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ANIMAL GENETICS |
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* Norsvin, NO-2304 Hamar, Norway;
and
Department of Animal and Aquacultural Sciences, Agricultural University of Norway, NO-1432 Aas, Norway; and
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Department of Animal and Dairy Science, University of Georgia, Athens 30606
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Key Words: Bayesian Analysis • Correlation • Heritability • Pigs • Reproduction • Threshold Models
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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; Hermesch et al., 2000; Noguera et al., 2002), indicating that different parities should be treated as different traits. In Norwegian Landrace (NL), as in other breeds, litter size has been the only reproductive trait of the sow included in the breeding goal and analyzed by a repeatability model. Among other traits, age at puberty and weaning-to-insemination interval influence the sow’s reproductive efficiency. These latter traits have revealed genetic variation in several studies (Rydhmer, 1993; ten Napel et al., 1995; Bidanel et al., 1996); however, multivariate analyses over parities are rare, although Hanenberg et al. (2001) performed multivariate analyses within each reproduction trait. A thorough understanding of the genetic relationships between these traits is crucial when designing a breeding program, especially in a prolific breed like NL, where potential antagonistic relations are more likely to be expressed since fitness components often show internal negative genetic correlations (Beilharz et al., 1993). The aim of this study was to estimate genetic parameters for traits affecting the sow’s contribution to reproductive efficiency and to quantify possible antagonistic genetic correlations.
Threshold models have been shown to be advantageous in simulation studies when categorical data were analyzed using an animal model, the number of categories is small, and the frequency is low (Meijering and Gianola, 1985; Hoeschele, 1988; Meuwissen et al., 1995). A mixed linear and a joint linear threshold animal model were therefore used to estimate variance components since return rate had a binary response.
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Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Reproductive Data
Data on purebred NL sows born between January 1990 and January 2000 were sampled from the nucleus and multiplying herds as recorded in the national recording scheme. Preliminary analysis showed that age at first farrowing was too dependent on age at first service to be included in the multitrait analysis (rg = 0.98). Age at first service was thereby kept in the analysis because it is available earlier in the sow’s life than age at first farrowing.
The following traits were extracted: age at first service (AFS); return rate of gilts (RRg); number of live-born pigs in first litter (NBA1); interval from weaning to first service after first litter (WTS1); return rate after first litter (RR1); number of live-born pigs in second litter (NBA2); and interval from weaning to first service after second litter (WTS2). Individual records were set to a missing value when not observed within intervals: 120 to 500 d for AFS, 1 to 50 d for WTS1 and WTS2, and 0 to 22 piglets for NBA1 and NBA2. Before analysis, a logarithmic transformation was performed for intervals of 6 d and more for both WTS1 and WTS2, according to ten Napel et al. (1995):
 | [1] |
The trait RRg was defined as a binary trait based on whether the gilt was reinseminated between 6 and 100 d after the first service or whether the gilt was culled within 130 d after first service due to not being pregnant. The trait RR1 was recorded in a similar way considering service and culling after weaning the first litter. Some gilts that were sold after service, but before farrowing, from nucleus to multiplying herds lost their identity because some managers of multiplying herds did not report their former identification to the breeding association. These gilts were sold with a "guaranteed pregnancy"; they are therefore treated as not having a return. It was not possible to follow performance after RRg for all gilts. Descriptive statistics for the reproductive traits are given in Table 1.
