Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

Ferreira, Abilio Galvão Trindade; Henrique, Douglas Sampaio; Vieira, Ricardo Augusto Mendonça; Maeda, Emilyn Midori; Valotto, Altair Antonio

doi:10.1590/0001-3765201520130514

Cited by 14 publications

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References 20 publications

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“…The best fit due to gamma-type function model was reported by Boujenane [ 14 ] in Moroccan Holstein-Friesian dairy cows and Jingar et al [ 12 ] in Karan Fries (crossbred) cows. The superiority in variability explained by gamma-type function in multiparous (second or more lactations) cows was in agreement with findings of previous studies [ 18 , 19 ] but contrast with reports of Koçak and Ekiz [ 20 ] in Holstein cows and Dohare et al [ 21 ] in Frieswal cows (62% Friesian and 38% Sahiwal inheritance). However, lowest adjusted R 2 value and highest values of RMSE, AIC and BIC were observed for quadratic model fitting, which in accordance with reports of Cilek and Keskin [ 22 ] who fitted gamma-type function, mixed log, quadratic model, cubic and exponential and polynomial regression model to lactation curve of Simmental cows.…”

Section: Resultssupporting

confidence: 92%

Non-linear modelling to describe lactation curve in Gir crossbred cows

Bangar

Verma

2017

J Anim Sci Technol

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BackgroundThe modelling of lactation curve provides guidelines in formulating farm managerial practices in dairy cows. The aim of the present study was to determine the suitable non-linear model which most accurately fitted to lactation curves of five lactations in 134 Gir crossbred cows reared in Research-Cum-Development Project (RCDP) on Cattle farm, MPKV (Maharashtra). Four models viz. gamma-type function, quadratic model, mixed log function and Wilmink model were fitted to each lactation separately and then compared on the basis of goodness of fit measures viz. adjusted R2, root mean square error (RMSE), Akaike’s Informaion Criteria (AIC) and Bayesian Information Criteria (BIC).ResultsIn general, highest milk yield was observed in fourth lactation whereas it was lowest in first lactation. Among the models investigated, mixed log function and gamma-type function provided best fit of the lactation curve of first and remaining lactations, respectively. Quadratic model gave least fit to lactation curve in almost all lactations. Peak yield was observed as highest and lowest in fourth and first lactation, respectively. Further, first lactation showed highest persistency but relatively higher time to achieve peak yield than other lactations.ConclusionLactation curve modelling using gamma-type function may be helpful to setting the management strategies at farm level, however, modelling must be optimized regularly before implementing them to enhance productivity in Gir crossbred cows.

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Section: Resultssupporting

confidence: 92%

Non-linear modelling to describe lactation curve in Gir crossbred cows

Bangar

Verma

2017

J Anim Sci Technol

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“…They concluded that the Wood model was close to the actual data in predicting peak yield and peak time. Also, Ferreira et al [1] showed that the Wood model compared to the Brody as well as the Dijkstra and Pollott models had the best fit (also according to AIC and R 2 values). Karangelil et al [3] analysed lactation curves in Chios sheep milked with an AMS.…”

Section: Resultsmentioning

confidence: 99%

“…The AMS provides data daily while test-day milkings record milk and milking parameters once a month. The literature shows that curves constructed based on test-day data are often modelled with the use of the following functions: Wilmink, Wood, Ali-Schaeffer, Brody, Pollott, Dijkstra, Legendre polynomials [1][2][3][4][5][6]. Ordinarily, in dairy production milkings, recording systems are based on test-day records [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Rowlands et al [6] compared peak days for primiparas and multiparas, reporting that primiparas reached lactation peak in the 10th week and multiparas in the 7th. Ferreira et al [1], who used different models to fit lactation curves for Holstein cows, reported that the Wood model (for the 75% quartile) estimated the peak day to be on the 68th day in the first lactation and 46th in the second. Similar to the results from the present study, the MY on the peak day was higher during the second lactation (28.18 kg in the 1st and 34.11 kg in the 2nd lactation).…”

