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Estimation of variances for gametic effects on litter size in Yorkshire and Landrace swine

A. Stella^*, K. J. Stalder, A. M. Saxton and P. J. Boettcher^,1

^* CERSA-Fondazione Parco Tecnologico Padano and and Istituto Biologia e Biotecnologia Agraria, Consiglio Nazionale delle Ricerche Segrate, Italy 20090; and and Department of Animal Science, University of Tennessee, Knoxville 37996-4574

	Abstract

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The objective of this study was to test for effects of gametic imprinting on litter size in swine by estimating variances for parent-specific gametic effects. Data were 64,047 and 137,009 multiparous records of number born alive for the U.S. Landrace and Yorkshire breeds, respectively. The statistical model included fixed effects of parity number and herd, and random effects of herd-year-season, mate, permanent environment, animal (additive genetic), and either maternal or paternal gametes. A Bayesian approach that used Gibbs sampling to obtain posterior distributions was employed. To aid in the interpretation of results, the Landrace data structure was used to simulate data with and without effects of imprinting. Analyses of the simulated records indicated that the model applied was capable of detecting effects of imprinting when such effects were present. Small, but non-zero, estimates of gametic variances were obtained when no imprinting was simulated. Estimates of the proportion of total variance accounted for by paternally transmitted gametes were 0.8 and 0.9% for Landrace and Yorkshires, respectively. These estimates were different from zero, but were similar to the results observed for data simulated without an imprinting effect. Corresponding results for maternally transmitted gametes were 1.6% for Landrace and 0.8% for Yorkshires. The estimate for Landrace was significantly greater than that observed for Yorkshires and for the simulations without a true effect and suggested the presence of a non-Mendelian genetic influence on litter size. Paternally imprinted genes are a plausible reason for the observed results. Assuming that the effect observed was due to paternal imprinting at a single biallelic locus, the substitution effect of the superior allele could be greater than 0.7 piglets per litter. Identification of a genetic marker for such an allele would be useful in marker-assisted selection of females. Other possible explanations exist for the increased gametic variance in the Landrace breed, but these explanations (such as maternal or cytoplasmic effects) may be less likely than paternal imprinting.

Key Words: Gametes • Imprinting • Litter Size • Pigs

	Introduction

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Gametic imprinting occurs when genes from parents of a particular sex are not expressed (Sapenzia, 1990). Studies of imprinting have generally taken one of two approaches. The first approach has used molecular and phenotypic data to find evidence of sex of parent-dependent expression of specific genes. This technique has been used to identify imprinting of the IGF-2 gene in swine (Jeon et al., 1999; Nezer et al., 1999).

The second approach has used pedigree and phenotypic data to estimate variance components indicative of imprinting. Three different statistical models have been proposed. The first model (Schaeffer et al., 1989) involves estimating effects of gametes from a given parental origin. Gametic effects are correlated according to the gametic relationship matrix (Smith and Allaire 1985). This model is the most appropriate method for estimating effects of imprinting (Essl and Voith, 2002b), but it has not been routinely applied due to a lack of software. Tier and Sölkner (1993) treated gametes as homozygous diploid individuals and included them in a standard relationship matrix. Twice the variance of these effects was considered equivalent to the gametic variance of Schaeffer et al. (1989). This approach has been applied to swine (De Vries et al., 1994) and beef cattle (Engellandt and Tier, 2002). Essl and Voith (2002a) proposed a third test based on the difference between variances of maternal and paternal gametic effects obtained from dam and sire models, respectively. Essl and Voith (2002a) applied both of these latter two methods to data from dairy cattle.

Studies of imprinting in livestock have generally been applied to production traits. According to certain theories about the evolutionary basis of imprinting (Reik and Walter, 2001), reproductive traits could also be affected. The objectives of this study were to develop software for and to apply the model proposed by Schaeffer et al. (1989) to test for effects of imprinting on litter size in swine.