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Statistical Analyses and Computations
Initially, fixed effects and covariates with significant effects (P < 0.05) were examined by ordinary least squares in univariate analyses by the use of the GLM procedures of SAS (SAS Inst., Inc., Cary, NC). For each trait, the following fixed effects were tested: litter breed denoted either purebred Landrace or Landrace x Yorkshire litter; parity of dam referred to the parity in which the individual was born (1, 2, 
3); double insemination was defined as 0 or 1 (1 if a new insemination occurred within 2 d after the first insemination); mating type referred to natural mating or professional- or owner-performed AI; and lactation length referred to days from farrowing to weaning. A contemporary herd-year-season group was constructed for all traits except for RRg and RR1. Due to the relatively small herd sizes, the season was set to four levels for AFS and NBA1 (January to March, April to June, July to September, and October to December) and to two levels for NBA2, WTS1, and WTS2 (April to September, October to March). For RRg and RR1, herd-year effect was a contemporary group and season was included as a separate fixed effect with four levels. This was done to avoid extreme case problems associated with the threshold model. Having both possible responses within each contemporary group ensures avoiding extreme case problems. The overall minimal number of observations within each effect was set to three. The model used for the different traits and number of levels associated with each effect is summarized in Table 2.
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Two different multitrait model approaches were used: a mixed linear model and a joint linear-threshold model. In the first approach, a mixed linear model was used on all the traits, ignoring the binary nature of the response in RRg and RR1. In the second approach, the threshold model was used for RRg and RR1, whereas the remaining traits (AFS, NBA1, NBA2, WTS1, and WTS2) were analyzed using linear models. The threshold model postulates an underlying continuous random variable, liability (
), such that an observed binary response takes the value 1 if is larger than a fixed threshold (
), and 0 otherwise. Given the mean and variance, liabilities were assumed to be normally distributed. Arbitrary values were set to = 0 and 
2e = 1 to overcome the unidentifiability of the threshold model.
For both approaches, the model can be expressed in the following matrix notation:
 | [2] |
where y was the vector representing the phenotypic observations for continuous traits and liabilities for the two binary responses. The vector b includes the fixed effects discussed earlier, a is the vector of additive genetic effects, and e is the vector of residual effects. Incidence matrices X and Z have the appropriate dimensions. A Bayesian implementation via Gibbs sampling was adopted. Conditionally on the position parameter vector, = (b',a'), and the residual (co)variance matrix, R, the observed responses and the liabilities were assumed to be normally distributed:
 | [3] |
where I is a 7 x 7 matrix:
 | [4] |
and 2eAFS, 2eRRg, 2eRR1, 2eNBA1, 2eNBA2, 2eWTS1, and 2eWTS2, were the residual variances for AFS, RRg, RR1, NBA1, NBA2, WTS1, and WTS2. Variances 2eRRg, and 2eRR1 were set to 1 for the linear threshold model approach.
A multivariate normal distribution with zero mean and a large variance (to convey little belief a prior) was assumed as prior for the vector b:
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The classical multivariate normal distributions were assumed as prior for direct additive effects:
 | [6] |
where G was a 7 x 7 (co)variance matrix of direct additive effects analogous to R, and A is a matrix of additive genetic relationship.
For all parameters included in the dispersion matrices R and G, uniform bounded priors were assumed.
The joint posterior density is obtained as the product of densities in Eq. [3] to [6],
 | [7] |
defined only within the boundary of the bounded priors for the dispersion parameters.
Implementation
For the mixed linear model, all conditional posterior distributions were in closed form and its implementation was straightforward. Using the linear threshold model, the joint posterior distribution in Eq. [7] was augmented with the liabilities described by Albert and Chip (1993) and Sorensen et al. (1995). The resulting conditional distributions were in closed form, being truncated normal for the liabilities, normal for the position parameters, and scaled-inverted Wishart distributions for the dispersion parameters.
In a Bayesian joint analysis of several binary and continuous responses using a threshold model, the major problem resides in the sampling of the residual (co)-variances matrix as a result of the fixation of some of the diagonal elements of the matrix to overcome the unidentifiability problem of the model. Hence, several alternative sampling techniques have been proposed based on the partition of the residual (co)variances matrix (Korsgaard et al., 1999). Although these methods are theoretically sound, some computational and implementation problems can emerge, especially with large numbers of traits. The method proposed by Rekaya and Averill (2003) was used in this study. It consists in working with the unidentifiable threshold model. Once draws from the unidentifiable model are obtained, they are transformed to the identifiable scale using the square root of the diagonal elements of the unidentifiable residual variance matrix. Mathematically, if 
is the residual variance covariance matrix of the unidentifiable model, the matrix R (with fixed diagonal elements corresponding to the binary traits fixed to 1) is easily obtained by
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where D = {d1, d2, ..., d7}, with di = 1 if the ith trait is continuous and di = the square root of the ith element of the matrix if the trait is binary.
