For carcass traits, we collected a total of 1,870, 696, and 1,723 pigs belonging to Berkshire, Duroc, and Yorkshire, respectively, with the pigs being born between the year 2007 and 2015. Similarly, data on 1,487, 643, and 914 pigs born between 2011 and 2015 were recorded for the two reproductive traits (number born alive [NBA] and total number born [TNB] for first three parities), pertaining to the respective pig breeds. The averages of the three parities were used for GEBV prediction. All Berkshire pigs were collected from Dasan breeding farm, in Namwon, Jeonnam, whereas the Duroc and Yorkshire samples were collected from Nong-Hyup breeding farms in Youngwang, Jeonnam, Korea.

The pigs were born from 52 sires and 570 dams for Berkshire, from 141 sires and 319 dams for Duroc, and from 87 sires and 643 dams for Yorkshire, respectively. The piglets were weaned at three to four weeks of age and moved into piglet pens, in each of which about 100 piglets were raised for 60 days. The pigs were then placed in growth/fattening pens with the size of 20 pigs for 90 to 120 days. The pigs were fed with commercial feeds according to the regimen of Purina Ltd in Nonghyup commercial farms, Youngsam, Chounbuk, Korea. The individuals were then transported to nearby abattoirs and slaughtered. All records of the pedigrees, genotypes and phenotypes were provided by the Nonghyup breeding company not explicitly for the purpose of this study.

The average slaughter ages were 208±18, 131±32, and 155± 10 days for Berkshire, Duroc and Yorkshire breeds, respectively. Hot carcass weight was measured immediately after slaughter on the floor of the abattoir. The carcasses were then cooled in a chilling room maintained at 0°C for 24 hours. The average of backfat at the first rib, last rib, and lumber vertebra was calculated with help of slide calipers [12].

For the reproductive traits, the numbers of piglets that are born alive (NBA) and total number of piglets born (TNB) were recorded for the first three parities, and the average of the three parities was calculated for the two traits.

The pigs were genotyped with Illumina Porcine SNP60K BeadChip (Illumina Inc, San Diego, CA, USA), on which 62,163 SNPs were embedded. All autosomal SNPs were used for quality control (QC) procedures. The SNPs were removed with call rates <90%, minor allele frequency <1%, and significant deviation from Hardy-Weinberg equilibrium at p< 0.000001. The individuals with genotyping call rate <90% were also deleted. PLINK software (v1.07) was used for the QC procedures [13]. After the QC tests, the genome-wide missing SNPs were imputed with the use of Beagle vs 3.3.2 [14]. Identity-by-state test was also carried out to check whether there are similar individuals or genotyping error in the datasets. The pairs of individuals with high similarity rate (>95%) were removed for GEBV evaluation.

The statistical significance of the fixed factors or covariates was tested using SAS general linear model procedure (SAS, version 9.2, SAS Institute, Cary, NC, USA) for fitting the factors into Animal model. For carcass traits, gender and slaughter age were fitted as a fixed effect and a covariate, respectively. For the reproduction traits, only birth year-season was fitted as a fixed effect in the animal model for ASREML analysis [15]. The linear mixed model for each trait is:

Where y represents vector of the phenotypic records for n number of animals, X denotes the design matrix of the fixed effects and/or covariates, b is the vector of the corresponding effects including overall mean, Z is the design matrix assigned to genomic breeding values, g is the vector of the breeding values, and e is the vector of residual error, which is assumed to be normally distributed with σe2.

In matrix notation, the mixed model equation is written as:

Where, α=σe2σa2, σa2 is the genetic variance, and σe2 is the error variance.

By solving the MME, the ĝ, breeding values could be obtained as:

The genomic relationship matrix (G) matrix was built using the genome-wide complex trait analysis (GCTA) tools [16]. The following equation was used to generate G matrix based on marker allele frequencies:

Where, M has dimensions of n×m, n is the number of individuals and m is the number of markers used. The genotypes of each marker are coded as AA = −1, AB = 0, BB = 1 for alternate alleles, A and B. In the P matrix, an element, P_j = 2(P_j–0.5), where P_j represents minor allele frequency at locus j. (M–P) represents incidence matrix (Z) for the markers.

After estimating marker effects, GEBV of an animal i was calculated using the following equation:

Where, z_ij denotes the genotype of i^th individual at the j^th marker locus, and ĝ_j represents allele substitution effect of the j^th marker.

