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1 Danish Institute of Agricultural Sciences, Department of Animal Breeding and Genetics, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
2 Danish Agricultural Advisory Service, National Centre, Danish Cattle Federation, Udkærsvej 15, Skejby, 8200 Aarhus N, Denmark
3 The Royal Veterinary and Agricultural University, Department of Animal Science and Animal Health, Grønnogardsvej 2, DK-1870, Frederiksberg C, Denmark
4 University of Georgia, Department of Animal and Dairy Science, 354, Animal and Dairy Science Complex, Athens 30602
Corresponding author: M. Hansen; e-mail: mxh{at}landscentret.dk.
| ABSTRACT |
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Key Words: stillbirth calving ease calf size genetic trend
Abbreviation key: CVM = complex vertebral malformation, HF = Holstein-Friesian, MAP = maximum a posteriori, MGS = maternal grandsire, ODBW = original Danish Black and White
| INTRODUCTION |
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The rate of stillbirth is highest for first-calving cows, partly because of a disproportion between the size of the calf and the size of the pelvic area (fetopelvic-complex), which causes a difficult calving (Meijering, 1984). Therefore, it is relevant to examine stillbirth, calving difficulty, and calf size, which have been recorded on Danish dairy farms since 1985. By including calving difficulty and calf size, it is possible to explain whether the increase in stillbirths is associated with an increase in calving difficulties and calf size. Calving difficulties are, from an economic point of view, also important, as they are associated with stillbirths, veterinary assistance, and additional work. They also reduce the dams milk production and fertility and increase the risk of culling (Dematawewa and Berger, 1997).
Linear models are currently applied for the national genetic evaluation of stillbirth and calving difficulty in Denmark (Danish Cattle Federation, 2003). A threshold model (Gianola and Foulley, 1983) may be a more valid model because it takes into account the categorical nature of these traits. However, high correlations (>0.92) between PTA from a linear and a threshold model have been found (Weller et al., 1988; Hagger and Hofer 1990). Threshold models have been implemented for official genetic evaluations of calving ease in France (Ducrocq, 2000) and in the US (Wiggans et al., 2003), but none of the countries that have an official genetic evaluation for stillbirth are currently using threshold models (Pasman and Reinhardt, 2002).
The major objective of this study was to estimate the genetic trend of stillbirth for first-calving Danish Holstein cows using a threshold model. The hypothesis was that an unfavorable genetic trend for stillbirth existed. As stillbirth is genetically associated with calving difficulty and calf size (Meijering, 1984; Hansen et al., 2003); the genetic trends of these traits were also computed to accomplish a better understanding of the stillbirth trend. The second objective was to compare PTA of stillbirth from a linear model with PTA from a threshold model.
| MATERIALS AND METHODS |
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Threshold model.
In the threshold model, the observed outcome (yi) for calf i is assumed to be ordered in k categories (k = 2 for stillbirth and k = 4 for calving difficulty and calf size). We assumed an unknown liability (Ui) with k 1 unknown thresholds (t = {t1,...,tk1}), which categorized the observed outcome. The model for the liabilities in matrix notation was
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where U was a vector of liabilities, b was a vector of fixed effects, h was a vector of effects of herd-year, s was a vector of sire effects, mgs was a vector of MGS effects, and e was a vector of residuals. X, W, Z1, and Z2 were incidence matrices relating the effects to the liabilities. The effects included in b were cross-classified effects, month of birth, calving age in months, sex x year of birth, and coefficients for the covariates of breed proportions and degree of heterozygosity. For the proportion of HF genes in the calf and in the dam, the coefficients were bHF-calf and bHF-dam, and for the proportion of heterozygosity between foreign HF and ODBW in the calf and in the dam, the coefficients were bHet-calf and bHet-dam.
It was assumed that the liabilities conditional on all of the effects were independent and normally distributed:
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If a = [s mgs]', the expectation of the random effects in the model was
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with the (co)variance
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where
and A is the additive relationship matrix, which contained 19,925 animals. The additive relationship matrix was created by tracing sire and dam paths as far as possible for 8252 bulls with records as a sire or a MGS.
Dispersion parameters used in this study (Table 2
) were based on (co)variances estimated by Hansen et al. (2003, 2004). For use in this study, they were scaled to a residual variance equal to one. In all analyses, the last threshold was set to 0, and therefore t1 and t2 were estimated for calving difficulty and calf size.
