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Multivariate analysis of litter size for multiple parities with production traits in pigs: I. Bayesian variance component estimation¹

Area de Producció Animal, Centre UdL-IRTA, Rovira Roure 177, 25198 Lleida, Spain

² Correspondence:
phone: 34-973-702576; fax: 34-973-238301; E-mail:
joseluis.noguera{at}irta.es.

	Abstract

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A total of 66,620 records from the first six parities for number of piglets born alive (NBA) from 20,120 Landrace sows and 24,426 records for weight (WT) and backfat thickness (BT) at 175 d of age were analyzed to estimate genetic parameters. The pedigree consisted of 47,186 individuals, including 392 sires and 5,394 dams. Estimates were based on marginal posterior distribution of the genetic parameters obtained using Bayesian inference implemented via the Gibbs sampling procedure with a Data Augmentation step. The posterior means and posterior standard deviation (PSD) for heritability of NBA ranged from 0.064 (PSD 0.005) in the first parity to 0.146 (PSD 0.019) in the sixth parity, always increasing with the order of the parity. The posterior means for genetic correlations of litter size between adjacent parities were, in most cases, greater than 0.80. However, genetic correlation were much lower between nonadjacent parities. For example, the genetic correlation was 0.534 (PSD 0.061) between the fourth and the sixth parity for NBA. The posterior means of heritability for WT and BT were 0.229 (PSD 0.018) and 0.350 (PSD 0.019), respectively. Posterior mean for genetic correlation between WT and BT was 0.339 (PSD 0.044). The posterior means for genetic correlation between production (WT and BT) and reproduction traits (NBA in different parities) were close to zero in most cases. Results from this study suggest that different parities should be considered as different traits. Moreover, selection for growth and backfat should result in no or very little correlated response in litter size.

Key Words: Genetic Parameters • Growth • Litter Size • Parity • Pigs

	Introduction

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Literature estimates of heritability of litter size range between 0 and 0.76 with an average of 0.10 (Rothschild and Bidanel, 1998). However, there is a controversy in the literature about considering litter size from different parities as repeated measures of the same trait (Southwood and Kennedy, 1990; See et al., 1993; Crump et al., 1997a) or different traits (Irgang et al., 1994; Roehe and Kennedy, 1995; Rydhmer et al., 1995).

Some authors have pointed out that most of the early studies were conducted with reduced data sets and with statistical approaches that could not use all the available information in an optimal way (Vangen, 1986; Haley et al., 1988; and Rothschild and Bidanel, 1998). In recent years, development of multivariate Bayesian methods (Van Tassell and Van Vleck, 1996) and the improvement in computing resources allow easier handling of large data set and models considering each parity as a different trait. These methods can provide not only estimates of the genetic parameters but a complete description of uncertainty of the estimates. Moreover, litter size traits can also be analyzed jointly with all traits included in the selection process to avoid possible consequences of selection bias (Gianola et al., 1989).

The general objective of this study was to get a new insight into the genetic relationship between different parities for the number of piglets born alive (NBA), jointly with production traits. Specific objectives were: 1) multivariate estimation of heritabilities and genetic correlations for the NBA in the first six parities and 2) multivariate estimation of genetic correlations between prolificacy in different parities and production traits (weight and backfat thickness at 175 d of age).

	Materials and Methods

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Field Data

Data from a purebred Landrace pig population were obtained from the GTEP-IRTA Information System (Noguera et al., 1992). This population is a maternal line currently selected for an index combining litter size, backfat, and growth performance. Reproduction and production records from 1988 to 1998 were analyzed. The individuals were from two selection herds with a total of approximately 1,000 sows and four multiplication herds made up of approximately 3,000 sows. Boars were kept in an artificial insemination center. In all cases, reproduction was carried out by artificial insemination, and the sows were mated twice to the same boar. In the multiplication herds, Landrace sows were crossed with Large White boars. Sows were managed in farrowing groups of 12 to 20 animals weekly. Total number of piglets born and NBA per parity were recorded. Cross-fostering within 48 h after birth was practiced to standardize litter size to no more than 10 piglets. After suckling for 23 to 28 d, piglets were allocated in pens with 12 individuals in each pen and were given ad libitum access to a pelleted diet (13.4 MJ/kg of ME, 18.3% of CP, 1.2% of lysine). At about 75 d of age, piglets were moved to a fattening building. In the selection herds, boars and gilts were performance tested. Both sexes were penned in groups of 10 to 12 animals separated by sex, and during the whole test period had ad libitum access to a cereal-based commercial diet (13.4 MJ/kg of ME, 17.5% CP, 1% lysine). Pigs tested at the same time and in the same fattening building were considered as one contemporary group (batch). Weight (WT) and backfat thickness (BT) were recorded at 175 d of age. Backfat thickness was measured by the Renco apparatus (A-mode equipment; Renco Corp., Minneapolis, MN) as the average of two ultrasonic measurements taken on each side of the spinal column, 5 cm from the mid-dorsal line at the position of the last rib.

