Genetic association between sow longevity and social genetic effects on growth in pigs

Objective Sow longevity is important for efficient and profitable pig farming. Recently, there has been an increasing interest in social genetic effect (SGE) of pigs on stress-tolerance and behavior. The present study aimed to estimate genetic correlations among average daily gain (ADG), stayability (STAY), and number of piglets born alive at the first parity (NBA1) in Korean Yorkshire pigs, using a model including SGE. Methods The phenotypic records of ADG and reproductive traits of 33,120 and 11,654 pigs, respectively, were evaluated. The variances and (co) variances of the studied traits were estimated by a multi-trait animal model applying the Bayesian with linear-threshold models using Gibbs sampling. Results The direct and SGEs on ADG had a significantly negative (−0.30) and neutral (0.04) genetic relationship with STAY, respectively. In addition, the genetic correlation between the social effects on ADG and NBA1 tended to be positive (0.27), unlike the direct effects (−0.04). The genetic correlation of the total effect on ADG with that of STAY was negative (−0.23) but non-significant, owing to the social effect. Conclusion These results suggested that total genetic effect on growth in the SGE model might reduce the negative effect on sow longevity because of the growth potential of pigs. We recommend including social effects as selection criteria in breeding programs to obtain satisfactory genetic changes in both growth and longevity.


INTRODUCTION
Sow longevity is most important factor for production efficiency and profitable pig farming. To ensure profitability for the producer, a sow should produce at least three litters before culled. The optimal time to replace a sow depends on factors such as the sow' s performance, its housing, feeding, and insemination costs, and the cost and genetic merit of the replacement gilt compared to the sow being replaced [1]. Early culling results in less piglets born alive over the sow's lifetime and leads to irregular replacement of sows. The longevity can be measured using stayability (STAY) to a certain age. STAY is the ability of a sow to survive until a specific parity in its life and is related to the number of piglets born alive over the lifetime [2]. Several studies estimated the heritability of STAY in sows and tried to find its early indicators, such as leg conformation [2][3][4][5]. Sows can be stressed in various stages (e.g., mating, gestation, and farrowing). Maternal stress during gestation can affect the physiological development of suckling piglets [6]. Low reproductive performance due to these stresses can result in the early culling of sows.
Recently, there has been an increasing interest in the relationship of social interaction of pigs with stress-tolerance and behavior. The genetic effect of an individual on the pheno-

Statistical analysis
The variances and (co) variances of the studied traits were estimated by an animal multi-trait model applying the Bayesian with linear-threshold models using Gibbs sampling. For ADG, the effects of birth year-month (168 levels), sex (male or female), and group size (11 levels) were fitted as fixed effects. In the model, age and age squared at target weight were fitted as covariates. The models also included the random effects of group identity (4,927 levels) and birth litter (8,712 levels). We accounted social early-life environmental effects (birth litter of piglets within a group) in the model to avoid bias in the estimated genetic parameters for social effects [9]. For STAY and NBA1, the effects of farrowing year-month at first parity (169 levels) were used as fixed effects and birth litter (5,365 levels) was used as a random effect.
Animals were fitted as a random effect in the model. The statistical model for each group of traits is presented below: y = Xb+Z D a D +Z S a S +W c +Vg+T pe +Ul+Qk+e(ADG), y = Xb+Z D a D +Ul+e(STAY,NBA1), where, y is the vector of observations, b is the vector of fixed effects, a D is the vector of direct genetic effects (DGE), a S is the vector of SGE, g is the vector of random group, where g ~N(0, 5 riod of 24 to 28 days. The breeder culled the pigs that showed repeated gestation failure or low productive performance. The average culling parity was 4.96±2.85, with a range of 1 to 15. STAY, nary response variable defined as the ability of a sow to survive until its second parity. The average TAY was recorded to be 1.85±0.35. NBA1 was recorded to be 10.38±2.84 piglets.

