Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins

Abstract

In order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin-Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second-and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second-and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first-and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second-and third-lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.

Comparison of non-linear models to describe the lactation curves for milk yield and composition in buffaloes (Bubalus bubalis)

“…Variations between the lactation curve characteristics of primiparous and multiparous buffaloes are likely to be responsible for the significant difference between goodness of fit of the models for the different lactations. In addition, the difference between fit of models may have arisen from the variations in mathematical functions of the models (Ghavi Hossein-Zadeh, 2014a). Consistent with the current study, Dimauro et al (2005) showed that the models commonly used to fit the lactation curve in dairy cattle are able to describe with a high degree of accuracy average curves of water buffaloes.…”

“…The state of pregnancy results in a markedly reduced MY for lactating buffalo cows, as happened in dairy cattle before the development of selection programs for the improvement of MY (Coulon et al, 1995). Latest peak production observed in first lactation for most models in the current study, while third lactation buffaloes generally had the earliest day of peak production and this might be explained by the milk secretary tissue in primiparous buffaloes taking longer to reach its peak activity than in multiparous buffaloes (Ghavi Hossein-Zadeh, 2014a). Different persistency measures and 305-day MY for average standard lactations of buffaloes according to parity class, predicted by different equations are presented in Table 9.…”

“…Thus, a mathematical function able to accurately describe the pattern of MY during the year and to predict future production supplies useful information to help the farmer and the agricultural extension workers in several management decisions. Such information is of great importance in the programs of genetic improvement, herd management, feeding, health monitoring and profits evaluation, besides the construction and validation of bio-economic models and software for livestock species (Ghavi Hossein-Zadeh, 2014a).…”

“…Mathematical modeling of lactation curve by appropriate functions of time widely applied in the dairy cattle industry (Silvestre et al, 2009;Gołębiewski et al, 2011;Ghavi Hossein-Zadeh, 2014a), and there are various mathematical equations describing lactation curves in dairy cows, from the more empirical equations that relate input to output statistically with little consideration of the biology of lactation (e.g. Wood, 1967;Rook et al, 1993), to the more mechanistic ones that describe the lactation curve based on the biology of lactation (e.g.…”

Application of growth models to describe the lactation curves for test-day milk production in Holstein cows

“…Several authors have shown variations in the general shape of the lactation curve (e.g. Landete-Castillejos & Gallego 2000;Fathi Nasri et al 2008;Ghavi Hossein-Zadeh 2014), the most common shape being a rapid increase after parturition to a peak a few weeks later, followed by a slow decrease until the cow is dried off. The other shape is a gradual decline from calving.…”