	Materials and Methods

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Real Data
Phenotypic data for litter size (number born alive) from purebred Landrace and Yorkshire females were obtained from the National Swine Registry (West Lafayette, IN). The original data included 67,349 Landrace records and 390,085 Yorkshire records for litters that were farrowed between 1986 and 2000. Editing procedures required 1) a litter size of 1 to 20 animals, 2) animals (dams of each litter) with known sires and mates, and 3) herds with at least two litters from two different dams. Sire information was more complete for the Landrace breed since nearly 250,000 records from the Yorkshire data were discarded due to lack of sire identification vs. only about 3,000 for Landrace. Final data sets included 64,047 records from 28,215 Landrace dams and 137,009 records from 63,876 Yorkshire dams. Each of the original records from the National Swine Registry included up to three generations of pedigree information, and these data were used to form a complete pedigree file for each breed by tracing ancestry as far back as possible (up to twenty generations). For Landrace, the final pedigree file included 36,804 animals. The Yorkshire pedigree file included 83,765 animals.

Methods
The models for evaluation of gametic effects included effects of contemporary group, parity, mate, and permanent environment, in addition to the genetic effects. Contemporary groups were defined on two levels, herds and herd-year-seasons (HYS) of farrowing. Data were from 735 Landrace and 2,455 Yorkshire herds. The HYS were of variable length, ranging from 2 mo to 1 yr, depending on the number of animals per HYS. Each HYS contained at least two contemporaries. The HYS were formed in a stepwise manner. Initially, HYS of 2-mo seasons were created. All HYS with at least two animals were kept. The HYS with a single animal were then merged with adjacent HYS, forming HYS four months in length. This process was repeated in 2-mo steps until reaching a maximum length of one year. Animals with no herdmates within the same year were not included in the analysis. This approach resulted in the definition of 8,440 and 22,702 HYS for Landrace and Yorkshires, respectively. Parity numbers ranged from 1 to 17 (and unknown) in the original datasets and these were defined into six different groups (1st, 2nd, 3rd to 5th, 6th to 9th, 10th, and unknown), based on average litter sizes and number of animals per parity. The effect of mate was included to account for effects of differences in fertility of service sires on litter size. The numbers of mates (service sires) were 5,289 and 14,193 for Landrace and Yorkshires, respectively.

The model for the estimation of gametic effects was defined by the equation:

[1]

where y_ijklmn is the observed value for litter size of the oth record; h_i is the fixed effect of the ith herd, p_j is the fixed effect of the jth parity group, hys_k is the random effect of the kth HYS, m_l is the random effect of the lth mate (i.e., service sire), pe_m is the random effect of the permanent environment of dam m, a_m is the random additive genetic effect of animal m, g_n is the random effect of the nth gamete (of either maternal or paternal origin for animal m), and e_ijklmno is the random residual for record o.

This model assumes that additive genetic effects are distributed MVN(0,A²_a) and gametic effects are distributed MVN(0,G²_g), where A and G are additive genetic and gametic relationship matrices (Smith and Allaire, 1985), respectively, and that variability in gametic effects is observed only in maternally or paternally transmitted gametes, not both. The model also assumes that other potential genetic influences such as effects of the fetuses, maternal effects, or cytoplasmic effects are negligible.

Variance components were estimated by a Bayesian procedure that employed Gibbs sampling to obtain posterior distributions of the various parameters (Sorensen, 1999). Prior distributions were uniform, normal, and inverted ² for fixed effects, random effects, and variances, respectively. Priors for variances were informative but received very little weight. Fixed and random effects were sampled from normal distributions and variance components were sampled from inverted ² distributions. For each analysis, three chains of 100,000 cycles were generated (i.e., 300,000 in total). Based on visual inspection, the first 5,000 samples from each chain were discarded as a burn-in period to ensure sampling from the appropriate marginal distributions. Posterior means and SD were estimated from the respective posterior distributions based on saving every twentieth sample. This sampling strategy was adopted to ensure that all posterior means were based on at least 75 independent samples.

Simulated Data
To aid in interpretation of results based on real data, similar analyses were also applied to sets of simulated data. Similar statistical analyses had been previously applied to other sets of real and simulated data (our unpublished observations) and two observations had been made. First, some population structures precluded the detection of imprinting effects. For example, when the model defined by Eq. [1] was previously applied to carcass data in swine (for which animals with data had no offspring), no significant gametic variance was observed, even when an effect of imprinting was simulated and added to each of the phenotypic records. In that analysis, gametic variance was partitioned into additive genetic variance. Second, in previous analyses of simulated data, estimates of gametic variance were small (<1.0% of total variance), but non-zero in situations where no imprinting effects were simulated. Therefore, the goals of the analyses of simulated data were 1) to determine if the population structure for the litter size data was sufficient for the detection of imprinting effects (i.e., to help avoid type-II errors) and 2) to observe estimates of gametic variance in situations for which no imprinting effects existed (i.e., to help avoid type-I errors).

