The phenotypic dataset on the growth rate of animals was obtained through performance tests of Yorkshire (YS; n = 21,762) and Landrace (LR; n = 13,166) pigs between 2005 and 2015. These pigs were born and raised in a closed nucleus (breeding) farm in South Korea. Animals were reared in pens where each pen housed 4 to 10 YS or 3 to 8 LR pigs of the same sex. Each group of animals comprised 1 to 7 YS or 1 to 6 LR full-sibs. The performance evaluations on the ADG of pigs started soon after each animal reached a live body weight of 30 kg, and were finished when a target weight of 90 kg was attained. On average, fewer than 160 days were required to attain this target weight. The animal phenotypes selected to be studied were based on the size of the group (frequency >10%). The average ADG was recorded to be 787.9±88.3 g/d in LR and 792.5±92.1 g/d in YS.

Complete pedigrees of the studied animals were obtained from the Korean Animal Improvement Association database. The total numbers of animals in the pedigree of the two breeds were 14,013 (LR) and 22,536 (YS). The numbers of individuals for which both parents were known were 13,916 (LR) and 22,324 (YS). In the whole pedigree, about 96% (LR) and 62% (YS) of the animals were inbred. The average inbreeding coefficients were 0.035 and 0.015 in LR and YS, respectively. The ranges of inbreeding coefficients were 0.0001 to 0.263 (YS) and 0.001 to 0.274 (LR). The observed average family sizes were 3.97 and 4.11 in LR and YS, with ranges of 2 to 15 and 2 to 17, respectively. The population structures of these breeds were determined using the CFC v1.0 software package [7].

The experimental protocols describing the management and care of the animals were reviewed and approved according to the guide for the care and use of laboratory animals (National Institute of Animal Science, Animal Care Committee of Korea) on 7 March 2014 (approval number: NIAS 2014-289). The management practices on the studied population stated that each pen was 2.5×3.6 m (~0.9 m²/pig) in size with solid concrete flooring. Pigs were fed ad libitum and water was constantly accessible through nipple drinkers. The feeding program was applied in accordance with pig testing standards of the Korean Animal Improvement Association (http://www.aiak.or.kr/eng/index.jsp).

The genomic DNA of pigs was extracted from their blood samples using a standard protocol. A total of 2,005 pigs from both LR (1,041) and YS (964) breeds were genotyped using the Illumina PorcineSNP60 v2 BeadChip panel, which comprised 61,565 SNP (single nucleotide polymorphism) markers [8]. The quality control (QC) procedure for the genotype data included the deletion of individuals with pedigree errors, removal of monomorphic SNP genotypes, SNPs on sex chromosomes or SNPs with minimum allele frequencies (<0.9), genotype call rate of <0.90, animal missing rate of >0.90, Hardy-Weinberg equilibrium of 0.15, and the SNPs with displaced segregation distortion [9,10]. After QC, the final dataset contained genotypes from a total of 1,915 pigs (LR, 1,029; YS, 886). The total number of autosomal SNPs was reduced to 37,779 in LR and 41,503 in YS, respectively. The correlations of off-diagonal elements of G and A₂₂ matrices were 0.75 and 0.76 for LR and YS, respectively.

The variances, covariances, and various model parameters obtained from the studied models for LR and YSs are presented in Tables 1 and 2, respectively. The Akaike information criterion (AIC) parameter of the pedigree-classical model was higher than the pedigree-social model in both breeds. This result showed that model including SGE fitted the data significantly better than a classical animal model. In addition, AIC parameter of the pedigree-social model was the highest in both breeds compared with those of all ssGBLUP methods. The AIC as an indicator of the goodness fit of the models indicates that the ssGBLUP models performed better in general, which was as expected due to the addition of genomic information alongside the pedigree relationship. This is a feasible approach with a single-step method as it provides more accurate predictions for both genotyped and nongenotyped animals [6,11,18,19]. Therefore, a ssGBLUP analysis including SGE in the model would be a better choice for the prediction of traits in pigs. However, differences were observed among the various model fits with different scaling factors in the single-step methods. Among the ssGBLUP models, the model with ω of 1.0 showed the worst fit, regardless of the breed. The best fitting models in this study were those with ω_0.6 and ω_0.5 in LR (Table 1) and YR (Table 2), respectively, as indicated by them having the lowest AIC estimates. The model AIC value increased with any level of ω other than 0.6 and 0.5 in LR and YS, respectively, indicating the worse fit of those models. Our results obtained through testing different levels of ω (0.1 to 1.0) indicate that a ssGBLUP method essentially relies on tuning the scales of matrices related to pedigree and genotype relationships, which will lead to less biased model estimates [6,15,17,20–22]. This study strongly coincides with many previous reports in that the choices of appropriate levels of constants (τ and ω) are rather arbitrary, and are to be determined through fine tuning. For instance, Misztal et al [17] reported the best combination of τ = 1.5 and ω = 0.6 in their study on dairy cattle. Another study in dairy cattle by Harris et al [23] also used both parameters at levels as low as 0.5. Likewise, Koivula et al [20] reported using various combinations of A and G matrices to find the best option in their study. In pig, Christensen et al [6] suggested a single-step method that is adjusted for the genomic relationship matrix. In another study by Misztal et al [24], a model with slower convergence at ω values greater than 1 was reported, as their H matrix was found to be nonpositive at higher values of this constant. In this context, it is crucial to find appropriate scaling parameters that will ensure better accuracy, lower bias, and easier convergence. It is also important to consider appropriate weights for relationship matrices through scaling factors as any smaller constant for ω is likely to decrease the emphasis on the genomic relationships and increase the importance of the pedigree relationships [20]. This might explain our estimates obtained with levels of ω lower than those in best fit models, where model estimates might have been associated with some biases due to the lower weight in genotyped animals through their genomic relationships.