tatistical analysis
he variances and (co) variances of the studied traits were estimated by an animal multi-trait model plying the Bayesian with linear-threshold models using Gibbs sampling. For ADG, the effects of birth ar-month (168 levels), sex (male or female), and group size (11 levels) were fitted as fixed effects. In e model, age and age squared at target weight were fitted as covariates. The models also included the ndom effects of group identity (4,927 levels) and birth litter (8,712 levels). We accounted social earlyfe environmental effects (birth litter of piglets within a group) in the model to avoid bias in the timated genetic parameters for social effects [9]. For STAY and NBA1, the effects of farrowing yearonth at first parity (169 levels) were used as fixed effects and birth litter (5,365 levels) was used as a ndom effect.
Animals were fitted as a random effect in the model. The statistical model for each group of traits presented below: y = Xb + Z D a D + Z S a S + W c + Vg + T pe + Ul + Qk + e (ADG), y = Xb + Z D a D + Ul + e (STAY, NBA1), here, y is the vector of observations, b is the vector of fixed effects, aD is the vector of direct genetic fects (DGE), aS is the vector of SGE, g is the vector of random group, where ~N(0, 2 ), l and k e the vectors of random birth litter and social early-life environment effect, respectively, and e is the ctor of residuals, where, ~N(0, 2 ). X, ZD, ZS, W, V, T, U, and Q are the corresponding incidence ), l and k are the vectors of random birth litter and social early-life environment effect, respectively, and e is the vector of residuals, where, e ~N(0, 5 reproductive performance. The average culling parity was 4.96±2 98 binary response variable defined as the ability of a sow to survive 99 STAY was recorded to be 1.85±0.35. NBA1 was recorded to be 10 100 101

