Abstract
A mathematical model of the lactation curve approximation provides summary information about dairy cattle production, which is useful in making management and breeding decisions and in simulating a dairy enterprise. Several nonlinear regression models have been developed during the past decades. Unfortunately, there is no unique algorithm in literature. The question of choosing the best function is brought up. We tested seven such models (Gaines, Nelder, Ning-Yang, Marek-Zelinkova, McMillan, Papajesic-Bodero, Wood) using milk yield data of more than 5 000 lactation cycles. Non-linear approximations showed high level of confidence in all models. Critical limitations of individual approaches are discussed using data of several individual cows with problematic approximations. We stress the limitations of individual—generally well-fitting—mathematical models at the level of individual animals. The best results were obtained with Wood, Nelder or Marek-Zelinkova models.
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References
Golebiewski M, Brzozowski P, Golebiewski L (2011) Analysis of lactation curves, milk constituents, somatic cell count and urea in milk of cows by the mathematical model of Wood. Acta Vet Brno 73–80
Gradiz L, Alvarado L, Kahi AK, Hirooka H (2009) Fit of Wood’s function to daily milk records and estimation of environmental and additive and non-additive genetic effects on lactation curve and lactation parameters of crossbred dual purpose cattle. Livestock Sci 124: 321–329
Karush W (1963) On the use of mathematics in behavioral reseach. In: Garvin V (ed) Natural language and the computer. McGraw-Hill, New York, pp 67–83
Kubacek L, Kubackova L, Volaufova J (1995) Statistical models with linear structures. Publishing House of the Slovak Academy of Sciences, Bratislava, Veda
Kubacek L (1995) On a linearization of regression models. Appl Math (1) 40:61–78
Leon-Velarde CU, McMillan I, Gentry RD, Wilton JW (1995) Models for estimating typical lactation curves in dairy cattle. J Anim Breed Genet 112(1995):333–340
Mellado J, Sepulveda E, Garcia JE, Rodriguez A, De Santiago A, Veliz FG, Mellado M (2014) Milk yield of Holstein cows induced into lactation twice consecutively and lactation curve models fitted to artificial lactations. J Integr Agric 13(6):1349–1354
Murphy MD, O’Mahony MJ, Shalloo L, French P, Upton J (2014) Comparison of modeling techniques for milk-production forecasting. J Dairy Sci 97:3352–3363
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 Prod Sci 58:55–63
Rao CR (1973) Linear statistical inference and its applications, 2nd edn. Wiley, New York
Rekik B, Gara AB, Hamouda MB, Hammami H (2003) Fitting lactation curves of dairy cattle in different types of herds in Tunisia. Livestock Prod Sci 83:309–315
Seber GAF, Wild CJ (2003) Nonlinear regression. Wiley, New Jersey
Silvestre AM, Martins AM, Santos VA, Ginja MM, Colaco JA (2009) Lactation curves for milk, fat and protein in dairy cows: a full approach. Livestock Sci 122:308–313
Wimmer G, Altmann G, Hrebicek L, Ondrejovic S, Wimmerova S (2003) Uvod do analyzy textov. Vydavatelstvo Slovenskej akademie vied, Bratislava
Wood PDP (1967) Algebraic model of the lactation curve in References cattle. Nature (London) 216:164–165
Zavadilova L, Jamrozik J, Schaeffer LR (2005) Genetic parameters for test-day model with random regressions for production traits of Czech Holstein cattle. Czech J Anim Sci 50(4):142–154
Zavadilova L, Nemcova E, Pribyl J, Wolf J (2005) Definition of subgroups for fixed regression in the test-day animal model for milk production of Holstein cattle in the Czech Republic. Czech J Anim Sci 50(1):7–13
Zelinkova G, Marek J (2010) Dependence of milk yield, fat: protein ratio and somatic cell counts. Proceedings of XI, Middle-European Buiatrics Congress, Brno
Acknowledgments
We thank Zdenek Kovar from Zahori for his support and data preparation.
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Marek, J., Rajmon, R., Haloun, T. (2015). Critical Evaluation of Seven Lactation Curve Estimation Models. In: Abraham, A., Jiang, X., Snášel, V., Pan, JS. (eds) Intelligent Data Analysis and Applications. Advances in Intelligent Systems and Computing, vol 370. Springer, Cham. https://doi.org/10.1007/978-3-319-21206-7_7
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DOI: https://doi.org/10.1007/978-3-319-21206-7_7
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