Hostname: page-component-7bb8b95d7b-dtkg6 Total loading time: 0 Render date: 2024-09-12T09:23:33.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins

Published online by Cambridge University Press:  29 July 2013

N. GHAVI HOSSEIN-ZADEH
N. GHAVI HOSSEIN-ZADEH*
Affiliation:
Department of Animal Science, Faculty of Agricultural Sciences, University of Guilan, PO Box 41635-1314, Rasht, Iran
*
Email: [email protected] or [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin–Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second- and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second- and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first- and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second- and third- lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.

Type
Animal Research Papers
Information
The Journal of Agricultural Science , Volume 152 , Issue 2 , April 2014 , pp. 309 - 324
Copyright
Copyright © Cambridge University Press 2013 

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

REFERENCES

Adediran, S. A., Malau-Aduli, A. E. O., Roche, J. R. & Donaghy, D. J. (2007). Using lactation curves as a tool for breeding, nutrition and health management decisions in pasture-based dairy systems. In Current Topics in Dairy Production, vol. 12. Proceedings of the Dairy Research Foundation Symposium (Ed. Fulkerson, B.), pp. 74–78. Sydney, Australia: The University of Sydney.Google Scholar
Burnham, K. P. & Anderson, D. R. (2002). Model Selection and Multimodel Inference: a Practical-Theoretic Approach, 2nd edn. Berlin, Germany: Springer–Verlag.Google Scholar
Cankaya, S., Unalan, A. & Soydan, E. (2011). Selection of a mathematical model to describe the lactation curves of Jersey cattle. Archiv Tierzucht 54, 27–35.Google Scholar
Dekkers, J. C. M., Jamrozik, J., Ten Hag, J. H., Schaeffer, L. R. & Weersink, A. (1996). Genetic and economic evaluation of persistency in dairy cattle. Interbull Bulletin 12, 97–102.Google Scholar
Dekkers, J. C. M., Ten Hag, J. H. & Weersink, A. (1998). Economic aspects of persistency of lactation in dairy cattle. Livestock Production Science 53, 237–252.Google Scholar
Dhanoa, M. S. (1981). A note on an alternative form of the lactation model of wood. Animal Production 32, 349–351.Google Scholar
Dhanoa, M. S. & Le Du, Y. L. P. (1982). A partial adjustment model to describe the lactation curves of a dairy cow. Animal Production 34, 243–247.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
Elahi Torshizi, M., Aslamenejad, A. A., Nassiri, M. R. & Farhangfar, H. (2011). Comparison and evaluation of mathematical lactation curve functions of Iranian primiparous Holsteins. South African Journal of Animal Science 41, 104–115.CrossRefGoogle 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, 633–641.Google Scholar
Fernandez, C., Sanchez, A. & Garces, C. (2002). Modeling the lactation curve for test-day milk yield in Murciano-Granadina goats. Small Ruminant Research 46, 29–41.CrossRefGoogle Scholar
Ferreira, E. B. & Bearzoti, E. (2003). Comparação de métodos no ajustamento de curvas de lactação de bovinos por meio de simulação. Ciência e Agrotecnologia 27, 865–872.Google Scholar
Gahlot, G. C., Gahlot, R. S. & Jairath, L. K. (1988). Pattern of lactation curve in Rathi cattle. Indian Journal of Animal Science 58, 1112–1114.Google Scholar
García, S. C. & Holmes, C. W. (2001). Lactation curves of autumn- and spring calved cows in pasture-based dairy systems. Livestock Production Science 68, 189–203.Google Scholar
Gengler, N. (1996). Persistency of lactation yields: a review. Interbull Bulletin 12, 87–96.Google Scholar
Gołębiewski, M., Brzozowski, P. & Gołębiewski, Ł. (2011). Analysis of lactation curves, milk constituents, somatic cell count and urea in milk of cows by the mathematical model of Wood. Acta Veterinaria Brno 80, 73–80.CrossRefGoogle Scholar
Hayashi, T., Nagamine, Y. & Nishida, A. (1986). A vibration model to describe the lactation curve of a dairy cow. Japanese Journal of Zootechnical Science (Nihon Chikusan Gakkaiho) 57, 471–478.Google Scholar
Johansson, I. & Hansson, A. (1940). Causes of variation in milk and butterfat yield of dairy cows. Kungliga Lantbruksakademiens Tidskrift 79, 1–127.Google Scholar
Korkmaz, M., Üçkardeş, F. & Kaygisiz, A. (2011). Comparison of wood, gaines, parabolic, hayashi, dhanno and polynomial models for lactation season curve of Simmental cows. Journal of Animal and Plant Sciences 21, 448–458.Google Scholar