Statistical analysis 102
The variances and (co) variances of the studied traits were estima 103 applying the Bayesian with linear-threshold models using Gibbs sam 104 year-month (168 levels), sex (male or female), and group size (11 l 105 the model, age and age squared at target weight were fitted as cova 106 random effects of group identity (4,927 levels) and birth litter (8,71 107 life environmental effects (birth litter of piglets within a group) 108 estimated genetic parameters for social effects [9]. For STAY and N 109 month at first parity (169 levels) were used as fixed effects and bir 110 random effect. ). X, Z D , Z S , W, V, T, U, and Q are the corresponding incidence matrices. To account for the differences in group size, as suggested by Canario et al [9], an additional covariate term known as dilution matrices. To account for the differences in group size, as suggested by Canario et al [9], an additional 123 ] ~ MVN (0, C ⊗ A), in which C is defined by the matrix, 127 ] ~ MVN (0, C ⊗ A), in which C is defined by the matrix, 127 , 129 in which C is defined by the matrix, where, 2 is variance of direct breeding values (DBV) for each trait, 2 is variance of social 131 breeding values (SBV) for ADG, is the covariance between DBV and SBV on same or different 132 traits, is the covariance between different DBV, A is pedigree-based relationship matrix, and C 133 ⊗ A denotes the Kronecker product of two matrices. 134 The birth litter effect and social early-life environment effect had the following MVN distribution: 135 where, 2 is variance of direct breeding values (DBV) for each trait, 2 is variance of social 131 breeding values (SBV) for ADG, is the covariance between DBV and SBV on same or different 132 traits, is the covariance between different DBV, A is pedigree-based relationship matrix, and C 133 ⊗ A denotes the Kronecker product of two matrices. 134 The birth litter effect and social early-life environment effect had the following MVN distribution: 135 , 139 is variance of direct breeding values (DBV) for each trait, fined by the matrix, , BV) for each trait, 2 is variance of social nce between DBV and SBV on same or different , A is pedigree-based relationship matrix, and C ent effect had the following MVN distribution: ] , is variance of social breeding values (SBV) for ADG, 6 ~ MVN (0, C ⊗ A), in which C is defined by the matrix, , variance of direct breeding values (DBV) for each trait, 2 is variance of social (SBV) for ADG, is the covariance between DBV and SBV on same or different the covariance between different DBV, A is pedigree-based relationship matrix, and C e Kronecker product of two matrices.
ter effect and social early-life environment effect had the following MVN distribution: , is the covariance between DBV and SBV on same or different traits, ( , 139 140 is the covariance between different DBV, A is pedigree-based relationship matrix, and C ( 1) ( ) , 139 140 A denotes the Kronecker product of two matrices.
The birth litter effect and social early-life environment effect had the following MVN distribution: ] ~ MVN (0, C ⊗ A), in which C is defined by the matrix, 127 , 129 130 where, 2 is variance of direct breeding values (DBV) for each trait, 2 is variance of social 131 breeding values (SBV) for ADG, is the covariance between DBV and SBV on same or different 132 traits, is the covariance between different DBV, A is pedigree-based relationship matrix, and C 133 ⊗ A denotes the Kronecker product of two matrices. 134 The birth litter effect and social early-life environment effect had the following MVN distribution: 135 , 139 140 in which K is defined by the matrix, ] ~ MVN (0, C ⊗ A), in which C is defined by the matrix, 127 , 129 130 where, 2 is variance of direct breeding values (DBV) for each trait, 2 is variance of social 131 breeding values (SBV) for ADG, is the covariance between DBV and SBV on same or different 132 traits, is the covariance between different DBV, A is pedigree-based relationship matrix, and C 133 ⊗ A denotes the Kronecker product of two matrices. 134 The birth litter effect and social early-life environment effect had the following MVN distribution: 135 where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV 146 of the i animal is defined as follows: According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV 146 of the i animal is defined as follows: phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 is variance of social early-life environment effect for ADG, where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV 146 of the i animal is defined as follows: phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 is the covariance between birth litter and social early-life environmental effect on the same or different traits, where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV 146 of the i animal is defined as follows: phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 158 is the covariance between birth litter on different traits, and I is an identity matrix of appropriate dimensions.
According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV of the i animal is defined as follows: where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 161 of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that the total heritable variance where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 161 determines the population's potential response to selection and can be expressed as: where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 According to Canario et al [9], the phenotypic variance where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The TBV phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 for ADG for such a model can be calculated as follows: where, 2 is variance of birth litter for each trait, 2 is variance of social early-life environment 141 effect for ADG, 2 is the covariance between birth litter and social early-life environmental effect on 142 the same or different traits, 2 is the covariance between birth litter on different traits, and I is an 143 identity matrix of appropriate dimensions. 144 According to Bijma [7], for traits affected by heritable social effects, the variance of total breeding 145 values (TBV) for ADG represents the total heritable variation that is exploitable for selection. The phenotype and the SBV ( , ) of the phenotypes of its n-1 group mates. Moreover, Bijma [7] stated that 153 the total heritable variance ( 2 ) determines the population's potential response to selection and can 154 be expressed as: 155 According to Canario et al [9], the phenotypic variance ( 2 ) for ADG for such a model can be 159 calculated as follows: 160 The total heritable variance for ADG can be expressed relative to phenotypic variance [13] as 164 The total heritable variance for ADG can be expressed relative to phenotypic variance [13] as follows: The covariance of between TBV for ADG (TBV ADG ) and DBV of STAY or NBA1 (DBV REP ) was computed as: To fit a model, THRGIBBS1F90 with Bayesian inference using Gibbs sampling was used [14]. T 178 Gibbs samplers were run as single chains of 1,200,000 rounds. The first 600,000 rounds discarded 179 burn-in thinning every 100 samples. This resulted in 6,000 samples being used for post-Gibbs analy 180 completed using POSTGIBBSF90 [14]. Significant difference from zero was based on the high 181 posterior density, which signifies a 95% confidence interval for the estimate (p<0.05). The (co)variances and parameters obtained from the model studied are presented in Table 1. All gen 187 variances were significantly larger than zero. 188 Average daily gain in social genetic effect model: The T 2 estimates for ADG was 0.48±0.05 189 were greater than classical heritability (h 2 = 0.34±0.02). The contribution of social genetic varia 190 (7.2 2 × 2 ) was 27% of the total heritable variance ( 2 ). Notably, even when the social variance w 191 To fit a model, THRGIBBS1F90 with Bayesian inference using Gibbs sampling was used [14]. The Gibbs samplers were run as single chains of 1,200,000 rounds. The first 600,000 rounds discarded as burn-in thinning every 100 samples. This resulted in 6,000 samples being used for post-Gibbs analyses completed using POSTGIBBSF90 [14]. Significant difference from zero was based on the highest posterior density, which signifies a 95% confidence interval for the estimate (p<0.05).