GEBV accuracies were evaluated by applying the standard error of GEBVs [6] obtained from ASREML output. The following calculation formula was used to estimate GEBV accuracies for an animal i.

Where, σa2 represents the genetic variance of the trait. Realized accuracies were also obtained with a replicated training-testing method via a 10-fold cross-validations method according to Badke et al [17]. The entire dataset was divided into 10 groups, in which one of the groups (10% animals) was treated as testing, i.e. the samples were assumed to have only genotype information and their phenotypes masked, while the remaining samples (90% of animals) was used as training or reference group with both genotype and phenotype known, to predict GEBVs in the test group. This cycle was repeated 10 times such that each of the animals in the dataset could get the chance to be treated once as a testing group. GEBV accuracies of the testing samples were measured by the correlations between the GEBV estimates and real phenotype values as follows:

Where, r is Pearson’s correlation coefficient, and y is individual phenotype.

Genetic and residual variances were also estimated with the use of ASREML 3.0 program [17]. The heritability values for BFT, CWT, NBA, and TNB were calculated for each breed using the following formula:

The pigs were slaughtered at 131 to 209 days with the highest slaughter age for Berkshire pigs, which might be due to its slow rate of growth (Table 1) [18]. The mean carcass weight ranged 84 to 103 kg with the lowest weight for Berkshire. Also, the Berkshire pigs yielded the greatest (23.8 mm) BFT, while the Duroc pigs had the lowest BFT (13.6 mm), which was in accordance with the previous reports [19]. For carcass weight, there was the greatest variation between individuals in the Duroc samples, while the Berkshire samples had the most various BFT measurements among the three breeds (Table 1).

After QC tests, the numbers of available SNPs for the carcass traits were 30,769, 26,374, and 30,071 in Berkshire, Duroc, and Yorkshire samples, respectively. Also, 39,095, 47,251, and 52,258 SNPs were available for the reproductive traits in the respective breeds. Among the SNPs, the 25,880 common SNPs were finally chosen for prediction of GEBVs, for which the average distance between adjacent SNPs across the autosomal chromosomes was 94.3±143.4 kb, covering 2,437.9 Mb of the porcine genome (results not shown).

Additive genetic and residual variances, and heritabilities were estimated under the GBLUP model for the carcass (Table 2) and the reproductive traits (Table 3), respectively. The heritabilities for BFT and CWT ranged 0.24 to 0.50 and 0.25 to 0.43, respectively, for the three pig breeds. In the Berkshire and Duroc populations, the BFT heritability estimates were 0.50 and 0.41, respectively. This result agreed with the previous reports [20,21], in which the estimated heritabilities of the trait ranged from 0.34 to 0.56 for the same breeds. For CWT, the estimated heritabilities of 0.25 to 0.43 for the three breeds fell within the range (0.13 to 0.43) of heritability estimates in previous reports [7,20]. These results show that the use of genome relationship matrices in heritability estimation of carcass traits in pigs were, in general, in good agreement with the use of pedigree-based relationship matrices.

The heritability estimates for NBA and TNB in the three breed populations ranged 0.03 to 0.32 and 0.15 to 0.46, respectively (Table 3). The lowest heritability values were observed in the Berkshire population (0.15 and 0.03 for TNB and NBA), while the greatest in the Duroc population (0.46 and 0.32 for TNB and NBA). In general, NBA has been reported to have very low heritability, i.e. <0.10 [22], which was in good agreement with the estimate in Berkshire in this study (Table 3). However, in Duroc, the heritability estimates for the reproductive traits were high, which may be partly due to a small sample size (Table 1). The TNB heritability was estimated as 0.15 in Berkshire, which was in good agreement with the heritability value in commercial pig populations reported by Cleveland et al [23] and Cleveland and Hickey [24]. In the three breed populations, heritability values for TNB were greater than those for NBA, which was also agreed with the previous reports [22,24].

The BLUP model accuracies of GEBV estimates of BFT were 0.59 and 0.72 for Yorkshire and Berkshire, respectively, and 0.59 and 0.63 for CWT in the respective pig breeds. However, in Duroc pigs, the model accuracies of GEBV were 0.33 for both BFT and CWT, which was lower than the former two breeds (Table 4). This may be partly due to a smaller training sample size of Duroc (n = 466), compared to those of Berkshire (888) and Yorkshire (1,208).