The genetic variances and total heritability estimates (T²) were mostly higher with ssGBLUP than in the pedigree-based analysis (Tables 1, 2). Among the ssGBLUP models, the genetic variances and T² were increased by decreasing ω in both breeds. Therefore, the T² of ω_0.1 model was the highest in both breeds (LR, 0.64; YS, 0.88). The best single-step models (ΔAIC = 0) showed larger estimates of direct and social variances than pedigree-based methods, and thus also larger covariance estimates, resulting in higher total heritability estimates with those models. The T² estimates with the best fitting models were 0.54 and 0.80 in LR and YS, respectively. They were also greater than those of the pedigree-based analysis method by 0.13 and 0.22 in these two breeds, respectively. However, our T² estimates for LR with the ω₁₀ model coincided strongly with those of Bergsma et al [25] and Duijvesteijn [3]. Comparing the breeds, both direct and social genetic contributions were higher in YS than in LR, so their T² estimates also exhibited the same trend. Note that even when the social variance is markedly smaller than direct genetic variance, its contribution to σTBV2 would be substantial due to the factor (n–1)², especially when group sizes are large, as was the case with YS. The lower T² estimates in LR could also be due to the larger nongenetic litter effects and negative covariances between direct and social effects. According to Bijma et al [1], the positive covariance between direct and social genetic variances is likely to increase the total heritable variation, which coincides well with the present study. The correlation coefficients between DBV and SBV were somewhat weaker in LR (−0.05 to 0.09) than in YS (0.28 to 31). Some earlier reports [2,3,26] also stated somewhat similar correlations, mostly positive but not significant. In this study, the positive correlation in YS could indicate that their pen mates might also have stimulated a greater ADG. Given that SBV is passed on to pen mates, the positive genetic correlation between the direct and associative effects indicates that pigs with a high DBV will also have a high SBV. In other words, the YR pigs in our study may show more positive responses to selection for social interactions than the LR pigs. Nonetheless, breed differences for social interactions are not unlikely. Bergsma et al [2] suggested that the absence of conflict between an individual’s own growth and mate growth might be a consequence of neutral or slightly cooperative social interactions. For the negative or neutral associative effects in LR pigs in this study, it is possible that these pigs were in less competition for food and growth as the amount of space that each of them had on average (3 to 8 pigs/9 m² pen) was lower than that of YR (4 to 10 pigs/9 m² pen).

Table 3 illustrates the accuracy for breeding values obtained with different models. The levels of theoretical accuracy obtained for DBV with PED_classic and PED_social models in each breed were same and also the lowest among the different models (LR, 0.52; YS, 0.55). The ω_1.0 models also performed poorly in DBV prediction (LR, 0.55; YS, 0.58). Among the ssGBLUP models, the theoretical accuracy of DBV was increased by decreasing ⌐ω in both breeds (LR, 0.55 to 0.66; YS, 0.58 to 0.64). The best fit models based on AIC exhibited an increase of accuracy by 5% to 8% compared with the ω_1.0 models in both breeds. The ranges of SBV accuracies with the PED_social in LR and in YS were 0.16 and 0.31, respectively. Similar to DBV, both PED_social and ω_1.0 models performed poorly in SBV prediction. However, unlike the DBVs from the single-step methods, the best fitting models exhibited notable increases in SBV accuracies by 39% (LR) and 19% (YS) with ω_0.6 and ω_0.5, respectively, compared with each of the breed’s worst fit (ω_1.0) model. In cross validation, the correlations between CBV and corrected phenotype were also mostly higher with ssGBLUP than in the pedigree-based analysis. However, there were little differences among the ssGBLUP models. The ranges of correlations between CBV and corrected phenotype in LR and YS were 0.31 to 0.33 and 0.21 to 0.22, respectively. The correlative prediction methods showed more variability in terms of ranking of models across traits and replicates so care should be taken interpreting these results with small sample sizes [27]. Putz et al [27] also suggested that for within-breed selection, theoretical accuracy using the prediction error variance was consistent and accurate in ssGBLUP. However, selection programmes should be careful which validation method they choose and should inspect multiple methods if possible [27]. Therefore, to minimize AIC and to increase theoretical accuracy in this study, the optimal values of ω in LR and YS were 0.6 and 0.5, respectively. Martini [28] reported that increasing τ or decreasing ω may mainly decrease inflation by decreasing the variance of the estimated breeding values, which indicate the possibility of further adjustment of τ in the H matrix.

The phenotypic variability of some traits that are expressed in the social environment could be significantly influenced by SGEs. Earlier reports on such traits, for instance, social dominance or aggressiveness, also suggested that SGEs can substantially influence total phenotypic variability [29–32]. The importance of SGEs can also be recognized from many previous reports [33–35], which showed that the higher SBV and some desirable characteristics in pigs i.e., fearlessness, stress-tolerance are associated to each other. These characteristics in commercial pig production are particularly beneficial for ease of farm management. For this reason, appropriate attention to such socially influenced traits alongside the pig population structure is vital when genomic selection is considered [36]. Certain strategies could also be applied during selection to achieve a high SBV for a desirable trait. One such approach is to select animals with higher TBVs to improve group performance, especially for growth traits [1–3]. Direct selection of pigs for SBV could be another strategy to alter their social behavior. Earlier evidence suggested that high SBV, due to apathy of the animal, could reduce negative social effects on the growth of others [37–39]. Moreover, the inclusion of SNP effects with SGEs in the model could provide better predictions [40]. For successful realization of TBV, it is also important to consider social environments, such as the mixing method of suckling piglets [41].