Convergence diagnostics were assessed using the method of Raftery and Lewis (1992) as implemented in the CODA software (Best et al., 1995). The required length of the burn-in period was always less then 3,759 iterations in both analyses for all parameters. Using the diagnostics plus visual inspections of trace plots, it was decided to run a total chain length of 70,000 iterations of the Gibbs sampler after a burn-in of 5,000 iterations. The latter 70,000 iterations were retained without thinning for post-Gibbs analysis.
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Results |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Crossbred litters gave more live-born piglets than did purebred litters. The effect of litter breed on NBA was higher in the first parity than in the second parity (0.38 vs. 0.15). Crossbred litters also influenced the WTS interval, with an estimated effect of a 0.5 d shorter interval after first parity and 0.82 d shorter interval after second parity if the sow had nursed a crossbred litter. Owner-performed AI gave more live born piglets than professionally performed AI in both first and second parity (0.35 and 0.26), and the estimated effect of double insemination on NBA1 and NBA2 was 0.4 piglets. Age at first service decreased with increased parity in which the sow was born (PD = 2, –2.66 d; PD = 3, –3.54 d).
Variance Components and Heritabilities
A summary of the posterior distributions for the additive genetic variances and heritabilities estimated using the mixed linear model and the joint linear threshold model are presented in Table 3. The estimated variance components from the two different models were quite similar. The highest heritability was estimated for AFS, followed by NBA2 and NBA1. The lowest heritability was estimated for RRg, RR1, and WTS2. There was a tendency for estimated heritabilities for the two binary traits to be higher using the joint linear threshold model, but the estimated heritabilities were still quite low. The Monte Carlo error for heritabilities ranged from 5.5 x 10–5 to 2.9 x 10–4, indicating that the estimates are quite accurate.
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Posterior means and standard deviations of estimated genetic and residual correlations using the mixed linear model are presented in Table 4 and using the joint linear threshold model in Table 5. The estimated correlations obtained using the two different approaches were quite similar between several traits, but with a clear tendency of being highest using the joint linear threshold approach.
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The estimated genetic correlations between parities were highest between NBA, followed by WTS and RR, all being highest using the joint linear threshold model approach. The Monte Carlo error for genetic correlations ranged from 9.9 x 10–5 to 1.0 x 10–4.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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; Hoeschele, 1988). The present study is unique in that an entire breeding population was used over a 10-yr period and also because the use of AI was as high as 96%. Such a high use of AI of boars from one AI station ensures good genetic linkage between the different herds. Because the breeding company is controlling the national recording scheme as well the only AI station in Norway, the use of unusual fixed effects was possible (e.g., double insemination and mating type). This might result in somewhat higher estimated genetic (co)variances than in other similar studies. Problems related to selection bias are expected to be minimal because selection was performed partly from the information included in the estimation. Litter size accounted for 29% of the annual genetic gain in the last part of the period (our unpublished data).
