Application of the Wood model to analyse lactation curves of organic dairy sheep farming
Juan Carlos Ángeles Hernández A F , Octavio Castelán Ortega B , Benito Albarrán Portillo C , Hugo H. Montaldo D and Manuel González Ronquillo B EA Programa de Maestría y Doctorado en Ciencias de la Producción y de la Salud Animal, Facultad de Medicina Veterinaria y Zootecnia, Universidad Nacional Autónoma de México, México.
B Departamento de Nutrición Animal, Facultad de Medicina Veterinaria y Zootecnia, Universidad Autónoma del Estado de México, Estado de México, México.
C Centro Universitario UAEM Temascaltepec, Universidad Autónoma del Estado de México, Estado de México, México.
D Departamento de Genética y Bioestadística, Facultad de Medicina Veterinaria y Zootecnia, Universidad Nacional Autónoma de México, México.
E Facultad de Ciencias, Escuela de Ciencias y Tecnología en Recursos Agrícolas y Acuícolas, Universidad de Magallanes, Chile.
F Corresponding author. Email: mvzjuancarlos@comunidad.unam.mx
Animal Production Science 54(10) 1609-1614 https://doi.org/10.1071/AN14272
Submitted: 13 March 2014 Accepted: 13 June 2014 Published: 19 August 2014
Abstract
The aim of the present study was to evaluate the performance of the Wood model to describe the characteristics of lactation curves of dairy ewes under organic management in Mexico. In total, 4861 weekly test-day milk yield records from 194 lactations of crossbred dairy ewes were analysed to assess the performance of an empirical model to fit their lactation curve. We used the mathematical model proposed by Wood. The evaluation criteria were the correlation coefficient (r) between the values of total milk yield observed and estimated, the coefficient of determination (R2), and the mean square prediction error (MSPE). In addition, the peak yield (PYest) and time at peak yield (PTest) were calculated. The Wood model showed adequate goodness of fit (r = 0.95, R2 = 0.92 and MSPE = 0.024). The Wood model detected that 52.06% of lactation curves had a continuously decreasing shape (atypical curve), probably as a consequence of the characteristic management of the organic system, mainly due to the genotype used and the nutritional management. Residuals were greater for atypical curves than for typical ones, indicating differences in the ability of the Wood model to fit the two types of shapes. In typical curves, the Wood model showed adequate estimates of total milk yield and time at peak yield. The peak yield was underestimated both in typical and atypical curves. The Wood model in atypical curves underestimated the time at peak yield and milk yields in late lactation. The Wood model showed a reasonable fit of lactation curve in dairy sheep in organic systems but presented deficiencies of fit in atypical curves; therefore, estimates should be interpreted carefully.
Additional keywords: goodness of fit, mathematical modelling, milk production, organic management.
References
Cannas A (2004) Feeding of lactation ewes. In ‘Handbook of milk of non-bovine mammals’. (Eds WY Park, GFW Haenlein) pp. 79–108. (Blackwell Publishing: Ames, IA)Cappio-Borlino A, Pulina G, Rossi G (1995) A non-linear modification of Wood’s equation fitted to lactation curves of Sardinian dairy ewes. Small Ruminant Research 18, 75–79.
| A non-linear modification of Wood’s equation fitted to lactation curves of Sardinian dairy ewes.Crossref | GoogleScholarGoogle Scholar |
Cappio-Borlino A, Macciotta NPP, Pulina G (1997) The shape of Sarda ewe lactation curve analyzed by a compartmental model. Livestock Production Science 51, 89–96.
| The shape of Sarda ewe lactation curve analyzed by a compartmental model.Crossref | GoogleScholarGoogle Scholar |
Congleton WR, Everett RW (1980) Error and bias in using the incomplete gamma function to describe lactation curves. Journal of Dairy Science 63, 101–108.
| Error and bias in using the incomplete gamma function to describe lactation curves.Crossref | GoogleScholarGoogle Scholar |
Dag B, Keskin I, Mikailsoy F (2005) Application of different models to the lactation curves on unimproved Awassi ewes in Turkey. South African Journal of Animal Science 35, 238–243.
EU (1999) Council Regulation No. 1804/1999 of July 1999, Supplementing Regulation (EEC) No. 2092/91. CELEX-EUR Official Journal L 222, pp. 1–28. Available at europa.eu.eur18524.doc.
González-Peña D, Acosta J, Guerra D, González N, Acosta M, Sosa D, Torres-Hernández G (2012) Modelling of individual lactation curves for milk production in a population of Alpine goats in Cuba. Livestock Science 150, 42–50.
| Modelling of individual lactation curves for milk production in a population of Alpine goats in Cuba.Crossref | GoogleScholarGoogle Scholar |
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 Science 124, 321–329.
| 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.Crossref | GoogleScholarGoogle Scholar |
Hovi M, Roderick S, Taylor N, Hanks J (2001) The production characteristics of organic dairy herds in the UK. In ‘Organic meat and milk from ruminants’. (Eds I Kyriazakis, G Zervas) pp. 127–133. (Wageningen Academic Publishers: Wageningen, The Netherlands)
Landete-Castillejos T, Gallego L (2000) Technical note: the ability of mathematical models to describe the shape of lactation curves. Journal of Animal Science 78, 3010–3013.
