, T. E. and Schaeffer, L. R. 1987. Accounting for covariance among test day yields in dairy cows. Canadian Journal of Animal Science 67: 637–644.Google Scholar
Barillet, F. and Astruc, J. M. 1998. Report of the working group on milk recording of sheep: survey of milk recording, use of AI and progeny test, pedigree information and supervisory systems, and on-farm computerisation of data collection in ICAR member countries. Proceedings of the 31st biennial session of the International Committee for Animal Recording (ICAR), Rotorua, New Zealand, 18-13 January 1998. EAAP publication no. 91, pp. 327–343.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
Dijkstra, J., France, J., Dhanoa, M. S., Maas, J. A., Hanigan, M. D., Rook, A. J. and 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.CrossRefGoogle Scholar
Elston, D. A., Glaseby, C. A. and Neilson, D. R. 1989. Non-parametric lactation curves. Animal Production 48: 331–339.Google Scholar
Epstein, H. 1985. The Awassi sheep with special reference to the improved dairy type. Animal Production and Health paper no. 57, Food and Agriculture Organization, Rome.Google Scholar
Gootwine, E., Bor, A., Braw-Tal, R. and Zenou, A. 1995. Reproductive performance and milk production of the improved Awassi breed as compared with its crosses with the Booroola Merino. Animal Science 60: 109–115.Google Scholar
Gootwine, E., Leibovich, H., Waisel, G., Zenou, A. and Spormas, I. 1994. ‘Ewe and Me’ on farm software for dairy and mutton sheep and goat flocks. Proceedings of the fifth world congress on genetics applied to livestock production, Guelph, vol. 22, pp. 67–68.Google Scholar
Groenewald, P. C. N., Ferreira, H. J., van der Merwe, H. J. and Slippers, S. C. 1995. A mathematical model for describing and predicting the lactation curve of Merino ewes. Animal Science 61: 95–101.Google Scholar
Grossman, M. and Koops, W. J. 1988. Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71: 1598–1608.Google Scholar
Guest, P. G. 1961. Numerical methods of curve fitting. Cambridge University Press.Google Scholar
International Committee on Animal Recording. 1992. Regulations for milk recording in dairy sheep. International Committee on Animal Recording, Rome.Google Scholar
Keown, J. F., Everett, R. W., Empet, N. B. and Wadell, L. H. 1986. Lactation curves. Journal of Dairy Science 69: 769–781.Google Scholar
Knight, C. H., Peaker, M. and Wilde, C. 1998. Local control of mammary development and function. Reviews of Reproduction 3: 104–112.CrossRefGoogle ScholarPubMed
Masselin, S., Sauvant, D., Chapoutot, P. and Milan, D. 1987. [Adjustment models for lactation curves.] Annales de Zootechnie 36: 171–206.Google 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
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
Olori, V. E., Brotherstone, S., Hill, W. G. and McGuirk, B. J. 1999. Fit of standard models of the lactation curve to weekly records of milk production of cows in a single herd. Livestock Production Science 58: 55–63.Google Scholar
Pérochon, L., Coulon, J. B. and Lescourret, F. 1996. Modelling lactation curves of dairy cows with emphasis on individual variability. Animal Science 63: 189–200.CrossRefGoogle Scholar
Pollott, G. E. 1999. Describing the lactation of dairy animals. Proceedings of the British Society of Animal Science, 1999, p. 197 (abstr.).CrossRefGoogle Scholar
Pollott, G. E. 2000. A biological approach to lactation curve analyses for milk yield. Journal of Dairy Science In press.Google Scholar
Portolano, B., Spatafora, F., Bono, G., Margiotta, S., Todaro, M., Ortoleva, V. and Leto, G. 1996. Application of the Wood model to lactation curves of Comisana sheep. Small Ruminant Research 24: 7–13.Google 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.Google Scholar
Sherchand, L., McNew, R. W., Rakes, J. M., Kellog, D. W. and Johnson, Z. B. 1992. Comparison of lactation curves fitted by seven mathematical models. Journal of Dairy Science 75: (Suppl. 1) 303.Google Scholar
Statistical Analysis Systems Institute. 1989. SAS/STAT user’s guide version 6, fourth edition, volume 2, GLM-VARCOMP. SAS Institute Inc., Cary, NC.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
Wilmink, J. B. M. 1987. Adjustment of test day milk, fat and protein yield for age, season and stage of lactation. Livestock Production Science 16: 335–348.Google Scholar
Wood, P. D. P. 1967. Algebraic model of the lactation curve in cattle. Nature, London 216: 164–165.Google Scholar
Yadav, M. C., Katpatal, B. G. and Kaushik, S. N. 1977. Components of inverse polynomial function of lactation curve, and factors affecting them in Hariana and Friesian crosses. Indian Journal of Animal Science 47: 777–781.Google Scholar