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Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, N-1432 Å s, Norway
Corresponding author: J. Ødegård; e-mail: jorgen.odegard{at}umb.no.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: clinical mastitis • dairy cattle • random regression model • somatic cell score
Abbreviation key: CM = clinical mastitis, DD = mean daughter deviation, LSCS = lactation mean SCS, RRC = random regression coefficient, RRM = random regression model.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Using an RRM, multiple random regression coefficients (RRC) are calculated per animal based on polynomials, which are functions of DIM. From the RRC, several different selection criteria can be calculated, such as PTA for specific DIM, weighted combinations of PTA at different DIM, and average PTA in a defined interval of lactation, or can be based on shape parameters for the trajectory of PTA by DIM. Currently, in some countries, EBV for SCS are calculated as the average of test-day EBV during the entire lactation (http://www.interbull.slu.se).
The different selection criteria can be compared based on their ability to predict incidence of mastitis in future daughters. This ability can be estimated by correlating the various selection criteria, predicted from first-crop daughters, with mean daughter deviations (DD) for clinical mastitis (CM) in second-crop daughters (Ødegård et al., 2003c). The criterion with the highest correlation to DD for CM is expected to have the highest predictive ability, being proportional to accuracy of selection. Accuracy of selection also depends on data structure, with number of first-crop daughters per sire as the single most important factor. In Norway, the number of first-crop daughters per sire is large (averaging 261 in this data set). The accuracies of selection in cross-sectional and RRM may be affected differently by changes in data structure. Thus, the aim of this study was to compare various selection criteria for SCS, computed from RRM and a cross-sectional model, for large and small first-crop daughter groups.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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) was extracted from a data set described by Ødegård et al. (2003b). Cows born <6 yr after their respective sires were defined as first-crop. Only daughters of the 2043 Norwegian Red sires progeny tested in the period from 1978 through 1995 were included. Records were restricted to those with SCC values between 5000 and 6,400,000 cells/mL in the period from 6 to 305 DIM. The SCS was defined as the natural logarithm of (SCC/mL) x 10–3. In addition, a data set with reduced daughter group sizes was created by randomly excluding 75% of the herd-year classes from the complete data set. This data set had a total of 133,408 cows, corresponding to an average of 65 daughters per sire. Summary statistics for the 2 datasets are given in Table 1.
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In the analyses, PTA for SCS were based on the information that would be available at the time of selection. To avoid relatives such as granddaughters contributing to the PTA, sires were separated into 3 groups: sires born before September 14, 1979; sires born in the period from September 14, 1979 to August 31, 1985; and sires born after August 31, 1985. Accordingly, the daughters of these sires were split into 3 datasets, and transmitting abilities for each sire group were predicted from the corresponding and preceding data set(s).
The pedigree file used in genetic analysis of SCS was that described by Heringstad et al. (1999) and contained 2159 sires, of which 2043 had daughters with data. The pedigree file used in genetic analysis of CM contained 2726 sires, of which 2411 had daughters with data.
Models
Cross-sectional model for SCS.
Lactation mean SCS (LSCS) was calculated as the arithmetic mean of test-day SCS for each cow and was analyzed with the following linear sire model (Ødegård et al., 2003b):
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where
| Yijklm | = | observation of LSCS for daughter m of sire l, calving at age i, in month j, and herd-year class k;
| Ai | = | fixed effect of age i at first calving, in 15 classes, where <20 mo is the first class, >32 mo is the last class, and the other classes are in single months;
| Mj | = | fixed effect of calendar month j of first calving, in 12 classes;
| HYk | = | fixed effect of herd-year class k;
| sl | = | random effect of sire l; and
| eijklm | = | random error term.
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The variance components estimated by Ødegård et al. (2003b) for the described model were used as input parameters in this analysis. The variances for sire and residual effects were 0.023 and 0.856, respectively. The heritability of LSCS was 0.11.
RRM for SCS.
Based on test-day SCS, RRC for sires were predicted with the following linear model (Ødegård et al., 2003a):
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where
| Yijklmpq | = | observation of SCS for daughter p of sire q, with age at calving i, calving month j, herd-year class k, DIM l, and herd test-day m;
| DIMl | = | fixed effect of DIM l, in 300 classes, where 6 d is the first class and 305 d is the last class;
| htdm | = | random effect of herd test-day m;
| Z(l)n | = | terms of a Legendre polynomial of order n for DIM l, where n = {0, 1, 2, 3} for permanent environmental effects and n = {0, 1, 2} for sire effects;
| rpn | = | random regression coefficient on Z(l)n for the permanent environmental effect of cow p; and
| rqn | = | random regression coefficient on Z(l)n for the transmitting ability of sire q.
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The other effects are as defined previously for LSCS. The variance components estimated by Ødegård et al. (2003a) for the described model were used as input parameters in this analysis. Heritabilities ranged from 0.07 to 0.10.
Genetic analysis of CM.
