View Full Table | Close Full ViewTable 1.

A summary of alternative random effect models applied to the data

 
Model Random effects1 Description
1 A + PE + E Typical repeated records model. Ignores group structures.
2 A + PE + P + E Model 1 + nongenetic spatial or pen specific effects, estimated across groups
3 A + PE + G + E Model 1 + nongenetic group effects. Group is effectively pen ´ subset sows housed together until farrowing
4 A + PE + G + S + E Model 1 + group + social genetic effects
5 A + PE + S + E Model 4 excluding nongenetic group effects
6 A + PE + G + S + En Model 4 + heterogeneous residuals
7 A + PE + S + E Model 5 + covariance (A, S)
8 A + PE + Sd + E Model 5 + covariance (A, S) + dilution (Sd)
9 A + PE + S + En Model 5 + covariance (A, S) + heterogeneous residuals
10 A + PE + Sd + En Model 5 + covariance (A, S) + dilution (Sd) + heterogeneous residuals
1A, additive genetic; PE, sow permanent environment; P, pen; G, gestation group (in pen); S, social genetic; E, residual; Sd, social genetic effects modeled with dilution factors; En, residuals modeled to n levels, as defined by nmax.



View Full Table | Close Full ViewTable 2.

Raw data characteristics for augmented and censored data

 
Trait1 n Mean (SD) Minimum Maximum CV (×100%)
TB 10,748 11.41 (3.58) 0 26 31.4
TB censored 10,663 11.50 (3.45) 1 26 30.0
NBA 10,748 10.18 (3.44) 0 21 33.8
NBA censored 10,663 10.26 (3.33) 0 21 32.5
GL 10,748 116.9 (2.21) 73 130 1.9
GL censored 10,663 117.0 (1.79) 109 130 1.5
1TB, total born; NBA, number born alive; GL, gestation length.



View Full Table | Close Full ViewTable 3.

Model comparisons for parameter estimates assuming homogenous residual variance and zero covariance between additive and social genetic effects1

 
Model σ2a σ2pe σ2g σ2s σ2e σ2p h2 pe2 g2 s2 T2 LogL ΔAIC
Total born (pigs/litter)
1 1.281 1.225 ne ne 8.76 11.3 0.11 ± 0.02 0.11 ± 0.02 ne ne ne −18,279.70 15.5
2 1.280 1.222 0.0153 ne 8.75 11.3 0.11 ± 0.02 0.11 ± 0.02 0.001 ± 0.002 ne ne −18,279.46 17.1
3 1.266 1.203 0.156 ne 8.64 11.3 0.11 ± 0.02 0.11 ± 0.02 0.010 ± 0.006 ne ne −18,276.69 11.5
4 1.220 1.212 0.0416 0.0210 8.64 11.2 0.11 ± 0.02 0.11 ± 0.02 0.004 ± 0.007 0.002 ± 0.001 0.16 ± 0.02 −18,270.78 1.70
5 1.218 1.216 ne 0.0240 8.67 11.2 0.11 ± 0.02 0.11 ± 0.02 ne 0.002 ± 0.001 0.16 ± 0.02 −18,270.93 0
6 1.220 1.212 0.0421 0.0210 8.56 11.1 0.11 ± 0.02 0.11 ± 0.02 0.004 ± 0.007 0.002 ± 0.001 0.16 ± 0.03 −18,270.74 3.62
8.66 11.2 0.11 ± 0.02 0.11 ± 0.02 0.004 ± 0.007 0.002 ± 0.001 0.16 ± 0.03
Number born alive (pigs/litter)
1 1.185 1.003 ne ne 7.92 10.1 0.12 ± 0.02 0.10 ± 0.02 ne ne ne −17,698.19 10.2
2 1.184 1.003 0.0178 ne 7.90 10.1 0.12 ± 0.02 0.10 ± 0.02 0.002 ± 0.002 ne ne −17,697.81 11.5
3 1.168 0.985 0.1651 ne 7.78 10.1 0.12 ± 0.02 0.10 ± 0.02 0.020 ± 0.006 ne ne −17,694.10 4.04
4 1.132 0.994 0.0900 0.0140 7.79 10.1 0.11 ± 0.02 0.10 ± 0.02 0.009 ± 0.007 0.001 ± 0.001 0.15 ± 0.02 −17,691.24 0.32
5 1.127 1.002 ne 0.0201 7.84 10.1 0.11 ± 0.02 0.10 ± 0.02 ne 0.002 ± 0.001 0.16 ± 0.02 −17,692.08 0
6 1.132 0.993 0.0885 0.0144 8.03 10.3 0.11 ± 0.02 0.10 ± 0.02 0.009 ± 0.007 0.001 ± 0.001 0.14 ± 0.02 −17,690.84 1.52
7.73 10.0 0.11 ± 0.02 0.10 ± 0.02 0.009 ± 0.007 0.001 ± 0.001 0.15 ± 0.03
Gestation length (days)
1 1.270 0.812 ne ne 2.07 4.15 0.31 ± 0.02 0.20 ± 0.03 ne ne ne −12,384.43 20.6
2 1.270 0.812 0.0002 ne 2.07 4.15 0.31 ± 0.02 0.20 ± 0.03 0.000 ± 0.002 ne ne −12,384.43 22.6
3 1.257 0.818 0.0535 ne 2.02 4.15 0.30 ± 0.02 0.20 ± 0.03 0.013 ± 0.005 ne ne −12,380.99 15.7
4 1.229 0.831 0.0198 0.0069 2.02 4.13 0.30 ± 0.02 0.20 ± 0.03 0.005 ± 0.006 0.002 ± 0.001 0.34 ± 0.03 −12,376.35 8.46
5 1.228 0.833 ne 0.0084 2.02 4.13 0.30 ± 0.02 0.20 ± 0.03 ne 0.002 ± 0.001 0.35 ± 0.03 −12,376.66 7.08
6 1.216 0.819 0.0259 0.0060 1.73 3.82 0.32 ± 0.03 0.21 ± 0.03 0.007 ± 0.007 0.002 ± 0.001 0.36 ± 0.03 −12,371.12 0
2.10 4.19 0.29 ± 0.02 0.20 ± 0.02 0.006 ± 0.006 0.001 ± 0.001 0.33 ± 0.03
1σ2a, additive genetic variance; σ2pe, permanent environmental variance; σ2g, group variance (group membership is defined by pen in model 2 and pen × gestation group in model 3); σ2s, variance due to social genetic effects; σ2e, residual variance; σ2p, phenotypic variance; h2 = σ2a/σ2p; pe2 = σ2pe/σ2p; g2 = σ2g/σ2p; s2 = σ2s/σ2p; T2 = [σ2a +(6 − 1) 2σ2s]/σ2p; LogL, log-likehood; ΔAIC, change in Akaike’s information criteria from the best (minimum) model AIC; ne, not estimated; parameters are presented using both levels of residuals in calculations for model 6.