The simulated data was obtained using the Landrace data as a template. Data were simulated according to Eq. [1]. The mean of simulated litter size was set at 10.0 and all effects were simulated by random sampling from normal distributions. Standard deviations for effects of parity, herd, HYS, mate, permanent environment, and residual were 0.5, 0.6, 0.13, 0.16, 0.34, and 5.65, respectively, and were based on a preliminary analysis of the data using REML. The underlying variance of single gametic effects was either 0.0 (i.e., no imprinting) or 0.15. The value of 0.15 was arbitrarily chosen to equal one-third of additive genetic variance. Two gametes were simulated for each animal, but only one of the two contributed to phenotypes, because only maternal or paternal imprinting was simulated in any given model. Additive genetic variance was either 0.54 (no imprinting) or 0.45. An infinitesimal model was assumed for both gametic and additive genetic effects and inbreeding of parents was accounted for in Mendelian sampling of genetic effects.

Five sets of data were simulated with no imprinting effect and these data sets were each evaluated twice, with models that included 1) maternal imprinting or 2) paternal imprinting. A sampling chain of 50,000 rounds was generated for each of these analyses. One set of data each was generated with real effects of paternal imprinting and maternal imprinting. Each of these datasets was analyzed twice, once with effects of gametes of paternal origin in the model (maternal imprinting) and once with maternal gametic effects (paternal imprinting). Each analysis included 100,000 rounds of Gibbs sampling. Prior values used for gametic and additive genetic variances were 0.10 and 0.50, respectively, for all models. The true values were used as priors for other sources of variance. Posterior means were calculated for the various parameters.

	Results

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Simulated Data
Table 1 shows posterior means and SD of variance components (across five replicates) obtained by analyzing data simulated without effects of imprinting. Results are presented for two models, the first estimated the variance of effects of gametes of paternal origin (i.e., maternal imprinting) and the second estimated the variance of gametes of maternal origin. Results were similar for both models. Estimates of variances for HYS, mate, and permanent environmental effects were quite accurate. Differences between true and estimated values were generally less than one-half of the respective posterior SD for these effects. However, estimates of genetic effects were somewhat biased. Although no imprinting effects were simulated, the estimates of the variances for these effects were significantly greater than zero for both models (for both paternal and maternal origin of gametes). The means of variances for these effects were 0.050 and 0.054 for paternal and maternal origins, respectively. Posterior means across individual replicates ranged from 0.032 to 0.068. In both instances, the posterior distributions were symmetrical (figures not shown) and did not include zero since the minimum sampled values for this effect were 0.019 and 0.017 for gametes of paternal and maternal origins, respectively. These variances were nonzero because a small proportion of the additive genetic variance was partitioned into the respective variances for gametic effects. Estimates of additive genetic variances were less than the true value (0.54) for both the models with expression of gametes of maternal (0.497) and paternal (0.509) origins. Residual variances were slightly higher than the true values (5.714 and 5.716 vs. 5.65), possibly because of the attempt to fit an incorrect model.

Two primary conclusions were drawn from the analyses of simulated data. The first was that (at least for these data) a low but non-zero estimate of gametic variance from this type of analysis cannot be interpreted as an indication of a small but real influence of gametic imprinting. Southwood et al. (1989) and Boettcher et al. (1997) reported similar results when applying models that included cytoplasmic effects to data for which no such effects were simulated. In those studies, the estimates of cytoplasmic variance were small but non-zero, even in situations where data were simulated without a true cytoplasmic effect, apparently due to partitioning of a small proportion of the additive genetic effect into the cytoplasmic genetic effect. The second conclusion was that the structure of data analyzed in these studies was sufficient to detect effects of gametic imprinting when they existed. Estimates of all variance components were correct when effects of expression of gametes of either paternal or maternal origin were simulated and the correct model was applied. As mentioned previously, some data structures (data from only a single generation, for example) are not sufficient for detecting such effects by applying similar approaches for analysis (our unpublished observations).