Heritability estimation
The (co)variances and parameters obtained from the model studied are presented in Table 1. All genetic variances were significantly larger than zero.
Average daily gain in social genetic effect model: The T 2 estimates for ADG was 0.48±0.05 and were greater than classical heritability (h 2 = 0.34±0.02). The contribution of social genetic variance (7. To fit a model, THRGIBBS1F90 with Bayesian inference using Gibbs sampling was used [14]. The 178 Gibbs samplers were run as single chains of 1,200,000 rounds. The first 600,000 rounds discarded as 179 burn-in thinning every 100 samples. This resulted in 6,000 samples being used for post-Gibbs analyses 180 completed using POSTGIBBSF90 [14]. Significant difference from zero was based on the highest 181 posterior density, which signifies a 95% confidence interval for the estimate (p<0.05). The (co)variances and parameters obtained from the model studied are presented in Table 1. All genetic 187 variances were significantly larger than zero. 188 Average daily gain in social genetic effect model: The T 2 estimates for ADG was 0.48±0.05 and 189 were greater than classical heritability (h 2 = 0.34±0.02). The contribution of social genetic variance 190 (7.2 2 × 2 ) was 27% of the total heritable variance ( 2 ). Notably, even when the social variance was 191 ). Notably, even when the social variance was markedly smaller than the direct genetic variance, its contribution to markedly smaller than the direct genetic variance, its contribution to 2 was largely due to the factor 192 (n-1) 2 . Our T 2 estimates with high h 2 for ADG was greater than those of prior studies [9,13] and 193 coincided with those of Duijvesteijn [15]. In this study, the breeder focused on only reproductive traits 194 for pig selection, such as litter size, which might be affected by the substantial genetic variation for 195 growth n the population. 196 Social early-life environmental variance ( 2 = 32±5) was greater than social genetic variance ( 2 197 = 18±5). This result was consistent with those of Canario et al [9] in that individuals experienced early 198 in life affected their social skill in adulthood. Sociable pigs in early-life could solve dominance conflicts 199 with unfamiliar pigs in adult life more quickly when they occurred [16]. Therefore, social effects are 200 due to both genetic and social early-life environmental effects. 201 was largely due to the factor (n-1) 2 . Our T 2 estimates with high h 2 for ADG was greater than those of prior studies [9,13] and coincided with those of Duijvesteijn [15]. In this study, the breeder focused on only reproductive traits for pig selection, such as litter size, which might be affected by the substantial genetic variation for growth n the population. Social early-life environmental variance ( 9 coincided with those of Duijvesteijn [15]. In this study, the breeder focused on only reproductive traits 194 for pig selection, such as litter size, which might be affected by the substantial genetic variation for 195 growth n the population. 196 Social early-life environmental variance ( 2 = 32±5) was greater than social genetic variance ( 2 197 = 18±5). This result was consistent with those of Canario et al [9] in that individuals experienced early 198 in life affected their social skill in adulthood. Sociable pigs in early-life could solve dominance conflicts 199 with unfamiliar pigs in adult life more quickly when they occurred [16]. Therefore, social effects are values than a normal linear model [2,5,18]. A threshold model was used as another form of analysis but 205 the estimated heritability for STAY of the present study was slightly lower than previous results 206 [5,18,19]. Particularly, the birth litter variance (0.19±0.04) was greater than the direct genetic variance 207 (0.10±0.03) in STAY and equaled 15% of the phenotypic variance in STAY. In the present study, the 208 rate of culled pigs before the second parity (STAY = 1) was lower (15%) than those of the other studies 209 [2,5,[17][18][19]. Therefore, the low frequency of STAY value 1 may result in slightly lower heritability. 210 Number of piglets born alive at the first parity: The estimated heritability for NBA1 of the current 211 study was 0.10±0.01 (Table 2). This result was in agreement with those of Engblom et al [2]. In addition, 212 they coincided with those for the total number of piglets born in the first litter of other studies [1,20]. 213

