IMPROVED LACTATION CURVE MODEL
Abstract
This article analyzes mathematical models of the lactation curve (LC), which describe variations in the milk yield of dairy cows. Special attention is given to the widely used Wood and Wilmink models, with an in-depth discussion of their structure, biological interpretation, and parameter effects. Considering the advantages and limitations of both models, a new improved model is proposed that combines the main curve of the Wood model with the short-term exponential component of the Wilmink model. The proposed model adapts better to initial conditions and provides a highly accurate representation of the LC. Its practical effectiveness is evaluated using 305-day real milk yield data from 300 cows, and compared with the Wood and Wilmink models using RMSE and R² metrics. The results show that the new model achieves higher accuracy in predicting milk yield.
References
1. H. Farhangfar and P. Rowlinson, 2007. Genetic Analysis of Wood`s Lactation Curve for Iranian Holstein Heifers. Journal of Biological Sciences, 7: 127-135.
2. Babadjanov E.S., Toliev X.I., Kenjaev X.B. Sog’in sigirlarning sut maxsuldorlik tahlili va laktatsiya egri chizig’ini qurish usuli // Muhammad al-Xorazmiy avlodlari. №1(23). Toshkent-2023. –B. 11-14. (05.00.00; №10)
3. M. Iewdiukow, O. M. Lema, J. I. Velazco, and G. Quintans // Is it possible to accurately estimate lactation curve parameters in extensive beef production systems?
4. Wood, P.D.P. (1967). Algebraik model for the lactation curve in cattle. Nature. (Wood modelining birinchi taklifi, gamma-funksiya asosida).
5. Wilmink, J.B.M. (1987). Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation. Livestock Production Science. (Wilmink modelining taklifi, eksponensial + chiziqli funksiya).
6. Guevara L, Lopez-Villalobos N, Pollott GE, Albarrán-Portillo B, Fernandes AM, Salinas-Martínez JA, Angeles-Hernandez JC. Evaluation of empirical and mechanistic models and sampling intervals to model the lactation curves of F1 dairy sheep. Trop Anim Health Prod. 2025 Mar 14;57(2):116. doi: 10.1007/s11250-025-04365-z. PMID: 40082283; PMCID: PMC11906548.
7. Grossman, M., & Koops, W.J. (1988). Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science. (Ko‘p fazali laktatsiya modellarining nazariyasi).
8. Boujenane, Ismaïl. (2013). Comparison of different lactation curve models to describe lactation curve in Moroccan Holstein-Friesian dairy cows. Iranian Journal of Applied Animal Science. 3. 817-822.
9. Sitkowska, Beata & Kolenda, Magdalena & Piwczyński, Dariusz. (2019). Comparison of the fit of automatic milking system and test-day records with the use of lactation curves. Asian-Australasian Journal of Animal Sciences. 33. 10.5713/ajas.19.0190.
10. Fathi, M. Hassan & France, J. & Odongo, N. & López, Secundino & Bannink, Andre & Kebreab, Ermias. (2008). Modelling the lactation curve of dairy cows using the differentials of growth functions. Journal of Agricultural Science 146 (2008). 146. 10.1017/S0021859608008101.