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Accurate mathematical models to describe the lactation curve of Lacaune dairy sheep under intensive management

Published online by Cambridge University Press:  20 December 2012

L. Elvira ,
F. Hernandez ,
P. Cuesta ,
S. Cano ,
J.-V. Gonzalez-Martin  and
S. Astiz
L. Elvira
Affiliation:
TRIALVET S.L., C/ Encina, 22, 28721 Cabanillas de la Sierra, Madrid, Spain
F. Hernandez
Affiliation:
Granja Cerromonte S.L., San Juan de la Encinilla, 05358 Ávila, Spain
P. Cuesta
Affiliation:
Informatics Department for Research Support, Complutense University of Madrid, Avda de la Complutense s/n, 28040 Madrid, Spain
S. Cano
Affiliation:
Informatics Department for Research Support, Complutense University of Madrid, Avda de la Complutense s/n, 28040 Madrid, Spain
J.-V. Gonzalez-Martin
Affiliation:
TRIALVET S.L., C/ Encina, 22, 28721 Cabanillas de la Sierra, Madrid, Spain Department of Animal Medicine and Surgery, Faculty of Veterinary Medicine, Complutense University of Madrid (UCM), Avda Pta. de Hierro s/n, 28040 Madrid, Spain
S. Astiz*
Affiliation:
Department of Animal Reproduction, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Avda Pta. de Hierro s/n, 28040 Madrid, Spain
*
†E-mail: astiz.susana@inia.es
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Abstract

Although the intensive production system of Lacaune dairy sheep is the only profitable method for producers outside of the French Roquefort area, little is known about this type of systems. This study evaluated yield records of 3677 Lacaune sheep under intensive management between 2005 and 2010 in order to describe the lactation curve of this breed and to investigate the suitability of different mathematical functions for modeling this curve. A total of 7873 complete lactations during a 40-week lactation period corresponding to 201 281 pieces of weekly yield data were used. First, five mathematical functions were evaluated on the basis of the residual mean square, determination coefficient, Durbin Watson and Runs Test values. The two better models were found to be Pollott Additive and fractional polynomial (FP). In the second part of the study, the milk yield, peak of milk yield, day of peak and persistency of the lactations were calculated with Pollot Additive and FP models and compared with the real data. The results indicate that both models gave an extremely accurate fit to Lacaune lactation curves in order to predict milk yields (P = 0.871), with the FP model being the best choice to provide a good fit to an extensive amount of real data and applicable on farm without specific statistical software. On the other hand, the interpretation of the parameters of the Pollott Additive function helps to understand the biology of the udder of the Lacaune sheep. The characteristics of the Lacaune lactation curve and milk yield are affected by lactation number and length. The lactation curves obtained in the present study allow the early identification of ewes with low milk yield potential, which will help to optimize farm profitability.

Keywords

Lacaunedairy sheeplactation curvecurve fittingfractional polynomial
Type
Farming systems and environment
Information
animal , Volume 7 , Issue 6 , June 2013 , pp. 1044 - 1052
Copyright
Copyright © The Animal Consortium 2012

