Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T04:18:01.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling lactation curves of dairy cows with emphasis on individual variability

Published online by Cambridge University Press:  02 September 2010

L. Pérochon ,
J. B. Coulon  and
F. Lescourret
L. Pérochon
Affiliation:
INRA, Laboratoire d'Ecopathologie, Theix, 63122 Saint-Genès-Champanelle, France
J. B. Coulon
Affiliation:
INRA, Laboratoire Adaptation des Herbivores aux Milieux, Theix, 63122 Saint-Genès-Champanelle, France
F. Lescourret
Affiliation:
INRA, Laboratoire d'Ecopathologie, Theix, 63122 Saint-Genès-Champanelle, France
Get access

Abstract

Five published equations were compared on their ability to adjust different patterns of lactation curves. The equation y(t) = a exp(b1t'2/2 + b2/t – c(l + t'/2)t') with t' = (t – 21·4)/l00 (i) was retained because of the quality of the adjustment and the absence of convergence problems when applied on individual curves. Including an effect of season (SE) and an effect of pregnancy (PE) improved the quality of individual adjustments (no. = 339). The final equation was equal to (i) + SE + PE with SE = a + b cos (2π(wc + w - l)/52) + c sin(2n(wc + w - 1)/52), with wc= week of the year at calving, w = week after calving and a = 0·0065, b = -1·26 and c = 0·374, and PE = a (wp –18) e-bwp, with w p = week of pregnancy and a, b fixed parameters. Individual cow characteristics were used to analyse equation (i) parameters. The predictions obtained with this equation and several predictive functions of the equation (i) parameters, which differed in the way they included or not the potential of production, were compared. With no indication of this potential, the prediction was very poor. With the initial production (mean production of the 4th, 5th and 6th days of lactation) as an estimate of this potential, 75% of the lactations had the median of absolute values of errors less than 2·95 kg/day. The results were highly improved by using the yield during the 5th week of lactation. The threshold of 2·95 was reduced to about 2 kg/day. The quality of the individual prediction was better for primiparous than for multiparous cows, and for French Friesian and Montbeliarde cows than for pure or crossbred Holstein cows. Although individual predictions were not always satisfactory, they provided excellent agreement when averaged per group (20 cows).

Keywords

dairy cowslactation curvemathematical models
Type
Research Article
Information
Animal Science , Volume 63 , Issue 2 , October 1996 , pp. 189 - 200
Copyright
Copyright © British Society of Animal Science 1996

