Animal phenotypes
Data were provided by Sunjin, the Korean company for pig genetic evaluation (Yorkshire Sunjin, Danyang, Korea,
http://dad.fao.org/). The breeder had selected pigs focused on reproductive traits, such as litter size. Pedigree was traced back 3 generations and included 37,858 animals with 385 sires, and 2,520 dams. A total of 37,745 animals with both sire and dam known were included.
The phenotypic dataset on the growth rate of animals was obtained from performance tests of Yorkshire pigs born between 2001 and 2015 (
N = 33,120). A total of 4 to 14 pigs of the same gender were kept in each pen to form the groups of pigs and the average group size was 8.2±2.0 pigs. The space allowance per pig was 0.8 to 1.2 m
2 at the start of the performance test. The 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 performance evaluations of the ADG of pigs started soon after each animal reached a live body weight of 30 kg and continued until a target weight of 90 kg was attained. On average, fewer than 160 days was required to attain this target weight. The average ADG was recorded to be 802±93 g/d.
The phenotypic records of the reproductive traits for 11,654 pigs born between 2001 and 2014 were evaluated in this study. Gilts at selection were contemporaries and managed under the same conditions (a single pen). Age at first mating of gilts was typically 230 to 250 d and mating was conducted twice (24 h and 36 h after mounting) by artificial insemination. All the naturally farrowed sows had a lactation period of 24 to 28 days. The breeder culled the pigs that showed repeated gestation failure or low reproductive performance. The average culling parity was 4.96±2.85, with a range of 1 to 15. STAY, binary response variable defined as the ability of a sow to survive until its second parity. The average STAY was recorded to be 1.85±0.35. NBA1 was recorded to be 10.38±2.84 piglets.
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:
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,Iσg2), 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,Iσe2). 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
(Average group size-1Group size-1) was added to the SGE and early-life environmental effects. DGE and SGE had the following multivariate normal (MVN) distribution:
in which C is defined by the matrix,
where,
σaD2 is variance of direct breeding values (DBV) for each trait,
σaS2 is variance of social breeding values (SBV) for ADG, σaDaS is the covariance between DBV and SBV on same or different traits, σaDaD is the covariance between different DBV, A is pedigree-based relationship matrix, and C⊗A denotes the Kronecker product of two matrices.
The birth litter effect and social early-life environment effect had the following MVN distribution:
in which K is defined by the matrix,
where,
σl2 is variance of birth litter for each trait,
σk2 is variance of social early-life environment effect for ADG,
σlk2 is the covariance between birth litter and social early-life environmental effect on the same or different traits,
σll2 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,
n indicates the average size (8.2 pigs) of social groups. The TBV is the heritable effect of an individual on trait values in the population, which is the sum of the individual’s DBV (
aD,i) of its own phenotype and the SBV (
aS,i) of the phenotypes of its
n–1 group mates. Moreover, Bijma [
7] stated that the total heritable variance (
σTBV2) determines the population’s potential response to selection and can be expressed as:
According to Canario et al [
9], the phenotypic variance (
σP2) for ADG for such a model can be calculated as follows:
The total heritable variance for ADG can be expressed relative to phenotypic variance [
13] as follows:
For STAY and NBA1, heritability estimates were calculated according to the equations below:
The covariance of between TBV for ADG (TBVADG) and DBV of STAY or NBA1 (DBVREP) was computed as:
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).