Genetic correlations 215
The estimated genetic correlations from the multivariate analysis are presented in Table 3. 216 Direct breeding value and social breeding values of average daily gain: The genetic correlation 217 = 32±5) was greater than social genetic variance ( was greater than those of prior studies [9,13] and study, the breeder focused on only reproductive traits t be affected by the substantial genetic variation for = 32±5) was greater than social genetic variance ( 2 Canario et al [9] in that individuals experienced early ble pigs in early-life could solve dominance conflicts hen they occurred [16]. Therefore, social effects are ental effects. variate analysis are presented in Table 3. lues of average daily gain: The genetic correlation = 18±5). This result was consistent with those of Canario et al [9] in that individuals experienced early in life affected their social skill in adulthood. Sociable pigs in early-life could solve dominance conflicts with unfamiliar pigs in adult life more quickly when they occurred [16]. Therefore, social effects are due to both genetic and social early-life environmental effects.
Stayability: The estimated heritability for STAY of the present study was 0.07±0.02. The heritability in the present study for STAY agreed with low to moderate heritability (0.06 to 0.18) reported in other studies [2,5,17,18]. Heritability of STAY in the threshold model normally showed greater heritability values than a normal linear model [2,5,18]. A threshold model was used as another form of analysis but the estimated heritability for STAY of the present study was slightly lower than previous results [5,18,19]. Particularly, the birth litter variance (0.19±0.04) was greater than the direct genetic variance (0.10 ±0.03) in STAY and equaled 15% of the phenotypic variance in STAY. In the present study, the rate of culled pigs before the second parity (STAY = 1) was lower (15%) than those of the other studies [2,5,[17][18][19]. Therefore, the low frequency of STAY value 1 may result in slightly lower heritability.
Number of piglets born alive at the first parity: The estimated heritability for NBA1 of the current study was 0.10±0.01 (Table  2). This result was in agreement with those of Engblom et al [2]. In addition, they coincided with those for the total number of piglets born in the first litter of other studies [1,20].

Genetic correlations
The estimated genetic correlations from the multivariate analysis are presented in Table 3.
Direct breeding value and social breeding values of average daily gain: The genetic correlation coefficient between DBV and SBV of ADG was neutral (0.03±0.11). This result strongly agreed with the study of Bergsma et al [8], in that the absence of conflicts between an individual's own growth and mate's growth might be a consequence of neutral or slightly cooperative social interactions. Moreover, Canario et al [9] suggested that a social effect on the growth rate of a group mate had no cost for the individual studied. In addition, the positive or neutral relationship between direct and SGE is likely to increase the total heritable variation [7,8].
Stayability and number of piglets born alive at the first parity: The genetic correlation coefficient between STAY and NBA1 was significantly positive (0.31±0. 16), indicating that the breeder in the current study culled sows based on NBA1. Low reproductive performance is a major reason for culling of sows [19,21]. The risk of culling is greater between the first and second litters than between the second and third litters [17]. Therefore, piglet production, particularly at first parity, is an important factor affecting the breeder's decision to cull sows after first farrowing. In addition, Engblom et al [2] reported that the estimated breeding values for NBA1 had a moderate correlation (0.25) with the number of piglets born alive over a lifetime, after accounting for censoring.
Direct breeding value of average daily gain, stayability, and number of piglets born alive at the first parity: The estimated genetic correlation coefficient between DBV of ADG and STAY was significantly negative (-0.30±0.13), suggesting that animals with high genetic potential for ADG could have a lower STAY. However, the genetic correlation coefficients between the DBV of ADG and NBA1 were neutral (-0.04± 0.07). Although genetic relationship between individual growth and the NBA1 was weak, the pigs with high growth can be              , direct genetic variance; , social genetic variance;   , total heritable variance;     , total heritability for model including social genetic effects; , random group variance;   , covariance between direct and social genetic effects;  at risk of early culling, genetically. Therefore, this risk may be more because of factors other than low piglet production at first parity. The high individual growth rate can cause leg problems such as osteochondrosis [22,23]. In this connection, leg problem is a main factor for culling sows and several studies suggest that leg conformation traits in a growth stage could be good early indicators of STAY [3][4][5][24][25][26].
Social breeding value of average daily gain, stayability, and number of piglets born alive at the first parity: The genetic correlation between the SBV of ADG and STAY was neutral (0.04 ±0.32), whereas that between the SBV of ADG and NBA1 tended to be positive (0.27±0.17), which ranged from -0.05 to 0.60. Maternal stress during gestation can affect the physiological development of suckling piglets [6]. Previous studies showed that higher SBV and some desirable characteristics in pigs, i.e., fearlessness and stress-tolerance, were associated with each other [11,12,27]. Higher SBV could occur because of the apathy of the animal, resulting in reduced negative effects on the growth of others [10,16]. Therefore, the pigs with this apathy may be less affected by various environments. Bailey et al [20] suggested that selection due to SGEs might push distinctive evolutionary dynamics in behaviors, such as competition, cooperation, or reproductive interactions.
Total breeding value of average daily gain, stayability, and number of piglets born alive at the first parity: The genetic correlation between TBV of ADG and STAY was negative (-0.23 ±0.20), but non-significant. Owing to the effect of SBV, this was weaker than the genetic correlation between DBV of ADG and STAY (-0.30±0.13). In addition, the genetic correlation between TBV of ADG and NBA1 (0.11±0.11) was more positive than that between DBV of ADG and NBA1 (-0.04±0.07). The associative component of TBV is expressed not only in individual growth, but also in the growth of group mates [7]. Notably, because each pig interacts with its group mates, TBV of a pig is the sum of DBV and the number of group mates× SBV [8]. In Table 2, the contribution of DBV variance (68%) to TBV was greater than that of SBV variance (27%). Although DBV had more effects than SBV on the genetic correlations of the TBV of ADG with that of other traits, SBV can potentially reduce a negative effect on the DBV of STAY. It was concluded that selection for SGEs on growth could be combined with selection not only for individual growth traits but also for longevity traits of pigs in the absence of antagonistic genetic correlations.