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

Batra, T. R. 1986. Comparison of two mathematical models in fitting lactation curves for pureline and crossline dairy cows. Canadian Journal of Animal Science 66: 405–414.CrossRefGoogle Scholar
Beever, D. E., Rook, A. J., France, J., Dhanoa, M. S. and Gill, M. 1991. A review of empirical and mechanistic models of lactational performance by the dairy cow. livestock Producion Science 29: 115–130.CrossRefGoogle Scholar
Brody, S., Turner, C. W. and Ragsdale, A. C. 1924. The relation between the initial rise and subsequent decline of milk secretion following parturition. Journal of Genetics and Physiology 5: 541–545.CrossRefGoogle Scholar
Chambers, J. M. and Hastie, T. J. 1992. Statistical models in S. Wadsworth and Brooks, Pacific Grove.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. and Everett, R. W. 1980. Application of the incomplete gamma function to predict cumulative milk production. Journal of Dairy Science 63: 109–119.CrossRefGoogle Scholar
Coulon, J. B., Chilliard, Y. and Remond, B. 1991. Effets du stade physiologique et de la saison sur la composition chimique du lait de vache et ses caractéristiques technologiques. 1NRA Productions Animates 4: 219–228.CrossRefGoogle Scholar
Coulon, J. B., Doreau, M., Remond, B. and Journet, M. 1984. Capacite d'ingestion des vaches laitiéres en début de lactation. 1. Evolution, liaison avec certains paramétres zootechniques et conséquences sur la production laitiére. Bulletin Technique CRZV Theix, INRA 55: 33–42.Google Scholar
Coulon, J. B., Hoden, A., Faverdin, P. and Journet, M. 1989. Dairy cows. In Ruminant nutrition. Recommended allowances and feed tables (ed. Jarrige, R.), pp. 74–91. INRA and John Libbey Eurotext.Google Scholar
Coulon, J. B., Lescourret, F., Faye, B., Landais, E., Troccon, J. L. and Perochon, L. 1993. Description de la base de données “LASCAR”, un outil pour l'étude des carriéres des vaches laitiéres. INRA Productions Animates 6: 151–160.CrossRefGoogle Scholar
Coulon, J. B., Pérochon, L. and Lescourret, F. 1995a. Modelling the effect of the stage of pregnancy on dairy cows' milk yield. Animal Science 60: 401–408.CrossRefGoogle Scholar
Coulon, J. B., Pérochon, L. and Lescourret, F. 1995b. Evolution de la production laitiére et du poids vif des vaches laitiéres au cours de leur carriére. Annales de Zootechnie 44: 189–199.CrossRefGoogle Scholar
Decaen, C., Calomiti, S. and Poutous, M. 1970. Evolution de la production laitiére de la vache au cours des 2 premiers mois de lactation. II. Analyse de la variation de la quantité de lait. Annales de Zootechnie 19: 205–221.CrossRefGoogle Scholar
Deluyker, H. A., Shumway, R. H., Wecker, W. E., Azari, A. S. and Weaver, L. D. 1990. Modeling daily milk yield in Holstein cows using time series analysis. Journal of Dairy Science 73: 539–548.CrossRefGoogle Scholar
Dhanoa, M. S. and Le Du, Y. L. P. 1982. Partial adjustment model to describe the lactation curve of a dairy cow. Animal Production 34: 243–247.Google Scholar
Faverdin, P., Hoden, A. and Coulon, J. B. 1987. Recommendations alimentaires pour les vaches laitiéres. Bulletin Technique 70. CRZV, INRA, Theix, pp. 133–152.Google Scholar
Genizi, A., Schindler, H., Amir, S., Eger, S., Zarchi, M. and Foote, R. H. 1992. A simulation study of the effects of the calving interval on milk yields of dairy cows in fixed time periods. Animal Production 55: 309–314.Google Scholar
Goodall, E. A. and Sprevak, D. 1984. A note on a stochastic model to describe the milk yield of a dairy cow. Animal Production 38: 133–136.Google Scholar
Goodall, E. A. and 1985. A bayesian estimation of the lactation curve of a dairy cow. Animal Production 40: 189–193.Google Scholar
Grossman, M., Kuck, A. L. and Norton, H. W. 1986. Lactation curves of purebred and crossbred dairy cattle. Journal of Dairy Science 69: 195–203.CrossRefGoogle Scholar
Hoden, A. 1978. Rationnement en début de la lactation. In La vache laitière, pp. 71–86. INRA Publications, Paris.Google Scholar
Institut National de la Recherche Agronomique. 1978. Alimentation des ruminants. INRA Publications, Paris.Google Scholar
Institut National de la Recherche Agronomique. 1989. Ruminant nutrition. Recommended allowances and feed tables (ed. Jarrige, R.). INRA and John Libbey Eurotext.Google Scholar
Lescourret, F., Coulon, J. B., Perochon, L. and Faye, B. 1994. Modelling the interrelationships between mastitis and milk production in dairy cows. Third international livestock farming system symposium. Macaulay Land Use Research Institute, Aberdeen, Scotland.Google Scholar
Lescourret, F., Pérochon, L., Coulon, J. B., Faye, B. and Landais, E. 1992. Modelling an information system using the merise method for agricultural research: the example of a database for a study on performances in dairy cows. Agricultural Systems 38: 149–173.CrossRefGoogle Scholar
Masselin, S., Sauvant, D., Chapoutot, P. and Milan, D. 1987. Les modèles d'adjustement des courbes de lactation. Annales de Zootechnie 36: 171–206.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
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
Rowlands, G. J., Lucey, S. and Russel, A. M. 1982. A comparison of different models of the lactation curve in dairy cattle. Animal Production 35: 135–144.Google Scholar
Schaeffer, L. R. and Burnside, E. B. 1976. Estimating the shape of the lactation curve. Canadian Journal of Animal Science 56: 157–170.CrossRefGoogle Scholar
Schutz, M. M., Hansen, L. B., Steuernagel, G. R. and Kuck, A. L. 1990. Variation of milk, fat, protein, and somatic cells for dairy cattle. Journal of Dairy Science 73: 484–493.CrossRefGoogle Scholar
Statistical Sciences. 1993. S-PLUS guide to statistical and mathematical analysis, version 3.2. StatSci, a division of MathSoft, Inc., Seattle.Google Scholar
Strandberg, E. and Lundberg, C. 1991. A note on the estimation of environmental effects on lactation curves. Animal Production 53: 399–402.Google Scholar
Tucker, H. A. 1985. Photoperiodic influences on milk production in dairy cows. In Recent advances in animal nutrition (ed. Haresign, W. and Cole, D. J. A.), pp. 211–221. Butterworths.CrossRefGoogle Scholar
Williams, J. C. 1993. Influence of farm, parity, season and litter size on the lactation curve parameters of white British dairy goats. Animal Production 57: 99–104.Google Scholar
Wood, P. D. P. 1967. Algebraic model of the lactation curve in cattle. Nature 216: 164–165.CrossRefGoogle Scholar
Wood, P. D. P. 1969. Factors affecting the shape of the lactation curve in cattle. Animal Production 11: 307–316.Google Scholar
Wood, P. D. P. 1970. A note on the repeatability of parameters of the lactation curve in cattle. Animal Production 12: 535–538.Google Scholar
Wood, P. D. P. 1974. A note on the estimation of total lactation yield from production on a single day. Animal Production 19: 393–396.Google Scholar
Wood, P. D. P. 1980. Breed variations in the shape of the lactation curve of cattle and their implications for efficiency. Animal Production 31: 133–141.Google Scholar
Wood, P. D. P., King, J. O. L. and Youdan, P. G. 1980. Relationships between size, live-weight change and milk production characters in early lactation in dairy cattle. Animal Production 31: 143–151.Google Scholar