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References

Ali, TE, Schaeffer, LR 1987. Accounting for covariance among test day yields in dairy cows. Canadian Journal of Animal Science 67, 637–644.Google Scholar
Albarrán-Portillo, B, Pollott, GE 2008. Genetic parameters derived from using a biological model of lactation on records of commercial dairy cows. Journal of Dairy Science 91, 3639–3648.Google Scholar
Barillet, F, Marie, C, Jacquin, M, Lagriffoul, G, Astruc, JM 2001. The French Lacaune dairy sheep breed: use in France and abroad in the last 40 years. Livestock Production Science 71, 17–29.CrossRefGoogle Scholar
Bebbington, M, Lai, CD, Zitikis, R 2009. Modeling lactation curves: classical parametric models re-examined and modified. Journal of Applied Statistics 36, 121–133.Google Scholar
Bradley, JV 1968. Distribution-free statistical tests. Prentice Hall, Englewood Cliffs, NJ, USA.Google Scholar
Cobby, JM, Le Du, YLP 1978. On fitting curves to lactation data. Animal Production 26, 127–133.Google Scholar
Cui, J, de Klerk, N, Abramson, M, Del Monaco, A, Benke, G, Dennekamp, MAWM, Sim, M 2009. Fractional polynomials and model selection in generalized estimating equations analysis, with an application to a Longitudinal Epidemiologic Study in Australia. American Journal of Epidemiology 169, 113–121.Google Scholar
Dijkstra, J, France, J, Dhanoa, MS, Maas, JA, Hanigan, MD, Rook, AJ, Beever, DE 1997. A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science 80, 2340–2354.Google Scholar
Durbin, J, Watson, GS 1951. Testing for serial correlation in least squares regression. Biometrika 38, 159–178.Google Scholar
Elston, DA, Glaseby, CA, Nelson, DR 1989. Non-parametric lactation curves. Animal Production 48, 331–339.Google Scholar
Groenewald, PCN, Ferreira, HJ, van der Merwe, HJ, Slippers, SC 1995. A mathematical model for describing and predicting the lactation curve of Merino ewes. Animal Science 61, 95–101.Google Scholar
Grossman, M, Koops, WJ 1988. Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71, 1598–1608.Google Scholar
Hernandez, F, Elvira, L, Gonzalez-Martin, JV, Gonzalez-Bulnes, A, Astiz, S 2011. Influence of age at first lambing on reproductive and productive performance of Lacaune dairy sheep under an intensive management system. Journal of Dairy Research 78, 160–167.CrossRefGoogle ScholarPubMed
Lambert, PC, Smith, LK, Jones, DR, Botha, JL 2005. Additive and multiplicative covariate regression models for relative survival incorporating fractional polynomials for time-dependent effects. Statistics in Medicine 24, 3871–3885.CrossRefGoogle ScholarPubMed
Masselin, S, Sauvant, D, Chapoutot, P, Milan, D 1987. Adjustment models for lactation curves. Annales de Zootechnie 36, 171–206.CrossRefGoogle Scholar
Morant, SV, Gnanasakthy, A 1989. A new approach to the mathematical formulation of lactation curves. Animal Production 49, 151–162.Google Scholar
Neal, HDStC, Thornley, JHM 1983. The lactation curve in cattle: a mathematical model of the mammary gland. Journal of Agricultural Science 101, 389–400.Google Scholar
Olori, VE, Brotherstone, S, Hill, WG, McGuirk, BJ 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
Oravcová, M 2007. Genetic evaluation for milk production traits in Slovakian Lacaune sheep. Slovak Journal of Animal Science 40, 172–179.Google Scholar
Oravcová, M, Margetín, M, Peškovičová, D, Daňo, J, Milerski, M, Hetényi, L, Polák, P 2006. Factors affecting milk yield and ewe's lactation curves estimated with test-day models. Czech Journal of Animal Science 51, 483–490.Google Scholar
Oravcová, M, Margetín, M, Peškovičová, D, Daňo, J, Milerski, M, Hetényi, L, Polák, P 2008. Factors affecting ewe's milk fat and protein content and relationships between milk yield and milk components. Czech Journal of Animal Science 52, 189–198.Google Scholar
Paladini, D, Rustico, M, Viora, E, Giani, U, Bruzzese, D, Campogrande, M, Martinelli, P 2005. Fetal size charts for the Italian population. Normative curves of head, abdomen and long bones. Prenatal Diagnosis 25, 456–464.Google Scholar
Peralta-Lailson, M, Trejo-González, AÁ, Pedraza-Villagómez, P, Berruecos-Villalobos, JM, Vasquez, CG 2005. Factors affecting milk yield and lactation curve fitting in the Creole sheep of Chiapas-Mexico. Small Ruminant Research 58, 265–273.Google Scholar
Pérochon, L, Coulon, JB, Lescourret, F 1996. Modelling lactation curves of dairy cows with emphasis on individual variability. Animal Science 63, 189–200.Google Scholar
Pollott, GE 2000. A biological approach to lactation curve analysis for milk yield. Journal of Dairy Science 83, 2448–2458.Google Scholar
Pollott, GE, Gootwine, E 2000. Appropriate mathematical models for describing the complete lactation of dairy sheep. Journal of Animal Science 71, 197–207.Google Scholar
Pollott, GE, Gootwine, E 2004. Reproductive performance and milk production of Assaf sheep in an intensive management system. Journal of Dairy Science 87, 3690–3703.Google Scholar
Pool, MH, Meuwissen, THE 2000. Reduction of the number of parameters needed for a polynomial random regression test day model. Livestock Production Science 64, 133–145.CrossRefGoogle Scholar
Portolano, B, Spatafora, F, Bono, G, Margiotta, S, Todaro, M, Ortoleva, V, Leto, G 1996. Application of the Wood model to lactation curves of Comisana sheep. Small Ruminant Research 24, 7–13.Google Scholar
Rook, AJ, France, J, Dhanoa, MS 1993. On the mathematical description of lactation curves. Journal of Agricultural Science 121, 97–102.Google Scholar
Royston, P, Altman, DG 1994. Regression using fractional polynomials of continuous covariates. Applied Statistics 43, 429–467.Google Scholar
Royston, P, Sauerbrei, W 2008. Multivariable model-building. Wiley, New York, NY, USA.Google Scholar
Ruiz, R, Oregui, LM, Herrero, M 2000. Comparison of models for describing the lactation curve of Latxa sheep and an analysis of factors affecting milk yield. Journal of Dairy Science 83, 2709–2719.Google Scholar
Sakul, H, Boylan, WJ 1992. Lactation curves for several US sheep breeds. Animal Production 54, 229–233.Google Scholar
Schaeffer, LR, Jamrozik, J, Kistemaker, GJ, Van Doormaal, BJ 2000. Experience with a test-day model. Journal of Dairy Science 83, 1135–1144.Google Scholar
Silvestre, AM, Petim-Batista, F, Colaco, J 2006. The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes. Journal of Dairy Science 89, 1813–1821.Google Scholar
Wilmink, JBM 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, PDP 1967. Algebraic model of the lactation curve in cattle. Nature 216, 164–165.Google Scholar
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