Real Data
Landrace Data.
Posterior means and SD of the various components of variance when analyses that assumed variability in effects of certain maternally or paternally transmitted genes were applied to the Landrace data are shown in Table 3. The first half of the table shows the estimates of variances from the model in which expression of genes of paternal origin (i.e., maternal imprinting) was assumed. None of the individual factors in the model accounted for as much as 10% of the total variance and residual effects accounted for >80% of the variability in litter size. Heritability for litter size was 0.078, which is at the lower end the range of estimates previously reported in the literature (e.g., Lamberson, 1990; Roehe and Kennedy, 1995; Chen et al., 2003). The posterior estimate of gametic variance was different from zero since the mean was 0.053 and the lowest sampled value was 0.018, but these values were very similar to estimates obtained from simulated data for which no effect of imprinting was simulated (Table 1). These results suggest that maternally imprinted loci have no detectable effect on litter size in the Landrace breed. At best, such effects could explain <1% of the variance, but such an effect is too small to be detected unambiguously by the analysis undertaken.

The posterior mean of additive genetic variance from the model with maternal expression (0.471) was less than the estimate with paternal expression (0.539). Consequently, the heritability from the maternal expression model was 1% lower (0.068 vs. 0.078) than from the model with maternal imprinting. The difference in the additive genetic variance between the two analyses was basically equal in magnitude to the difference in gametic variances between the two models. The residual variance and its proportion of total variance were essentially the same from the two analyses.

Yorkshire Data.
Results from analyses of the Yorkshire data are in Table 4. Estimates from both of the models (for expression of genes from gametes of either paternal or maternal origin) were very similar to each other. Specifically, both the posterior means and SD of variances for HYS and mate effects were equal up to three decimal places. Posterior means for all other sources of variance differed only at the third decimal place (i.e., would round to the same values at the second decimal place). Of particular interest in this study were the estimates of the gametic variances. Posterior means were 0.060 and 0.057 when expression of genes of paternal and maternal origins, respectively, was assumed. These estimates were only somewhat greater than the overall means across replicates from data simulated without an imprinting effect (Table 1), and were lower than some of the posterior means from the five individual replicates. This result suggests that the true value of the gametic effect is not large in the Yorkshire population from which these data were recorded.

	Discussion

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The results of these analyses suggest that litter size in the U.S. Landrace population is affected by some genetic factor beyond the simple additive genetic effects of the sow. One plausible source of this effect is variability in genes that are paternally imprinted or expressed only when transmitted by the dam of the sow. Gametic imprinting has been previously demonstrated for the IGF-2 gene in swine, with effects on muscle mass and fat deposition (Jeon et al., 1999; Nezer et al., 1999). De Koning et al. (2000) found evidence of imprinted effects on several traits for four different chromosomal regions in swine. Effects of imprinting on traits associated with reproduction have been observed in mice (Constancia et al., 2002). According to some theories about the presence of gametic imprinting, traits associated with reproduction are likely candidates because imprinted genes may offer individuals of one sex the possibility of exerting more control over the transmission of his or her genes than the other mate (Reik and Walter, 2001). An unusual twist between the results reported here and previous studies on mice (Constancia et al., 2002) is that the observed imprinted effects in this study affect the number of grand-offspring of the individual whose genes are expressed preferentially rather than the number of offspring, inasmuch as the work of Constancia et al. (2002) dealt with imprinting in genes of the fetus rather than genes of the dam.

Another interesting aspect of the results was that a significant estimate of gametic variance was observed only for the Landrace breed. To ensure that this result was not due to differences in data structure between the populations, we resimulated data with variable effects of gametes of maternal origin using the Yorkshire population as a template and estimated variances using a model that included these effects. The resulting estimates for gametic variance were correct, indicating the differences observed were not due to data structure.

Given that the differences between Landrace and Yorkshire were not due to differences in the structure of the data, one may be tempted to conclude that no genes associated with litter size are imprinted in the Yorkshire breed. However, nonsignificant gametic variances from this analysis are not necessarily indicative that gametic imprinting does not occur within the population tested. Rather, a significant estimate of gametic variance for a given parental origin suggests that genetic variability exists in imprinted genes that affect litter size. Only a very small proportion of genes is expected to be imprinted (Barlow, 1995). Perhaps an equally small number of imprinted genes control litter size in both breeds, but polymorphism or variation in the effect of only one (or very few) of these genes is present only in the Landrace breed. Alternative alleles of the estrogen receptor allele have been shown to have different (unimprinted) effects on litter size in certain breeds and lines of swine (Rothschild et al., 1996). However, in other populations, this gene can either be nonpolymorphic or have no observable difference between alternative alleles (Drogemuller et al., 2001).