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confidence: 99%

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Comparison of the fit of automatic milking system and test-day records with the use of lactation curves

Sitkowska

Kolenda

Piwczyński

2020

Asian-Australas J Anim Sci

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Objective: The aim of the paper was to compare the fit of data derived from daily automatic milking systems (AMS) and monthly test-day records with the use of lactation curves; data was analysed separately for primiparas and multiparas.Methods: The study was carried out on three Polish Holstein-Friesians (PHF) dairy herds. The farms were equipped with an automatic milking system which provided information on milking performance throughout lactation. Once a month cows were also subjected to test-day milkings (method A4). Most studies described in the literature are based on test-day data; therefore, we aimed to compare models based on both test-day and AMS data to determine which mathematical model (Wood or Wilmink) would be the better fit.Results: Results show that lactation curves constructed from data derived from the AMS were better adjusted to the actual milk yield (MY) data regardless of the lactation number and model. Also, we found that the Wilmink model may be a better fit for modelling the lactation curve of PHF cows milked by an AMS as it had the lowest values of Akaike information criterion, Bayesian information criterion, mean square error, the highest coefficient of determination values, and was more accurate in estimating MY than the Wood model. Although both models underestimated peak MY, mean, and total MY, the Wilmink model was closer to the real values.Conclusion: Models of lactation curves may have an economic impact and may be helpful in terms of herd management and decision-making as they assist in forecasting MY at any moment of lactation. Also, data obtained from modelling can help with monitoring milk performance of each cow, diet planning, as well as monitoring the health of the cow.

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“…Among them, we can list some models that fitted lactation profiles adequately (Ferreira et al, 2015), i.e., the models proposed by Brody et al (1924), Wood (1967), and Dijkstra et al (1997), and we suggest the Gamma probability density function as a generalized form of Wood's model.…”

Section: Introductionmentioning

confidence: 99%

The geometry of the lactation curve based on Wood's equation: a two-step prediction

Oliveira

Sant’Anna

Lourenço

et al. 2020

Revista Brasileira De Zootecnia

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-Lactation records from cows of the southwestern Paraná state, Brazil, form the dataset of this study. We applied the information-theoretic approach to evaluate the ability of the nonlinear Wood, Brody, Dijkstra, and Gamma functions to fit to these data by employing a two-step technique based on nonlinear mixed-effects models and generalized linear mixed-effects models. Wood's equation was fitted with the combination of a first-order autoregressive correlation structure and a variance function to account for heteroscedasticity. This version was the best choice to mimic lactation records. Some geometric attributes of Wood's model were deduced, mainly the ascending specific rate from parturition to peak milk yield and the descending specific rate as a measure of the lactation persistence of the milk yield at peak production. Breed and parity order of the cows were assumed as fixed effects to obtain a reliable model fitting process. Regardless of breed, first-order parity cows had greater persistency than their older counterparts, and the greater the ascending rate of milk yield from the parturition to the peak, the sharper the decrease in milk yield post-peak; therefore, the rates (absolute values) of ascending and descending phases correlated positively. Nonetheless, the actual estimated values of the descending phase rates are negative. Wood's equation was flexible enough to mimic either concave-and convex-shaped lactation profiles. The correlations between both peak milk yield and random estimates for β with total milk yield per lactation were positive. However, peak milk yield might not be the only variable used for ranking cows; the total milk yield integrates all information of the lactation profile through the estimated parameters of Wood's equation.

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Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

Cited by 14 publications

References 20 publications

Non-linear modelling to describe lactation curve in Gir crossbred cows

Non-linear modelling to describe lactation curve in Gir crossbred cows

Comparison of the fit of automatic milking system and test-day records with the use of lactation curves

The geometry of the lactation curve based on Wood's equation: a two-step prediction

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