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where
is the cumulative distribution function of a standard normal distribution, and xi, wi, z1i, and z2i are rows of their respective incidence matrices.
Estimates of location parameters were obtained by use of the software package cblup90iod (Misztal et al., 2002), where algorithms for the threshold models are based on Janss and Foulley (1993) and Hoeschele et al. (1995). To reduce computing time, mixed model equations were solved by iteration on data in combination with the preconditioned conjugate gradient algorithm (Tsuruta et al., 2001).
Genetic trend.
Two kinds of additive genetic trends were evaluated. The first trend was the average solutions of genetic effects for all records plotted against the calving year. This trend explains how additive genetic effects have contributed to the phenotypic trend. For each record, a direct effect was calculated as
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a maternal effect as
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and the sum of all additive genetics effect as
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where
is the sire solution for the bull in the subscript,
is the MGS solution,
is the estimate of the breed effect for the individual given in the subscript, and pHF is the proportion of HF genes in the individual given in the subscript.
The second additive genetic trend was evaluated by plotting average PTA against the birth-year of the AI bulls. For the direct trend only, bulls with >10 records as a sire were included, and for the maternal trend only, bulls with >10 records as MGS were included. The PTA of direct effects were derived as
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and the PTA of maternal effects were derived as
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where
is the solution for the bull as sire,
is the solution for the bull as MGS,
is the solution of the breed effect given in the subscript, and pHF-bull is the proportion of HF in the bull.
For both genetic trends, the average solutions in the present year (sollia) were transformed to probability solutions on the observable scale (solobs) as
![]() | ([1]) |
where
is the cumulative distribution function of a standard normal distribution, sollia(base) is the average solution in the year used as reference, and freq is the overall frequency of the trait.
By this method, the trends were presented as the change in probability of, e.g., stillbirth relative to the year of reference. Estimates of effects of breed and heterozygosity were transformed to the observable scale in a similar manner as in Eq. (1)
assuming sollia(base) was zero.
Threshold vs. linear model for stillbirth.
The evaluation of PTA for stillbirth from the threshold model was compared with PTA from a linear model containing similar effects by estimating correlations between the PTA from the 2 models for classes of bulls with different numbers of records. From the threshold model, both PTA on the liability scale and on the observable scale was used. The PTA were transformed to the observable scale as
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where PTAlia(base) is the average PTA for all bulls with records, and freq is the overall frequency of stillbirth.
The PTA of Danish AI bulls born in 1996 from the linear and the threshold model were plotted. This should visualize the difference between the 2 models for bulls with a typical progeny test for stillbirth at first calving. These bulls had, on average, 77 records (ranging from 29 to 134) as sires of cows. As a sire of calf, the bulls had on average 34 records (ranging from 11 to 69) from their test inseminations, but 15 bulls had also later records as a proven bull included.
| RESULTS |
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The regression coefficients for the degree of heterozygosity (bHet-calf and bHet-dam) were in general all small. These regression coefficients can be interpreted as the effect of animals with 100% heterozygosity (F1 cross) compared with animals with no heterozygosity (purebreds). The effect in the calf (bHet-calf) was (on the observable scale) between 0.00 and 0.01 for all traits. The maternal heterozygosity was not important for stillbirth and calf size, but the probability of a difficult calving was 0.02 lower for dams with 100% heterozygosity compared with purebred dams.
Threshold vs. Linear Model of Stillbirth
The correlations between PTA for stillbirth from the linear and the threshold model were high (0.96 to 1.00) for both direct and maternal effects (Table 4
). The correlations were generally highest for bulls with most records. The PTA from the linear model were slightly more correlated with PTA from the threshold model expressed on the observable scale than with PTA expressed on the liability scale.
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For both the threshold and the linear model, the ranking of sires was almost identical whether effects of breed and heterosis were included or excluded from the model. The correlations between PTA were all higher than 0.996 for both maternal and direct effects (results not shown).
| DISCUSSION |
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An unfavorable additive genetic trend for both the direct and maternal effect of stillbirth was found when evaluating all records from 1985 to 2002. The increase in direct effects of stillbirth was associated with an increase in direct effects of calving difficulty and especially calf size. It can be concluded that the larger calves of HF compared with ODBW have resulted in more calving difficulties and more stillbirths in the Danish Holstein population. Supporting this conclusion is the high genetic correlation (0.69 to 0.93) between direct effects of stillbirth and calving difficulty and stillbirth and calf size (Hagger and Hofer, 1990; Hansen et al., 2003).