Litter environmental correlation
The correlations of birth litter and social early-life environmental effects are presented in Table 4. Overall, they were relatively low and mostly non-significant. Significant positive correlations were found between birth litter and social early-life environmental effect on ADG (0.43±0.11), which differed from the neutral genetic correlation between DBV and SBV for ADG (0.03±0.11; Table 3). This result indicated that social effects from early-life experiences were dependent on birth litter environment. In other words, positive birth litter environment for growth rate increases social skills later in life. The correlation between birth litter and social early-life environmental effects on ADG was much higher than that of Canario et al [9]. However, our result also suggested that pigs with high social effects on the growth of a group mate did not incur a cost for itself. A significant negative correlation was found between birth litter effects on ADG and STAY (D ADG -D STAY = -0.38±0.13; Table 4), suggesting that pigs in positive litter environment for its growth rate had a poorer STAY. This result was similar to the negative genetic correlation between DBV of ADG and STAY (DBV growth -DBV STAY = -0.30±0.13; Table 3). Canario et al [9] demonstrated that the social skills that pigs develop in their litter environment have a long-lasting effect on the growth of social partners. In addition, previous studies on STAY accounted for the effect of litter on the estimating paraeter [2,17,19]. The early-litter environment can affect phenotype later in life in terms of both growth and longevity traits, and there can be positive or negative correlation between these traits in the litter environment. Therefore, accounting for multivariate litter effect is required in multi-trait estimation of growth rate and STAY.

CONCLUSION
When the heritability of ADG was considered as a SGE, it showed 14% higher value than in a normal model. This can lead to a high genetic gain in swine breeding program. The direct effect on growth rate had a negative genetic relationship with the STAY of sows but social effect on growth rate had a neutral genetic relationship. In addition, the genetic relationship between social effects on ADG and NBA1 tended to be positive, unlike the neutral correlation of the direct effects on ADG and NBA1. Therefore, accounting for social effect is essential for the estimation of growth rate, and selection of the TBV of growth rate might reduce the negative effects of STAY on the individual growth potential of pigs. In addition, there can be positive or negative correlation between direct effect and social effect on growth rate and STAY in the litter environment, suggesting that accounting for multivariate litter effects is important for multi-trait-based estimation of growth rate and STAY. Therefore, the genetic correlations studied showed no antagonism of social effect with longevity. We re commend including social effects as selection criteria in breeding programs for achieving satisfactory genetic changes in both growth and longevity.

CONFLICT OF INTEREST
We certify that there is no conflict of interest with any financial organization regarding the material discussed in the manuscript.