Mathematical Representations of Correlations Among Yield Traits and Somatic Cell Score on Test Day

Norman, H.D.; VanRaden, P.M.; Wright, J.R.; Smith, L.A.

doi:10.3168/jds.s0022-0302(99)75466-4

Cited by 7 publications

(11 citation statements)

References 9 publications

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“…The phenotypic correlation slightly decreased for each additional day in the interval between observations. Similar results were observed by Norman et al (1999) who analyzed bovine lactations in the USA and Canada under the autoregressive structure [ar(1)].…”

Section: Resultssupporting

confidence: 73%

Milk and fat production of crossbred Holstein-Gir cows (Bos taurus taurus-Bos taurus indicus) in the agreste region of the Brazilian state of Pernambuco

et al. 2008

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The productive performance of four Holstein-Gir genetic groups (1/2H, 1/4H, 5/8H, 5/8Hinter se) and the effects of non-genetic factors on production traits was evaluated using a data set of 7,951 test-day samples collected between January 1980 and December 1999 from the Arcoverde Experimental Station in the Brazilian state of Pernambuco (Empresa Pernambucana de Pesquisa Agropecuária). The statistical model included the fixed effects of calving year (1980 to 1999) and month (January to December), genetic group of the cow, age at months of calving (33 to 190) and days in milk at each test-day. Random effects were sire, cow and residual with test-days treated as repeated records within each cow within each lactation. For the four genetic groups the milk yield (MY) means were 1/2H = 8.61 kg ± 1.16 kg, 1/4H = 5.34 kg ± 0.46 kg, 5/8H = 7.42 kg ± 0.39 kg and 5/8Hinter se = 5.76 kg ± 0.46 kg; the fat yield (FY) means were 1/2H = 0.375 kg ± 0.052 kg, 1/4H = 0.231 kg ± 0.026 kg, 5/8H = 0.299 kg ± 0.025 kg and 5/8Hinter se = 0.231 kg ± 0.026 kg; and the fat percentage (FP) means were 1/2H = 4.45 kg ± 0.29%, 1/4H = 4.08 kg ± 0.12%, 5/8H = 3.87 kg ± 0.10% and 5/8Hinter se = 3.89 kg ± 0.12%. Phenotypic correlations between tests were MY = 0.97, FY = 0.94 and FP = 0.98. The best productive performance was for the 1/2H group, followed by the 5/8H group. The performance of the synthetic group was substantially below the performance of the 5/8H group.

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Section: Resultssupporting

confidence: 73%

Milk and fat production of crossbred Holstein-Gir cows (Bos taurus taurus-Bos taurus indicus) in the agreste region of the Brazilian state of Pernambuco

et al. 2008

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“…Meyer et al (1989) reported a similar pattern for environmental correlations among TD records for milk, fat and protein yields. Norman et al (1999) reported comparable findings with smaller correlations with increased number of intervals between TD records. They also reported the smallest correlations were for pairs of TD records at early and late stages of lactation.…”

Section: Covariance Structuressupporting

confidence: 72%

“…The estimate of the total environmental covariance between any 2 records cannot drop below the estimate of permanent environmental variance. Norman et al (1999) found that correlations among TD records for milk yield traits and SCS were well modeled with the autoregressive correlation structure. They compared the AR(1) with other structures such as identity (I), intercept (J), and heterogeneous variances at the beginning, middle, or late stages of lactation among other structures.…”

Section: Covariance Structuresmentioning

confidence: 97%

Evaluation of Autoregressive Covariance Structures for Test-Day Records of Holstein Cows: Estimates of Parameters

Sawalha

Keown

Kachman

et al. 2005

Journal of Dairy Science

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The objective of this study was to compare test-day (TD) models with autoregressive covariance structures for the estimation of genetic and environmental components of variance for milk, fat and protein yields, and somatic cell score (SCS) in Holstein cows. Four models were compared: model I (CS model) was a simple TD repeatability animal model with compound symmetry covariance structure for environmental effects, model II (AR pe model) and model III (AR e model) had first-order autoregressive covariance structures for TD permanent or residual environmental effects, respectively, and model IV (305-d model) was a simple animal model using 305-d records. Data were 106,472 first-lactation TD records of 12,071 Holstein cows calving from 1996 through 2001. Likelihood ratio tests indicated that AR pe and AR e models fit the data significantly better than the CS model. The AR e model resulted in slightly smaller estimates of genetic variance and heritability than did the CS model. Estimates of residual variance were always smaller with the CS model than with the AR e model with the autoregressive covariance structure among TD residual effects. Estimates of heritability with different TD models were in the range of 0.06 to 0.11. The 305-d model resulted in estimates of heritability in the range of 0.11 to 0.36. The autoregressive covariance structure among TD residual effects may help to prevent bias in heritability estimates for milk, fat and protein yields, and SCS. (Key words: milk yield, test day, autoregressive covariance)Abbreviation key: AIC = Akaike information criterion, AR(1) = first-order autoregressive, CS = compound symmetry, TD = test day.

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“…Methods currently used to predict total lactation yields for genetic evaluation purposes are based on correlation between tests in different stages of lactation (Norman et al, 1999). Table 6 reports correlation between actual and predicted lactation yields in first parity cattle by using different number of tests available and different approaches.…”

Section: Exploring the Correlation Structure Among Test Day Records Amentioning

confidence: 99%

The mathematical description of lactation curves in dairy cattle

Macciotta

Dimauro²,

Rassu³

et al. 2011

Italian Journal of Animal Science

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This review gives an overview of the mathematical modelling of lactation curves in dairy cattle. Over the last ninety years, the development of this field of study has followed the main requirements of the dairy cattle industry. Non-linear parametric functions have represented the preferred tools for modelling average curves of homogeneous groups of animals, with the main aim of predicting yields for management purposes. The increased availability of records per individual lactations and the genetic evaluation based on test day records has shifted the interest of modellers towards more flexible and general linear functions, as polynomials or splines. Thus the main interest of modelling is no longer the reconstruction of the general pattern of the phenomenon but the fitting of individual deviations from an average curve. Other specific approaches based on the modelling of the correlation structure of test day records within lactation, such as mixed linear models or principal component analysis, have been used to test the statistical significance of fixed effects in dairy experiments or to create new variables expressing main lactation curve traits. The adequacy of a model is not an absolute requisite, because it has to be assessed according to the specific purpose it is used for. Occurrence of extended lactations and of new productive and functional traits to be described and the increase of records coming from automatic milking systems likely will represent some of the future challenges for the mathematical modelling of the lactation curve in dairy cattle

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Mathematical Representations of Correlations Among Yield Traits and Somatic Cell Score on Test Day

Cited by 7 publications

References 9 publications

Milk and fat production of crossbred Holstein-Gir cows (Bos taurus taurus-Bos taurus indicus) in the agreste region of the Brazilian state of Pernambuco

Milk and fat production of crossbred Holstein-Gir cows (Bos taurus taurus-Bos taurus indicus) in the agreste region of the Brazilian state of Pernambuco

Evaluation of Autoregressive Covariance Structures for Test-Day Records of Holstein Cows: Estimates of Parameters

The mathematical description of lactation curves in dairy cattle

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