The GEBV accuracies for the BFT and CWT in Berkshire agreed with Baby et al [20], who reported 0.68 and 0.60 for the respective traits under a GBLUP model in Berkshire. Also, several studies reported that BFT GEBV accuracies in the three pig breeds ranged 0.58 to 0.86 under various GEBV models [17,25,26].

The realized accuracies of GEBV estimates were in general lower than the model based accuracies for the carcass traits. In the Duroc population the realized accuracy for CWT was 0.09, while the model accuracy of the trait was 0.33, which might be partly due to a sampling effect of the small reference size of the breed (Table 4).

The results of the GEBV prediction accuracies for NBA and TNB in Berkshire, Duroc, and Yorkshire pigs are presented in Table 5. The accuracies obtained from the BLUP model ranged 0.32 to 0.54 and 0.39 to 0.56 for NBA and TNB, respectively. However, the realized accuracy estimates were higher than the model based accuracies, ranging 0.50 to 0.70 and 0.70 to 0.87, for the respective traits, which may be partly due to sampling effect, i.e. small sample size of the reference (training) population size.

The model accuracy estimate of TNB (0.56) in the Yorkshire population was in good agreement with Uimari et al [27] in Finish Yorkshire. Forni et al [28] applied single-step BLUP analyses to predict GEBV accuracies for TNB, resulting in the accuracy values of 0.28 to 0.49, overlapping the estimates of this study (Table 5). In general, the GEBV accuracies for TNB were higher than for NBA in the three breeds, which may be partly due to greater heritabilities of TNB than of NBA, because a high heritability tends to increase accuracy of genomic prediction [9].

The realized accuracies (0.70 to 0.87) of TNB agreed with Cleveland et al [24], in which the GEBV accuracies of the trait ranged 0.82 to 0.83 in a Landrace population with the sample size of 3,000 pigs. Both the model based accuracy estimates and the realized accuracy estimates were the greatest in the Duroc population (Table 5). This might be caused by the overestimation of the heritabilities, resulting from the very small reference population size in Duroc (Table 3).

In this study, GEBV accuracies for carcass and reproduction traits in pigs were evaluated based on two approaches, BLUP model-based or realized accuracy, i.e. correlation between predicted GEBVs and phenotypes. For the carcass traits, the model based accuracies were higher than the realized accuracies, while, for the reproductive traits, vice versa, across the three pig breed populations (Tables 4, 5). There are several factors influencing GEBV accuracies such as reference population size, heritability of trait, model assumptions, magnitude of genetic relatedness between training set and testing individuals, phenotype heterogeneity, density (or number) of the genome-wide markers [26]. Effective population sizes (Ne) were estimated for each breed according to Lee et al [9] that was based on effective number of chromosome segments and off-diagonal elements in genome relationship matrix, resulting in 162, 638, and 200 for Berkshire, Duroc and Yorkshire, respectively. Berkshire has a smaller Ne than Yorkshire, which may partly cause greater GEBV accuracies in carcass traits of the testing samples in Berkshire than in Yorkshire, even if the training sample size of Yorkshire was greater than Berkshire (Table 4).

It seems that the GEBV estimates of the carcass traits were less biased than those of the reproductive traits, because prediction of the estimates were based on greater reference population sizes and higher heritabilities (Tables 4, 5). For the two carcass traits (Table 4), the higher GEBV accuracies obtained in the model-based methods may be caused by the presence of individuals in the training set that are more genetically related to the selection candidates [25]. However, this result may be unexpected when the reference population size was too small, e.g. for the reproductive traits (Table 5), so that a small number (one tenth) of testing samples were so closely related to the rest (nine tenth) of the reference (training) samples, resulting in much higher realized accuracy.

Our results suggest that GEBV estimates for carcass and reproductive traits can be obtained with reasonable degree of prediction accuracy, even if small or moderate sizes of reference populations were used in the Korean breeding pig farms. However, much careful selection of animals based on the estimated GEBVs is needed, because GEBV accuracies could depend on alternate prediction methods. Instead, increase of GEBV accuracy can be warranted by incorporating large reference population sizes, e.g. several thousands of animals with both SNP genotypes and phenotypes, which would be more beneficial for low inheritable traits such as reproductive traits.