León JM, Macciotta NPP, Gama LT, Barba C, Delgado JV (2012) Characterization of the curve in Murciano–Granadina dairy goats. Small Ruminant Research 107, 76–84.
| Characterization of the curve in Murciano–Granadina dairy goats.Crossref | GoogleScholarGoogle Scholar |
Macciotta NPP, Vicario D, Cappio-Borlino A (2005) Detection of different shapes of lactation curves for milk yield in dairy cattle by empirical mathematical models. Journal of Dairy Science 88, 1178–1191.
| Detection of different shapes of lactation curves for milk yield in dairy cattle by empirical mathematical models.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2MXitFygur4%3D&md5=89216d6c066253e3b2ddf2959d2948a3CAS |
Macciotta NPP, Dimauro C, Rassu SPG, Steri R, Pulina G (2011) The mathematical description of lactation curves in dairy cattle. Italian Journal of Animal Science 10, 213–223.
| The mathematical description of lactation curves in dairy cattle.Crossref | GoogleScholarGoogle Scholar |
Olori VE, Brotherstone S, Hill WG, McGuirk BJ (1999) Fit of standard models of lactation curves to weekly records of milk production of cows in a single herd. Livestock Production Science 58, 55–63.
| Fit of standard models of lactation curves to weekly records of milk production of cows in a single herd.Crossref | GoogleScholarGoogle Scholar |
Pollott GE, Gootwine E (2000) Appropriate mathematical models for describing the complete lactation of dairy sheep. Animal Science 71, 197–207.
Portolano B, Spatafora F, Bono G, Margiotta S, Todaro M, Ortoleva V, Leto G (1997) Application of the Wood model to lactation curves of Comisana sheep. Small Ruminant Research 24, 7–13.
| Application of the Wood model to lactation curves of Comisana sheep.Crossref | GoogleScholarGoogle Scholar |
Pulina G, Macciotta N, Nudda A (2005) Milk composition and feeding in the Italian dairy sheep. Italian Journal of Animal Science 4, 5–14.
Ronchi B, Nardone A (2003) Contribution of organic farming to increase sustainability of Mediterranean small ruminants livestock systems. Livestock Production Science 80, 17–31.
| Contribution of organic farming to increase sustainability of Mediterranean small ruminants livestock systems.Crossref | GoogleScholarGoogle 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.
| Comparison of models for describing the lactation curve of Latxa sheep and an analysis of factors affecting milk yield.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3cXosVCrsrw%3D&md5=ad16750e5f9d073454840cfd7c67b37aCAS | 11104292PubMed |
SAS Institute (2002) ‘Statistical analysis systems user’s guide.’ (SAS: Cary, NC)
Shanks RD, Berger PJ, Freeman AE, Dickinson FN (1981) Genetic aspects of lactation curves. Journal of Dairy Science 64, 1852–1860.
| Genetic aspects of lactation curves.Crossref | GoogleScholarGoogle Scholar | 1:STN:280:DyaL38%2FpvVynsw%3D%3D&md5=15ebe44f9b751f1e29e3d3e4ca1409e8CAS | 7198657PubMed |
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.
| The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XktVOht7k%3D&md5=216fc9a71c1a1897f83bdd821bea8f92CAS | 16606753PubMed |
Tzouramani I, Sintori A, Liontakis A, Karanikolas P, Alexopoulos G (2011) An assessment of the economic performance of organic dairy sheep farming in Greece. Livestock Science 141, 136–142.
| An assessment of the economic performance of organic dairy sheep farming in Greece.Crossref | GoogleScholarGoogle Scholar |
Wasike CB, Kahi AK, Peters KJ (2011) Modeling of lactation curves of dairy cows based on monthly test day milk yield records under inconsistent milk recording scenarios. Animal 5, 1780–1790.
| Modeling of lactation curves of dairy cows based on monthly test day milk yield records under inconsistent milk recording scenarios.Crossref | GoogleScholarGoogle Scholar | 1:STN:280:DC%2BC38vovFSksA%3D%3D&md5=825a480a2e74a36a35803d98e395e4f4CAS | 22440419PubMed |
Wolfová M, Wolf J, Krupová Z, Kica J (2009) Estimation of economic values for traits of dairy sheep: I. Model development. Journal of Dairy Science 92, 2183–2194.
| Estimation of economic values for traits of dairy sheep: I. Model development.Crossref | GoogleScholarGoogle Scholar | 19389977PubMed |
Wood PDP (1967) Algebraic model of the lactation curve in cattle. Nature 216, 164–165.
| Algebraic model of the lactation curve in cattle.Crossref | GoogleScholarGoogle Scholar |