Assuming the variability observed is associated with polymorphism at a single biallelic locus, the substitution affect of the superior allele could be substantial. If alternative alleles each had frequencies of 50%, the gametic variance of 0.121 would correspond to a difference of approximately 0.70 piglets per litter. This substitution effect would increase for greater disparities in gene frequencies.

The analysis applied to the data was based on the assumption of a normal distribution of gametic effects rather than a biallelic locus. Therefore, we used simulation to confirm the ability of the previously described model (Eq. [1]) to detect gametic variability associated with a single, biallelic loci. We used the Landrace data structure to simulate litter size controlled in part by an imprinted biallelic locus. We simulated two alleles, each with frequencies of 0.5 and with effects differing by 0.75 piglets. A single replication was generated each for a paternally and maternally imprinted gametic effect. Estimates of variances were 0.152 (paternal imprinting) and 0.138 (maternal), neither significantly different from the expected value of 0.141 (posterior SD were approximately 0.03 in each case).

Although variability in paternally imprinted genes that affect litter size may be the most plausible reason for the significant gametic variance observed in the Landrace breed, other possible explanations exist. As was noted earlier in the explanation of the analysis, the model used assumed that other genetic effects, such as fetal, maternal, or cytoplasmic effects, had no influence on litter size. If such factors were important but ignored, they could cause a bias in the estimate of gametic variance. The genotypes of the pigs of the litters were not considered in this study. In theory, differences in genotypes of embryos could cause variability in their survival. However, Gama et al. (1991) estimated the direct genetic effects of embryonic survival and reported a heritability of <1%. Maternal sisters share the same maternal effect and cytoplasmic effects and would be expected to have correlated effects due to maternally expressed genes. Thus, these factors could affect estimates of the influence of paternally imprinted genes. However, the importance of these factors is questionable. Previous studies have estimated variance for maternal effects on litter size and the influence of this factor has generally been quite small, usually <1% of the total variance in most situations (e.g., Roehe and Kennedy, 1995; Chen et al., 2003). With respect to cytoplasmic effects, Robison (1998) reported differences of approximately 0.75 piglets in mean litter size between lines formed by reciprocal crossing of Yorkshires and Duroc breeds. He attributed the difference to cytoplasmic effects. However, the study of Robison (1998) dealt with differences in cytoplasmic effects between breeds rather than variability within a given breed. No other evidence for cytoplasmic effects on litter size within a breed has been published. If the results of this study were due to cytoplasmic effects rather than imprinted effects, such a result would be biologically interesting in its own right. Molecular genetic approaches may be needed to precisely define the biological cause for the results observed in this study. The identification of the gene or genes associated with the observed effect could produce information useful in marker assisted selection programs.

In theory, accounting for effect of imprinting (or another non-Mendelian factor) in national genetic evaluations could improve accuracy of EBV. However, such a procedure would add an additional level of complexity to the model. A gametic model such as the one applied in this study includes an additional number of factors equal to twice the number of animals. Given the relatively small influence of this factor on phenotypic variability (less than 2% of the total variance), and the fact that it seems to be maternally transmitted, accuracies of EBV of boars from current genetic evaluations that ignore imprinting may not be improved greatly by adapting the currently used genetic models to account for gametic effects.

	Implications

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Evidence for variability of paternally imprinted genes influencing litter size was found for Landrace. Such effects accounted for approximately 2% of the total phenotypic variance. Genetic factors other than paternal imprinting could explain the non-zero estimate of gametic variance. Assuming that the effect is due to polymorphism at a single paternally imprinted locus, the substitution effect could exceed 0.70 pigs per litter. Increased knowledge about a locus with such an effect would be valuable information in a breeding program, primarily in selection of females. Additional research, likely using molecular genetic approaches, is needed to confirm the precise source of the unexplained variability.

¹ Correspondence: Palazzo LITA, Via Fratelli Cervi 93, 20090 Segrate (phone: +39 0221013508; fax: +39 0226412135; E-mail: boettch{at}ibba.cnr.it).

Received for publication February 25, 2003. Accepted for publication May 21, 2003.

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