Landete-Castillejos, T. & Gallego, L. (2000). The ability of mathematical models to describe the shape of lactation curves. Journal of Animal Science 78, 3010–3013.CrossRefGoogle ScholarPubMed
Macciotta, N. P. P., Vicario, D. & Cappio-Borlino, A. (2005). Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models. Journal of Dairy Science 88, 1178–1191.Google Scholar
Morant, S. V. & Gnanasakthy, A. (1989). A new approach to the mathematical formulation of lactation curves. Animal Production 49, 151–162.Google Scholar
Nelder, J. A. (1966). Inverse polynomials, a useful group of multi-factor response functions. Biometrics 22, 128–141.Google Scholar
Olori, V. E., Brotherstone, S., Hill, W. G. & McGuirk, B. J. (1997). Effect of gestation stage on milk yield and composition in Holstein–Friesian dairy cattle. Livestock Production Science 52, 167–176.CrossRefGoogle Scholar
Olori, V. E., Brotherstone, S., Hill, W. G. & 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.CrossRefGoogle Scholar
Papajcsik, I. A. & Bodero, J. (1988). Modeling lactation curves of Friesian cows in a subtropical climate. Animal Production 47, 201–207.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
Pollott, G. E. (2004). Deconstructing milk yield and composition during lactation using biologically based lactation models. Journal of Dairy Science 87, 2375–2387.Google Scholar
Quinn, N., Killen, L. & Buckley, F. (2006). Modelling fat and protein concentration curves for Irish dairy cows. Irish Journal of Agricultural and Food Research 45, 13–23.Google Scholar
Rodriguez-Zas, S. L., Gianola, D. & Shook, G. E. (2000). Evaluation of models for somatic cell score lactation patterns in Holsteins. Livestock Production Science 67, 19–30.Google Scholar
Rook, A. J., France, J. & Dhanoa, M. S. (1993). On the mathematical description of lactation curves. Journal of Agricultural Science 121, 97–102.CrossRefGoogle Scholar
SAS (2002). SAS User's Guide v. 9.1: Statistics. Cary, NC: SAS Institute, Inc.Google Scholar
Sauvant, D. (1988). Modelling of lactation and nutrition. In Modelling of Livestock Production Systems (Eds Korver, S. & Van Arendonk, J. A. M.), pp. 41–55. Dordrecht, The Netherlands: Kluwer.Google Scholar
Schutz, M. M., Hansen, L. B. & Steuernagel, G. R. (1990). Variation of milk, fat, protein and somatic cells for dairy cattle. Journal of Dairy Science 73, 484–493.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., Kellog, 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
Sikka, L. C. (1950). A study of lactation as affected by heredity and environment. Journal of Dairy Research 17, 231–252.Google Scholar
Silvestre, A. M., Petim-Batista, F. & Colaço, J. (2005). Genetic parameter estimates of Portuguese dairy cows for milk, fat and protein using a spline test-day model. Journal of Dairy Science 88, 1225–1230.CrossRefGoogle ScholarPubMed
Silvestre, A. M., Petim-Batista, F. & Colaso, J. (2006). The accuracy of seven mathematical functions in modelling dairy cattle lactation curves based on test-day records from varying sample schemes. Journal of Dairy Science 89, 1823–1821.CrossRefGoogle ScholarPubMed
Silvestre, A. M., Martins, A. M., Santos, V. A., Ginja, M. M. & Colaco, J. A. (2009). Lactation curves for milk, fat and protein in dairy cows: a full approach. Livestock Science 122, 308–313.CrossRefGoogle 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, 1691–1700.Google Scholar
Tekerli, M., Akinci, Z., Dogan, I. & Akcan, A. (2000). Factors affecting the shape of lactation curves of holstein cows from the balikesir province of Turkey. Journal of Dairy Science 83, 1381–1386.CrossRefGoogle ScholarPubMed
Thornley, J. H. M. & France, J. (2005). Mathematical Models in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences, 2nd edn. Wallingford, UK: CAB International.Google Scholar
Val-Arreola, D., Kebreab, K., Dijkstra, J. & France, J. (2004). Study of the lactation curve in dairy cattle on faros 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
Weller, J. I., Ezra, E. & Leitner, G. (2006). Genetic analysis of persistency in the Israeli Holstein population by the multitrait animal model. Journal of Dairy Science 89, 2738–2746.Google Scholar
Wiggans, G. R. & Shook, G. E. (1987). A lactation measure of somatic cell count. Journal of Dairy Science 70, 2666–2672.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. (1976). Algebraic models of the lactation curves for milk, fat and protein production, with estimates of seasonal variation. Animal Production 22, 35–40.Google Scholar