A description of the data is presented in Tables 1 and 3. To avoid outliers, records were required to be from sows with age of farrowing between 280 and 530 d for the first parity, 433 to 684 for the second parity, 544 to 846 for the third, 693 to 990 for the fourth, 883 to 1,140 for the fifth, and 975 to 1,288 for the sixth. Records from sows with farrowing ages out of these ranges in each parity were removed. Discarded data were approximately 2% of total recorded data. In total, 66,620 reproduction records were used in the analysis for NBA, with an average number of litters per sow of 3.34. With respect to production data, 24,426 animals with WT and BT records were included, and from those, 4,797 individuals had both production and reproduction records. All ancestors genetically linked to recorded animals were included in the pedigree. The pedigree file contained 47,186 individuals, from which 392 were sires and 5,394 dams of recorded animals.

For each of the first six parities, the following model was assumed for NBA:

where

y_ijk

observation ijk for NBA,

HYS_i

fixed effect of herd-year-season i(i = 1 to 226),

AF_j

fixed effect of age of sow at farrowingj(j = 1 to 10),

u_k

breeding value of animalk,

e_ijk

random residual term.

The age of the sow at farrowing was distributed in 10 classes separately for each parity, with approximately 10% of the total of farrowings per class. Four classes were considered for each herd and year: December to February, March to May, June to August, and September to November summing up to 226 levels per parity. The breed of the service boar was accounted for implicitly by the herd-year-season effect. Lactation length and the weaning to conception interval in the preceding parity were not included in the model because previous analyses of those traits in the same population showed that the effects were nonsignificant (Babot et al., 2000). Moreover, maternal effects were not included because of the very low maternal heritability estimated for NBA in the first parity (posterior mean and posterior standard deviation estimates were 0.004 and 0.002, respectively).

For WT the model of analysis was:

where

y_ijkl

observationijkl for weight,

S_i

fixed effect of sexi(i = male or female),

B_j

fixed effect of batchj(j = 1 to 270),

_i

sex-related covariatei with age of recording (AG) corrected at 175 d of age,

c_k

random effect of birth litterk,

u_l

breeding value of animall,

e_ijkl

random residual term.

The same model was assumed for BT.

Bayesian Analysis

A Bayesian analysis was performed for the multivariate implementation of the previous models. Inference was made from the joint posterior distribution of parameters and data obtained by multiplying the likelihood by the prior distributions. The likelihood was defined as multivariate normal for observed and missing data for NBA, WT, and BT given the systematic effects for litter size (HYS, AF), WT (S, B, ) and BT (S, B, ), litter effects (c) for WT and BT, breeding values (u) for NBA, WT and BT and the residual (co)variance matrix (R).

Prior distributions for systematic effects were assumed to be uniform (U) between a range of expected values. For breeding values, prior distribution was a multivariate normal distribution with mean zero and varianceG A, whereA is the numerator relationship matrix andG is an 8 x 8 genetic relationship matrix between traits. Prior distributions for litter and residual effects were multivariate normal with mean zero and variances C IandR I, where C is a 2 x 2 (co)variance matrix between litter effects of WT and BF andR is a 8 x 8 (co)variance matrix between residuals.

Prior distributions for (co)variance components were inverted Wishart distributions (W^-1) with 10 df. This value is small in relation to the number of levels for each effect, 24,426, 47,186, and 6,820 for the genetic, residual and litter effects, respectively. They were chosen to be proper and with little weight on the posterior distribution. Its location parameters SG,SC, and SR were chosen to be consistent with the literature estimates of variance components and heritabilities (Clutter and Brascamp, 1998; Rothschild and Bidanel, 1998). Prior total variance was 7 for reproductive traits, 100 for WT, and 20 for BT. Prior heritability was 0.14 for reproductive traits, 0.20 for WT, and 0.30 for BT. Genetic and environmental correlations were assumed to be null.