The heritabilities for NBA1 and NBA in later parities (i.e., using repeatability models for second and later parities) were 0.11 and 0.10, respectively, as summarized by Peskovicova et al. (2002). The high posterior density 95% confidence intervals from both approaches have a tendency of being somewhat higher in the present study. The weaning-to-service interval has been thoroughly studied by ten Napel and de Vries (1994) and ten Napel et al. (1995, 1998), analyzing data from a selection experiment for reduced WTS. The posterior heritability estimate for WTS1 agrees with the average heritability estimates reported to be close to 0.1 in a review by Rydhmer (2000), but the posterior estimates for WTS2 were somewhat lower. Hanenberg et al. (2001) reported a decrease in heritability for WTS for later parities, although the decrease was not observed until after the third parity. The maternal heritability of conception rate, or return rate, has rarely been estimated in sows, but based on the present study and the study by Varona and Noguera (2001), it seems to be low. The paternal heritability of conception rate was estimated by Varona and Noguera (2001) to be almost as high as the maternal heritability. In the present study, including the paternal genetic effect was not attempted. Hanenberg et al. (2001) estimated a maternal heritability of whether the sow farrowed after first insemination in the first two parities to be 0.02 and 0.01, respectively, using a linear animal model. Brandt and Grandjot (1998) used a similar definition and estimated a heritability of 0.03 over parities. Similar heritabilities have also been estimated in dairy cattle (Pryce et al., 1998).
Neither the nucleus nor the multiplying herds have records for time of first estrus; however, AFS is a practical way of analyzing field data when age at puberty is not recorded and AFS has been used in genetic analysis of sows reproductive age (Hanenberg et al., 2001), resulting in similar estimates to those in this study. Age at first farrowing has been used as a measure of reproductive efficiency (Rydhmer et al., 1995). It includes age at first estrus/service, conception rate, and gestation length. Preliminary analysis in this study showed that AFF was too dependent on AFS to be included in the multitrait analysis (rg = 0.98), supporting the fact that genetic variation in AFS probably constitutes a large part of the genetic variation in AFF. Age at first service was therefore kept in the analysis because it is available earlier in the sow’s life. The genetic variation in gestation length is small, although a moderate part of it can be explained through genetic differences (h2 of approximately 0.30; Hanenberg et al., 2001), decreasing the importance of gestation length as a potential selection candidate to improve the efficiency of the sow per time unit. In Norway, weaning before 35 d is prohibited; therefore, decreasing the lactation period to increase the efficiency of the sow per time unit is not an issue. Therefore, AFS and WTS are time periods that are potential candidates to improving the efficiency of the sow per time unit.
Nonetheless, this study shows that selection for decreased AFS will increase the gilts probability to return and also decrease the number of live-born piglets in the first parity. An antagonistic genetic correlation between AFS and (non)return rate has been estimated in dairy cattle (Pryce et al., 1998). One possible explanation in pigs may be that gilts that are bred at a lower proportion of their mature size are challenged simultaneously with the drive to grow, support pregnancy, etc. Through efficient breeding programs, the mature size of pigs has increased approximately 30% over the last 20 yr (Whittemore, 1994). The genetic correlations between the sow’s age at first service and later events (AFS-RR1 and AFS-NBA2) are all weaker. This indicates that decreasing AFS through selection will not have such an effect on these latter traits, as it seems to have on RRg and NBA1. Again, a biological explanation could be that the sow then will be older and closer to her adult weight, consequently using fewer resources for growth, etc.
When uterus capacity and ovulation rate are unbalanced, selection for litter size puts the most emphasis on the limiting traits (Bennett and Leymaster, 1990). Uterine capacity is an important component of the variability in litter size; however, ovulation rate has shown to be the more limiting component (Bennett and Leymaster, 1989). Selection for litter size is associated with an increase in both ovulation rate and uterine capacity. As ovulation rate increases, litter size will increase until it reaches a plateau where uterine capacity becomes the limiting factor (Leymaster and Johnson, 1994). The results from this present study indicate that selection for increased litter size will reduce the probability of a return. When fewer than four or five embryos are present at d 12 in the uterus, the sow returns to heat after a normal 21-d interval (Dziuk, 1985). When ovulation rate is increased, the proportion of sows having fewer embryos than this limit would decrease. Based on the knowledge that uterine capacity has a genetic component that is affected by selection for litter size, the probability of a return might also be decreased due to improved uterine capacity/reduced fetal mortality when selecting for litter size.
The estimated genetic correlation between RR and WTS interval implies that selection toward a shorter interval will decrease the probability of the gilt/sow being reinseminated or culled due to returning to estrus. Efficient sows that rebreed within a normal interval are more likely not to have problems with ovulation or fetal mortality, which again would lead to a new estrus.
