The objective of this study was to compare the fit of seven functions to cumulative daily milk yield records of grazing F1 (Holstein × Zebu) cows in a dual-purpose cattle production unit of the Mexican tropics. Fifty-seven lactations from cows that calved from 1998 to 2001 were used. The functions were quadratic without intercept, three with two segments (both segments linear, the first segment quadratic and the second linear, and both segments quadratic), and three classical growth functions (Gompertz, logistic, and Richards). The Akaike information criterion corrected (AICC) was used as criterion of fit, being the function with the best fit the one with the lowest AICC value. The best fit was for the segmented function with both segments quadratic, followed closely by the Richards function. The derivatives of these functions give the daily milk yield curve (kg/cow/day), so the former results in a straight line per segment and the latter in the usual shape of the typical lactation. However, as cumulative records produce a monotonic increasing line, neither function can distinguish a priori the presence of a lactation peak. For this reason, it is advisable to examine the common dispersion plot of daily milk yield of each cow, and if a peak is not evident, then proceed to fit the segmented function; otherwise, the function of Richards should be used. The need to study the causes for the absence of a lactation peak in tropical dual-purpose cows is highlighted.
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Absalón-Medina VA, Nicholson CF, Blake RW, Fox DG, Juárez-Lagunes FI, Canudas-Lara EG, Rueda-Maldonado BL. 2012. Economic analysis of alternative nutritional management of dual-purpose cow herds in central coastal Veracruz, Mexico. Tropical Animal Health and Production 44(6):1143–50.
Akers RM. 2016. Lactation and the mammary gland. John Wiley & Sons.
Bodisco V, Cevallos E, Carnevali A. 1966. Influencia de la estación climática sobre la producción de vacas criollas lecheras. I Reunión Latinoamericana de Producción Animal. Memorias. México, D. F. Pp 141–153.
Carvalheira JG, Blake RW, Pollak EJ, Quaas RL, Duran-Castro CV. Application of an autoregressive process to estimate genetic parameters and breeding values for daily milk yield in a tropical herd of Lucerna cattle and in United States Holstein herds. Journal of dairy science. 1998 Oct 1;81(10):2738–51.
Castillo-Gallegos, E. 2018. Characterization of the lactation curve of f1 Holstein-Zebu cows. Ecosistemas y Recursos Agropecuarios, 5(14), 335-343.
Castillo-Gallegos E, Valles-de la Mora B, Mannetje L‘t, Aluja-Schunemann. 2005. Effect of Arachis pintoi introduction on soil variables in native grass pastures in the Mexican humid tropics. Técnica Pecuaria en México, 43(2):287–295.
Chilliard Y. Physiological constraints to milk production: factors which determine nutrient partitioning, lactation persistency and mobilization of body reserves. World Review of Animal Production 1992;27:19–26.
Combellas J, Tesorero M. 2003. Cow-calf relationship during milking and its effect on milk yield and calf live weight gain. Livestock Research for Rural Development. Volume 15, Article #24. Retrieved February 26, 2018, from http://www.lrrd.org/lrrd15/3/comb153.htm
Corro M, Rubio I, Castillo E, Galindo L, Aluja A, Galina CS, Murcia C. 1999. Effect of blood metabolites, body condition and pasture management on milk yield and postpartum intervals in dual-purpose cattle farms in the tropics of the State of Veracruz, Mexico. Preventive Veterinary Medicine, 38:101–17.
Cunha DNFV, Pereira JC, Silva FF, Campos OF, Braga JL, Martuscello JA. 2010. Selection of models of lactation curves to use in milk production simulation systems. Revista Brasileira da Zootecnia, 39:891–902.
De Alba MJ. 2011. El Libro de los Bovinos Criollos de América. Colegio de Postgraduados, Montecillo, México Pp 444.
Dijkstra J, France J, Dhanoa MS, Maas JA, Hanigan MD, Rook AJ, Beever DE. A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science. 1997 Oct 1;80(10):2340–54.