The Gibbs Sampler

The Bayesian analysis was carried out with the Gibbs sampling algorithm (Geman and Geman, 1984; Gelfand and Smith, 1990) to obtain autocorrelated samples from the joint posterior density and subsequently from the marginal posterior densities of all the unknowns in the model. The Gibbs sampler is an iterative scheme drawing samples from full conditional distributions, which can easily be obtained from the joint posterior distribution. For this analysis, full conditional distributions of systematic effects, breeding values, and litter effects were univariate normal, and full conditional distributions of genetic, residual, and litter (co)variance matrices were inverted Wishart. Specifics on distributions can also be found in Wang et al. (1994) and Van Tassell and Van Vleck (1996). Moreover, the Gibbs sampling is combined with a Data Augmentation step (Tanner and Wong, 1987) to sample from predictive distributions of missing data. The Data Augmentation step is performed in each iteration by sampling the augmented data given all the parameters in the model.

The Gibbs sampling was carried out in three different chains of 50,000 iterations after discarding the first 10,000. Starting points were different in each chain. Analysis of convergence was performed for all heritabilities. Because heritabilities are a combination of dispersion parameters, they are expected to converge more slowly. The procedure of Raftery and Lewis (1992) was applied, using the program GIBBSIT with percentile 50 and a covering probability of 0.01. Moreover, the algorithm of García-Cortés et al. (1998) was also applied. Effective sample size was evaluated using the algorithm of Geyer (1992), and Monte Carlo errors were computed following Van Tassell and Van Vleck (1996). Finally, a sensitivity analysis was performed by using alternative prior distributions for (co)variance components with extreme positive and negative genetic correlations (r_g = 1 and r_g = -1).

	Results

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Analysis of Convergence, Effective Sample Size, and Sensitivity of the Gibbs Sampler

The number of iterations discarded (10,000) was more than proposed by any of the procedures of Raftery and Lewis (1992) and García-Cortés et al. (1998). They recommend discarding 3,134 iterations with one procedure and 6,536 with another. As an example, the trace plot of the coupled chains of the heritability for NBA in first parity is presented in Figure 1. All other heritabilities reached convergence following the same rate. The effective sample sizes calculated with the procedure of Geyer (1992) were small (46.64 to 499.07) due to the complexity of the model. Therefore, a complete description of the posterior marginal densities of any variable was not available. However, the Monte Carlo error for heritabilities ranged from 0.002 to 0.004, and for genetic correlations ranged from 0.007 to 0.042. Thus, posterior mean estimates are accurate enough. These posterior means and standard deviations were directly estimated from the mean and standard deviation of the samples.

View larger version (11K): [in this window] [in a new window]   Figure 1. Trace plots of convergence for heritability of NBA in first parity.

Reproduction Traits

Means, phenotypic standard deviations, and coefficients of variation for NBA are presented in Table 1. Posterior means and posterior standard deviations (PSD) of additive genetic variances of NBA in different parities ranged from 0.362 (PSD 0.031) in the first parity to 0.857 (PSD 0.111) in the sixth parity. After correction of systematic effects, total variance of NBA in different parities ranged from 5.486 (PSD 0.077) in the third parity to 5.869 (PSD 0.125) in the sixth parity (Table 2).

View this table: [in this window] [in a new window]   Table 2. Posterior means of heritabilities (diagonal), genetic correlations (above diagonal), residual correlations (under diagonal), additive genetic variance () and total variance () for NBA in different parities. Values between brackets are the corresponding posterior SD

View larger version (15K): [in this window] [in a new window]   Figure 2. Posterior densities of heritabilities of number of piglets born alive for parities one to six.

Phenotypic means, standard deviations, and coefficients of variation of production traits are presented in Table 3. Posterior marginal means for the percentage of variation of litter effect (c²) were 0.118 for WT and 0.075 for BT. The means of the posterior marginal distribution of the heritabilities were 0.229 (PSD 0.018) and 0.350 (PSD 0.019) for WT and BT, respectively (Table 4). Posterior densities are presented in Figure 3. Posterior marginal mean estimates of genetic and residual correlations between WT and BT were moderate and positive, 0.339 (PSD 0.044) and 0.388 (PSD 0.013), respectively.

View this table: [in this window] [in a new window]   Table 4. Posterior means of heritabilities (diagonal), genetic correlations (above diagonal), residual correlations (under diagonal), additive genetic variance () and total variance () for WT (kg2) and BT (mm2). Values between brackets are the corresponding posterior SD

View larger version (11K): [in this window] [in a new window]   Figure 3. Posterior densities of heritabilities of weight and backfat thickness at 175 d.

Posterior means of genetic and environmental correlations between reproduction (NBA at different parities) and production traits (WT and BT) are presented in Table 5. Posterior mean estimates of genetic correlations between NBA and WT are close to zero. In most cases, HPD of 95% contain zero correlation. All posterior means of genetic correlations between BT and NBA were very low, and in parities 1, 2, 5, and 6 the HPD of 95% included zero. The posterior means of environmental correlations between NBA for the six parities jointly analyzed with WT or BT were all close to zero. Highest posterior densities of 95% include zero correlation in all cases except for correlations with second-parity NBA.

