The Accuracy of Seven Mathematical Functions in Modeling Dairy Cattle Lactation Curves Based on Test-Day Records From Varying Sample Schemes

Silvestre, A.M.; Petim-Batista, F.; Colaço, Jorge

doi:10.3168/jds.s0022-0302(06)72250-0

Cited by 108 publications

(122 citation statements)

References 29 publications

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“…Results obtained in this study for individual lactations of standard length agree with previous reports for dairy cattle (Olori et al, 1999;Macciotta et al, 2005;Silvestre et al, 2006), with a better fit for polynomials (AS, LEG and SPL) compared with models with three parameters. No studies are currently available in the literature on fitting individual extended lactation curves.…”

Section: Resultssupporting

confidence: 90%

Analysis of lactation shapes in extended lactations

Steri

Dimauro

Canavesi³

et al. 2012

animal

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In order to describe the temporal evolution of milk yield (MY) and composition in extended lactations, 21 658 lactations of Italian Holstein cows were analyzed. Six empirical mathematical models currently used to fit 305 standard lactations (Wood, Wilmink, Legendre, Ali and Schaeffer, quadratic and cubic splines) and one function developed specifically for extended lactations (a modification of the Dijkstra model) were tested to identify a suitable function for describing patterns until 1000 days in milk (DIM).Comparison was performed on individual patterns and on average curves grouped according to parity (primiparous and multiparous) and lactation length (standard <305 days, and extended from 600 to 1000 days). For average patterns, polynomial models showed better fitting performances when compared with the three or four parameters models. However, LEG and spline regression, showed poor prediction ability at the extremes of the lactation trajectory. The Ali and Schaeffer polynomial and Dijkstra function were effective in modelling average curves for MY and protein percentage, whereas a reduced fitting ability was observed for fat percentage and somatic cell score. When individual patterns were fitted, polynomial models outperformed nonlinear functions. No detectable differences were observed between standard and extended patterns in the initial phase of lactation, with similar values of peak production and time at peak. A considerable difference in persistency was observed between 200 and 305 DIM. Such a difference resulted in an estimated difference between standard and extended cycle of about 7 and 9 kg/day for daily yield at 305 DIM and of 463 and 677 kg of cumulated milk production at 305 DIM for the first-and second-parity groups, respectively. For first and later lactation animals, peak yield estimates were nearly 31 and 38 kg, respectively, and occurred at around 65 and 40 days. The asymptotic level of production was around 9 kg for multiparous cows, whereas the estimate was negative for first parity.

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Section: Resultssupporting

confidence: 90%

Analysis of lactation shapes in extended lactations

Steri

Dimauro

Canavesi³

et al. 2012

animal

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“…They also noticed that the occurrence of the curves without a peak arose from the peculiar combination of TD yields and their distribution along the entire lactation. Silvestre et al (2006) confirmed that the goodness of fit of lactation models depends on data availability and structure. They stated that some models such as WIL or ALI were particularly affected by the interval between tests, mostly between calving and the first TD.…”

Section: Discussionmentioning

confidence: 58%

“…At the same time, breeders expect predictions of cumulative yield with minimum error. Some researches maintain that well-fitted lactation curves may accomplish that (Olori et al, 1999;Quinn et al, 2005;Silvestre et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Modeling lactation curves of Polish Holstein-Friesian cows. Part II: Prediction of 305-d lactation milk, fat and protein yields

Otwinowska-Mindur¹,

Ptak²,

Jagusiak³

et al. 2014

J. Anim. Feed Sci.

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“…Liu et al (2006) for milk yield and Coffey et al (2002) for the traits feed intake and energy balance). Sylvestre et al (2006) hyphothesised that this function is able to fit daily data superior than functions with less than five parameters such as Wilmink (1987), Wood (1967) or Legrende polynomials of less than four degrees. Also for modelling of feed intake and energy balance amongst others, Woodford et al (1984), de Vries et al (1999 and Collard et al (2000) used the Ali and Schaeffer function.…”

Section: Model I (Fr)mentioning

confidence: 99%

“…Wood, 1967;Grossman and Koops, 1988;Kirkpatrick et al, 1994;Jamrozik and Schaeffer, 1997;van der Werf, 2001;Sylvestre et al, 2006). Ló pez- Romero and Carabañ o (2003) noted that functions frequently used for the modelling of lactation curves are those proposed by Ali and Schaeffer (1987) or Wilmink (1987).…”

Section: Model I (Fr)mentioning

confidence: 99%

Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

Kramer

Stamer²,

Spilke

et al. 2008

Animal

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The aim of the present study was to investigate the daily measured traits milk yield, water intake and dry matter intake with fixed and random regression models added with different error covariance structures. It was analysed whether these models deliver better model fitting in contrast to conventional fixed and random regression models. Furthermore, possible autocorrelation between repeated measures was investigated. The effect of model choice on statistical inference was also tested. Data recording was performed on the Futterkamp dairy research farm of the Chamber of Agriculture of SchleswigHolstein. A dataset of about 21 000 observations from 178 Holstein cows was used. Average milk yield, water intake and dry matter intake were 34.9, 82.4 and 19.8 kg, respectively. Statistical analysis was performed using different linear mixed models. Lactation number, test day and the parameters to model the function of lactation day were included as fixed effects. Different structures were tested for the residuals; they were compared for their ability to fit the model using the likelihood ratio test, and Akaike's and Bayesian's information criteria. Different autocorrelation patterns were found. Adjacent repeated measures of daily milk yield were highest correlated (p 1 5 0.32) in contrast to measures further apart, while for water intake and dry matter intake, the measurements with a lag of two units had the highest correlations with p 2 5 0.11 and 0.12. The covariance structure of TOEPLITZ was most suitable to indicate the dependencies of the repeated measures for all traits. Generally, the most complex model, random regression with the additional covariance structure TOEPLITZ(4), provided the lowest information criteria. Furthermore, the model choice influenced the significance values of one fixed effect and therefore the general inference of the data analysis. Thus, the random regression 1 TOEPLITZ(4) model is recommended for use for the analysis of equally spaced datasets of milk yield, water intake and dry matter intake.

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The Accuracy of Seven Mathematical Functions in Modeling Dairy Cattle Lactation Curves Based on Test-Day Records From Varying Sample Schemes

Cited by 108 publications

References 29 publications

Analysis of lactation shapes in extended lactations

Analysis of lactation shapes in extended lactations

Modeling lactation curves of Polish Holstein-Friesian cows. Part II: Prediction of 305-d lactation milk, fat and protein yields

Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

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