El Faro, L., & Albuquerque, L. G. D. (2003). Estimação de parâmetros genéticos para produção de leite no dia do controle e produção acumulada até 305 dias, para as primeiras lactações de vacas da raça Caracu. Revista Brasileira de Zootecnia, 32(2), 284–294.
Januś E, Borkowska D. 2013. Dry period length in Montbéliarde cows and its association with selected production and functional characteristics, Archives Animal Breeding, 56:555–563.
Kamidi RE. (2005) A parametric measure of lactation persistency in dairy cattle. Livestock Production Science, 96:141–148.
López S, France J, Odongo NE, McBride RA, Kebreab E, AlZahal O, McBride BW, Dijkstra J. 2015. On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions. Journal of Dairy Science, 98:2701–2712.
Madalena FE, Martinez ML, Freitas AF. 1979. Lactation curves of Holstein-Friesian and Holstein-Friesian x Gir cows. Animal Production, 29:101–107.
Marquardt, D. W. (1963). An algorithm for least squares estimation of parameters. Journal of the Society of Industrial Applied Mathematics, 11, 431–441. Available in: http://www.dista.unibo.it/~bittelli/materiale_lettura_fisica_terreno/marquardt_63.pdf.
Montiel F, Ahuja C. 2005. Body condition and suckling as factors influencing the duration of postpartum anestrus in cattle: a review. Animal Reproduction Science, 85:1–26.
Motulsky, H. J. “Equation: Segmental Linear Regression”, GraphPad Curve Fitting Guide. Accessed 16 September 2017. https://www.graphpad.com/guides/prism/7/curve-fitting/index.htm?reg_segmental_linear_regression.htm
Parra-Bracamonte GM, Magaña JG, Delgado R, Osorio-Arce MM, Segura-Correa JC. 2005. Genetic and non-genetic effects on productive and reproductive traits of cows in dual purpose herds in Southeastern Mexico. Genetics and Molecular Research 4: 482-490.
Pollot, G. 2000. A biological approach to lactation curve analysis for milk yield. Journal of Dairy Science 83:2448–2458. https://doi.org/10.3168/jds.S0022-0302(00)75136-8
SAS Institute Inc. 2013. SAS/STAT® 12.3 User’s Guide. Cary, NC.
Sidibé-Anago AG, Ouedraogo GA, Ledin I. 2008. Effect of suckling period on calf growth and milk yield of Zebu cows. Tropical Animal Health and Production, 40:491–499.
Silvert W (1979) Practical curve fitting. Limnology and Oceanography 24: 767–773.
Sørensen JT, Enevoldsen C. 1991. Effect of dry period length on milk production in subsequent lactation. Journal of dairy science. 74:1277–1283.
Upadhyay VK, Tomar AK, Patel BH, Golher DM, Sahu S, Bharti PK. Effect of early weaning on milking behaviour, production and reproduction of Tharparkar cows. Indian J. Dairy Sci. 2015;68:5.
Watters RD, Guenther JN, Brickner AE, Rastani RR, Crump PM, Clark PW, Grummer RR. 2008. Effects of dry period length on milk production and health of dairy cattle. Journal of Dairy Science, 91(7):2595–603.
The Center for Teaching, Research and Extension in Tropical Animal Husbandry of the Faculty of Veterinary Medicine and Animal Science of the National Autonomous University of México (CEIEGT, FMVZ, UNAM its Spanish acronym) allowed the use of the milk production records and provided computational facilities to conduct this investigation.
Conflict of interest
The authors declare that they have no conflict of interest.
Statement of animal rights
In the conduction of the experiment, the authors fulfilled the Official Mexican Norm NOM-062-ZOO-1999 on production, care, and use of experimental animals (CICUAE: http://www.fmvz.unam.mx/fmvz/principal/cicuae.html).
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Castillo-Gallegos, E., Marín-Mejía, B.d.J. Segmented regression to describe cumulative milk production of grazing dual-purpose Holstein-Zebu cows. Trop Anim Health Prod 51, 809–818 (2019). https://doi.org/10.1007/s11250-018-1760-y
- Dual-purpose cattle
- Lactation curve