The positive genetic correlations between AFS and WTS1/WTS2 are in agreement with the findings of Hanenberg et al. (2001), confirming that selection for a decreased age at first service will have a favorable effect on the interval from weaning to service. The genetic effect in this study is strongest on the interval after the second parity. Again, the conclusion can be drawn that the sow’s resource situation is generally more severe in primiparous sows than in sows ending their second parity. It should be mentioned that the average AFS in this study was almost 15 d shorter than that in the data used by Hannenberg et al. (2001). In a study by Sterning et al. (1998) on 436 Swedish Yorkshire sows, gilts expressing late puberty had greater litter weight gain and also greater weight loss during lactation than gilts expressing early puberty. They also concluded that sows that were younger at puberty had shorter WTS1 interval and better estrous symptoms after the first parity than sows that were older at puberty.
Tantasuparuk et al. (2001b) argued that phenotypically, WTS interval of primiparous sows could be used as a predictor of the sow’s longevity and total piglet production. A greater weight loss during lactation could delay the return to estrus after weaning (Sterning et al., 1990; Tantasuparuk et al., 2001a). In a tropical climate with somewhat restrictive feeding, a larger number of live-born piglets, a higher litter birth weight, a larger number of piglets weaned, or a higher litter weaning weight caused a higher relative weight loss of the primiparous sow (Tantasuparuk et al., 2001a). Other trials have also revealed that relative weight gain is influenced by the number of piglets nursed (Knudson et al., 1987). Cameron et al. (2002) argued that selection for reproduction and leanness without increasing lactation feed intake would likely result in a larger proportion of young sows consuming a insufficient amount of feed to adequately support lactation. This could lead to increased losses of BW and fat content, probably resulting in more culling of sows due to reproductive failure and a decreased lifetime performance (Eissen et al., 2000).
The present study does not support these antagonistic genetic correlations between NBA and WTS because the genetic correlations were estimated to be close to zero. A possible explanation might be that as NL gilts and sows have a sufficiently high appetite to avoid weight loss, there is consequently no effect on estrus. Unpublished analyses (B. Holm) estimated a positive genetic correlation between individual feed consumption and NBA1 and NBA2 (i.e., selection for increased NBA would increase the feed consumption). Also, in the selection experiment for decreased WTS by ten Napel et al. (1998), the conclusion was that correlated responses due the selection were small and depended highly on the environment in which the population is selected. Another issue is whether selection for litter size at the time period in question is changing ovulation rate or uterine capacity. The genetic correlation between litter size and other reproductive traits might depend on which of these components are most affected.
Based on the results of present study, selection for most of the analyzed traits will more or less affect other traits contributing to the efficiency of the sow per time unit. It also seems likely that litter size in the first two parities in NL is controlled by the same genes to a higher degree than other breeds (Roehe and Kennedy, 1995; Hermesch et al., 2000; Noguera et al., 2002). However, litter size in succeeding parities should be regarded as different traits since the variance is not equal and the genetic correlation is different from one. Potential selection candidates to include in a fertility index in NL would be AFS, NBA1, NBA2, and WTS1. The return rate trait can be excluded due to the low heritability and because the genetic correlation to NBA and WTS are favorable. Excluding return rate also avoids the problem with including binary traits in an ongoing breeding program.
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Implications |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Footnotes |
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2 Correspondence: P.O. Box 504 (phone: 476-494-8042; fax: 476-494-7960; e-mail: bjarne.holm{at}iha.nlh.no).
Received for publication June 29, 2004. Accepted for publication September 29, 2004.
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Literature Cited |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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This article has been cited by other articles:
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T. Serenius and K. J. Stalder Selection for sow longevity J Anim Sci, April 1, 2006; 84(13_suppl): E166 - E. [Abstract] [Full Text] [PDF]
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) and heritability (h2)