For CM, variance components and solutions for fixed and random effects were estimated with the following linear sire model (Heringstad et al., 1999):
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where
| Yijklm | = | observation of clinical mastitis (0 = healthy, 1 = diseased) for daughter m of sire l, calving at age i, in month j, and herd-year class k and fixed and random effects were as in the model for LSCS.
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All genetic analyses were carried out using the DMU software package (Madsen and Jensen, 2000).
DD for CM
The DD for CM were defined as the average per sire of mastitis observations for second-crop daughters deviated from solutions of fixed effects. A total of 931,873 second-crop daughters of the 382 sires that had >300 second-crop daughters were included in calculation of DD. Observations from herd-year classes with only a single record were discarded.
Selection Criteria
PTA from cross-sectional model.
For a given sire q, the selection criteria from the cross-sectional model was PTA of LSCS (PTA). LSCSq
PTA at specific DIM.
For RRM, PTA for sire q at a specific DIM a was calculated using the following formula:
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PTA average for defined intervals of the lactation.
The average PTA for a sire q in an interval of the lactation from DIM a to DIM b was calculated as
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The following 4 sets of values were used for a and b: 1) 6 and 305 DIM, 2) 6 and 155 DIM, 3) 155 and 305 DIM, and 4) 105 and 205 DIM; generating 4 different selection criteria.
Ranking of Selection Criteria
Assuming the same selection intensity for all criteria, the correlation between selection criteria and second-crop DD for CM can be used for ranking, as it is proportional to accuracy and, hence, to expected genetic response in the desired trait (CM) (Ødegård et al., 2003c). A weighted correlation was calculated for each criterion, using the number of second-crop daughters per sire as the weight.
Direct Regression on RRC
As the different selection criteria from the RRM all are linear combinations of the RRC, a weighted (by number of second-crop daughters per sire) multiple regression model was applied to estimate the linear combination of RRC that best fitted DD of CM. However, the corresponding multiple correlation was theoretically a measure of fit rather than a measure of predictive ability and should, therefore, be regarded primarily as an upper limit of predictive ability for a selection criterion derived from the RRM.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The correlations between DD for CM and the different selection criteria are presented in Table 2. For complete daughter groups, the correlations ranged between 0.41 and 0.48. Two criteria from the RRM, PTA305 and PTA155 to 305, showed lower correlations to DD than PTA from a cross-sectional model (PTALSCS). Among all criteria, PTA30 had the highest correlation with DD, closely followed by PTA6 to 305. These criteria had correlations with DD that were from 1.7 to 1.8% higher than the correlation between DD and the cross-sectional model, and their predictive abilities were thus only slightly lower than the upper limit estimate of the multiple regression model (Table 3).
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shows the correlation between DD and sires’ PTA by DIM (6 to 305). The highest correlations were found approximately 1 mo after calving. Hence, selecting for lower SCS at this stage of lactation should have a preference. Furthermore, frequency of CM treatments was highest precisely at this stage of lactation. A plausible explanation for the results observed could be that the relationship between CM and SCS on the observable scale (direct relationship between a binary and continuous trait) influences the genetic covariance between the traits (Ødegård et al., 2004). If so, the maximum genetic covariance between the traits would be expected to coincide with the highest frequency of CM. However, this correlation also depends on accuracy of PTA.
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). As expected, the lowest correlation was found between PTA6 and PTA305, which represent the extremes of the lactation. The highest correlation was found between PTA6 to 305 and PTA105 to 205, representing overlapping intervals.
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). Theoretically, the RRM should make better use of the information contained in the data. However, when using the RRM, the number of parameters in the model increases far more (e.g., one equation per sire cross-sectionally vs. 3 equations per sire and 4 equations per cow in RRM) than the number of data points (1 vs. 4 records per cow). Consequently, RRM are probably more likely to confound effects, which will affect the predictive ability of sire effects, but not necessarily the fit of the model, as considered by Ødegård et al. (2003a). Further, problems with confounding in complex models may, in turn, result in more imprecise estimates of (co)variance components, and this problem is often aggravated because of the computational limitations in (co)variance component estimation. Thus, by reducing number of first-crop daughters per sire, the effect of possibly inaccurate (co)variance estimates and confounding of random effects (such as sire and permanent environment) becomes more severe, especially for RRM. This explains the better performance of the cross-sectional model for this data structure. However, for data sets with more records per cow and larger herd-test-day groups, the RRM may be less sensitive to changes in size of first-crop daughter groups. Reducing daughter groups also led to some re-ranking of sires and less variability among the selection criteria derived from the RRM (Table 2), which may be explained by loss of accuracy caused by a reduced number of test-day records. The recorded SCS is probably affected by unobserved cases of subclinical mastitis. Therefore, selection for reduced SCS is expected to have an effect on subclinical as well as CM. However, because of the lack of data for subclinical cases, ranking of the different selection criteria was solely based on recorded CM.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Received for publication October 11, 2004. Accepted for publication December 16, 2004.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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