Abstract:RESUMO Curvas de lactação representam a produção de leite de uma fêmea leiteira em função do tempo. Uma vez que tais curvas variam aleatoriamente de animal para animal, devido a fatores tanto genéticos quanto ambientais, o modelo misto conhecido como regressão aleatória é apropriado para ajustar os dados de produção de um rebanho. A regressão aleatória foi avaliada neste estudo mediante simulação de dados. Produções de cinco animais em cinco idades foram simuladas em mil conjuntos de dados independentes, em tr… Show more
“…Functions that describe milk production in time can be very applicable in genetic breeding programmes, herd nutritional management, decision-making on the culling cows and simulation systems of milk production over the lactation. The lactation curve is also important because its wide characterization of the animal production throughout lactation allows estimating the peak yield (PY), persistency of lactation and days in milk (Ferreira & Bearzoti 2003). There are different mathematical models 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.…”
In order to describe the lactation curves of milk yield traits, six standard growth models (Brody, logistic, Gompertz, Schumacher, Von Bertalanffy and Morgan) were used. Data were 911,144 test-day records for unadjusted milk yield , 4% fat-corrected milk yield and energy-corrected milk yield from the first lactation of Iranian Holstein cows, which were collected on 834 dairy herds in the period from 2000 to 2011. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS. The models were tested for goodness of fit using adjusted coefficient of determination, root means square error, Durbin-Watson statistic, Akaike's information criterion (AIC) and Bayesian information criterion (BIC). The Morgan model provided the best fit of the lactation curves due to the lower values of AIC and BIC than other models, but the Brody model did not fit the production data as well as the other equations. The results showed that the Morgan equation was able to estimate the time to the peak and peak yield more accurately than the other equations. Overall, evaluation of the different growth equations indicated the potential of the nonlinear functions for fitting monthly productive records of Holstein cows.
“…Functions that describe milk production in time can be very applicable in genetic breeding programmes, herd nutritional management, decision-making on the culling cows and simulation systems of milk production over the lactation. The lactation curve is also important because its wide characterization of the animal production throughout lactation allows estimating the peak yield (PY), persistency of lactation and days in milk (Ferreira & Bearzoti 2003). There are different mathematical models 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.…”
In order to describe the lactation curves of milk yield traits, six standard growth models (Brody, logistic, Gompertz, Schumacher, Von Bertalanffy and Morgan) were used. Data were 911,144 test-day records for unadjusted milk yield , 4% fat-corrected milk yield and energy-corrected milk yield from the first lactation of Iranian Holstein cows, which were collected on 834 dairy herds in the period from 2000 to 2011. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS. The models were tested for goodness of fit using adjusted coefficient of determination, root means square error, Durbin-Watson statistic, Akaike's information criterion (AIC) and Bayesian information criterion (BIC). The Morgan model provided the best fit of the lactation curves due to the lower values of AIC and BIC than other models, but the Brody model did not fit the production data as well as the other equations. The results showed that the Morgan equation was able to estimate the time to the peak and peak yield more accurately than the other equations. Overall, evaluation of the different growth equations indicated the potential of the nonlinear functions for fitting monthly productive records of Holstein cows.
“…Mathematical models for describing a lactation curve include negative exponentials, incomplete gamma, and polynomials, all of which can estimate the milk yield average at a given time [4]. The lactation curve is also important because its wide characterization of the animal production throughout lactation allows estimating the peak yield (PY), the time of peak, days in milk, and the total milk yield [5].…”
The aim was to compare standard lactation curve models using fortnightly milk records in Frieswal cattle.
Materials and Methods:A total of 2904 fortnightly milk yield (FMY) records from 132 Frieswal cattle maintained at Military Farm, Bareilly, Uttar Pradesh were taken for study. The Wood (WD), Morant and Gnanasakthy (MG), Mitscherlich x Exponential (ME), and Wilmink (WK) models were fitted on average FMY (AFMY) by nonlinear regression using statistical package SAS 9.3 version. The goodness of fit of models was judged by the adjusted coefficient of determination (Adj. R 2 ) and root mean square error.
Results:The AFMY ranges from 127.09 kg (first fortnight) to 110.04 kg (last fortnight) with peak fortnight yield of 189.51 kg and peak period at fourth fortnight. Predicted peak yield by different models ranges from 182.7 to 190.2 kg. The herd average milk yield was predicted with a high degree of accuracy (Adj. R 2 >92%) by all models with the maximum accuracy (Adj. R 2 =99.20%) obtained by ME model followed by MG (Adj. R 2 =98.8%) and WK model (Adj. R 2 =96.0%).
Conclusion:The ME model provided best fit for FMY data in Frieswal cattle followed by WK and MG model, whereas WD model fitted least.
“…Equations that describe milk production in time can be very useful in genetic breeding programmes, herd nutritional management, and decision making on the culling of cows and milk production simulation systems. The lactation curve is also important because its wide characterization of production throughout lactation allows estimation of peak yield (PY), days in milk (DIM) and lactation persistency (Ferreira & Bearzoti 2003). Furthermore, advances in genetic selection and husbandry practice have made today's dairy cattle quite different from those of only 10 years ago, and are likely to have affected the shape of the lactation curve of dairy cattle as well as milk yield (MY).…”
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.
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