The effect of HF additive genes in the dam was unfavorable for stillbirth but favorable for calving difficulty. This means that HF had maternal effects, which affects the survival of the calf (or fetus) negatively, but these effects were not due to increased calving difficulty. Instead, these effects may relate to a poorer environment in the uterus for the survival of the calf. Also, the total genetic change per calving year was clearly favorable for the maternal effect of calving difficulty but slightly unfavorable for the maternal effect of stillbirth. These findings are in contrast to the positive genetic association between maternal effects of stillbirth and calving difficulty (Danish Cattle Federation, 2003; Hansen et al., 2003; Steinbock et al., 2003). Future studies of factors involved in this maternal effect of stillbirth seem necessary because the causes of stillbirths not associated with calving difficulty are unknown (Meijering, 1984).
Complex vertebral malformation (CVM), which leads to abortions and stillbirth, has had a small influence on the genetic trend in stillbirth. In the data set, all sires were classified as free of CVM, possible carrier of CVM, and carrier of CVM. Less than 3% of the calves had sires with unknown status (possible carrier). The genetic trend of direct effects of all calves compared with the genetic trend of calves with a sire tested as CVM carrier is presented in Figure 6
. The genetic trend is almost identical for calves with sires tested free of CVM as the genetic trend for all of the calves. However, in the end of the period, the genetic level of calves with CVM increased. This result is apparently because the frequency of cows carrying CVM had increased, which resulted in more CVM homozygous fetuses and calves. The relatively low impact of CVM on the genetic trend can be explained by the fact that 77% of CVM homozygous fetuses were aborted before 260 d after insemination and, therefore, were not recorded as stillbirths (Nielsen et al., 2003).
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As expected from other studies of calving traits using sire MGS models (Weller et al., 1988; Hagger and Hofer, 1990), relatively small differences in PTA from the linear and the threshold model were found in this study. However, for traits with a low number of records per sire (e.g., direct effects of stillbirth and calving difficulty at first calving), the threshold model might give better prediction, as the difference between the models was largest with small progeny groups. Ramirez-Valverde et al. (2001) concluded that the linear sire MGS model performed as good as the threshold sire MGS model, but when fitting an animal model, the threshold model was superior. Therefore, the need for a genetic evaluation with a threshold model does not seem to be strong as long a sire MGS model is fitted, but when fitting an animal model, the superiority of a threshold model might be larger.
Despite small differences between PTA from the linear and the threshold sire MGS models, a notable difference in breed estimates was found in this study, which indicates that some effects might not be estimated adequately when a linear model is used for categorical traits.
When transforming estimates on the liability scale to the observed scale, a mean probability must be chosen. We decided to use the overall frequency, as this analysis is a description of the past. If the models should be used to predict future records, a more recent frequency (e.g., the last year) would be a better choice. For stillbirth, this would have resulted in a higher frequency, which would give larger differences between the PTA on the observed scale.
By including the breed effects in the model, the calves and dams were corrected for all of the additive genetic differences between the two breeds. It was possible to infer a larger part of the additive genetic effects in the calves and dams than if the breed effects were omitted. However, an animal model with genetic groups would be preferable to take account of all additive genetic effects in the individuals.
The present study ignored twins, abortions, calves with unknown sex, calves with unknown sires or MGS, and calves with privately owned service sires or MGS. Therefore, the presented stillbirth rate is not representative for the whole population. If all calvings were included, the stillbirth rate at first calving was 12% in 2002. Philipsson and Steinbock (2003) argue a stillbirth rate around 11 to 12% is alarming. Other breeds such as the Danish Red, Danish Jersey, and the Swedish Red and White have shown that it is possible to have a considerable lower stillbirth rates (5 to 6%) at first calving (Nielsen et al., 2002; Philipsson and Steinbock, 2003). Based on a considerable genetic variation of stillbirth in Holsteins (Steinbock et al., 2003; Hansen et al., 2004), it is possible to reduce the stillbirth rate by selection of sires. Today, only the maternal effects of stillbirth and calving difficulty are included in the breeding goal for Danish Holsteins. Dekkers (1994) showed that the inclusion of direct effects in the breeding goal is even more important than maternal effects. Therefore, the inclusion of direct effects of stillbirth and calving difficulty in the Danish breeding goal needs to be examined.
| CONCLUSION |
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Received for publication September 25, 2003. Accepted for publication December 17, 2003.
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