	Discussion

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Litter size mean and variance usually evolve during the productive life of the sows. Thus, it is possible that different genes or different combinations of the genes are involved in each parity, due to hormonal and physiological maturation of sows. However, a high genetic correlation between parities is expected if many genes involved in the expression of litter size at different parities are the same. Estimates of genetic correlations obtained between adjacent parities are in agreement with this expectation. However, our estimates of genetic correlations were substantially reduced when parities are not adjacent. In their review on this topic, Haley et al. (1988) showed that genetic correlations between adjacent parities are high, although probably less than one, and that they were also high between parities 1 and 3, and 2 and 4. Their estimates for the genetic correlation between parities 1 and 4 were markedly reduced. They considered, however, that all these estimates were likely biased due to the culling of sows based on earlier litter records not accounted for by the statistical model. More recent studies using statistical procedures to avoid selection bias have also obtained conflicting results (Irgang et al., 1994; Roehe and Kennedy, 1995; Alfonso et al., 1997). Several reasons can be mentioned for these discrepancies. In the first place, new methodologies, such as Restricted Maximun Likelihood or Bayesian analysis, which allow complex modelling of multivariate analysis, have only recently been available. Secondly, computational requirements for analysis of large data sets impose simpler analytical models, i.e., bivariate analysis instead of multivariate analysis. Our data were analyzed jointly for litter traits for the first six parities together with production traits (WT and BT) to avoid selection bias.

Our results suggest that different parities should be considered as different traits. Testing genetic correlation between parities for differences from 1.0 is difficult when the data set is large. We did not attempt to test this hypothesis. However, results from the marginal posterior distributions suggest that there are genetic differences between parities, in particular between the first and the sixth parities with respect to the others.

Genetic evaluations performed using the true model with known parameters will yield maximun response to selection. However, the operational model for genetic evaluation might be chosen compromising the closeness to the true model and its complexity. From a practical point of view, an operational model for predicting breeding values might consider the first and sixth parities as different traits and common genetic expression (repeatability animal model) among the second through fifth parities. The use of a model that discriminates among parities is also more flexible to define selection criteria by giving different weights to each parity.

For production traits, the estimates of heritability are also in the range of previous studies for WT (Kuhlers and Jungst, 1991, Hovernier et al., 1992; Ducos, 1994) and BT (Ducos, 1994; Ducos and Bidanel, 1996; Rodriguez et al., 1996). The estimate of genetic correlation between BT and WT agrees well with the results of Hovernier et al. (1992) and Ducos et al. (1992), but they differ from those of Kennedy et al. (1985), Kuhlers and Jungst (1991), and Bidanel et al. (1994), who found genetic correlations closer to zero. These discrepancies could be attributed to the number and location of measurement sites for BT, type of equipment, performance test conditions, like age at test, feed value, feeding practice, or more simply, to sampling.

Genetic correlations between production and reproduction traits have been reported to be very close to zero when litter size from difference parities are treated as repeated measured of the same trait (Ducos and Bidanel, 1996; Kerr and Cameron, 1996; Crump et al., 1997b) or as different traits (Brien, 1986; Ducos and Bidanel, 1996; Rydhmer et al., 1995). Our results are consistent with earlier studies, except for genetic correlations between BT and NBA in parities 3 and 4, where HPD of 95% did not include the zero. These results may suggest that gilts with increased fat deposition at the end of the 175 d test have greater energy reserves for later parities with higher prolificacy. Further research may be needed for a better understanding of these results.

Finally, our results suggest that efforts to map QTL affecting reproduction traits should take into account genes segregating for litter traits in different parities. Consequently, this information should be incorporated in experimental designs for QTL mapping and in marker-assisted selection programs aimed to increase reproductive efficiency in pigs.

	Implications

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Considering litter size in different parities of sows as different traits is justified from the posterior mean estimates of heritabilities and genetic correlations obtained in this study. Heterogeneity of heritabilities for number born alive at different parities and correlations less than 0.9 between parities suggest the use of multiple trait models rather than the repeatability model for the genetic evaluation of selection candidates. The low genetic correlations between production traits (weight and backfat at 175 d of age) and number born alive suggest that selection for growth and backfat should produce little or no correlated response in litter size.

	Footnotes

 
¹ Financial support was provided by INIA, Spain (grant 9084). We acknowledge L. Gómez-Raya for his useful comments, J. Pomar for his collaboration, and Maite Arbonés for her technical support.

Received for publication September 7, 2001. Accepted for publication June 12, 2002.

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