View Full Table | Close Full ViewTable 4.

Parameter estimates from models fitting different dilution factors1

 
Dilution Model σ2a σ2pe σ2s σas σ2e σ2p h2 pe2 s2 T2 ras ΔAIC
Total born (pigs/litter)
0 7 1.229 1.220 0.017 0.056 8.69 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.38 ± 0.22 29.2
0.2 8 1.226 1.221 0.020 0.055 8.68 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.35 ± 0.21 29.5
0.4 8 1.225 1.222 0.021 0.053 8.68 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.32 ± 0.19 30.1
0.6 8 1.226 1.222 0.023 0.049 8.68 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.29 ± 0.19 31.4
0.8 8 1.230 1.221 0.022 0.045 8.68 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.27 ± 0.19 33.5
1 8 1.237 1.219 0.019 0.040 8.68 11.3 0.11 ± 0.02 0.11 ± 0.02 0.002 ± 0.001 0.19 ± 0.03 0.26 ± 0.19 36.7
Custom 8 1.201 1.306 0.059 0.002 8.43 11.2 0.11 ± 0.02 0.12 ± 0.02 0.005 ± 0.001 0.24 ± 0.03 0.00 ± 0.12 0
Number born alive (pigs/litter)
0 7 1.134 1.007 0.013 0.053 7.87 10.1 0.11 ± 0.02 0.10 ± 0.02 0.001 ± 0.001 0.20 ± 0.03 0.44 ± 0.25 28.4
0.2 8 1.132 1.007 0.015 0.053 7.87 10.1 0.11 ± 0.02 0.10 ± 0.02 0.001 ± 0.001 0.20 ± 0.03 0.41 ± 0.23 28.6
0.4 8 1.130 1.007 0.016 0.052 7.86 10.1 0.11 ± 0.02 0.10 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.38 ± 0.22 29.1
0.6 8 1.130 1.006 0.017 0.050 7.86 10.1 0.11 ± 0.02 0.10 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.36 ± 0.21 30.1
0.8 8 1.133 1.004 0.017 0.047 7.86 10.1 0.11 ± 0.02 0.10 ± 0.02 0.002 ± 0.001 0.20 ± 0.03 0.34 ± 0.21 31.8
1 8 1.139 1.002 0.015 0.043 7.87 10.1 0.11 ± 0.02 0.10 ± 0.02 0.001 ± 0.001 0.19 ± 0.03 0.33 ± 0.22 34.2
Custom 8 1.101 1.107 0.056 0.0002 7.59 10.1 0.11 ± 0.02 0.11 ± 0.02 0.006 ± 0.001 0.25 ± 0.03 0.00 ± 0.12 0
Gestation length (d)2
0 9 1.231 0.835 0.006 0.024 1.76 3.85 0.32 ± 0.03 0.21 ± 0.03 0.001 ± 0.001 0.42 ± 0.04 0.31 ± 0.19 0.32
0.2 10 1.217 0.823 0.007 0.026 1.75 3.85 0.32 ± 0.03 0.21 ± 0.03 0.002 ± 0.001 0.42 ± 0.04 0.29 ± 0.17 0
0.4 10 1.215 0.824 0.008 0.025 1.74 3.85 0.32 ± 0.03 0.21 ± 0.03 0.002 ± 0.001 0.43 ± 0.04 0.26 ± 0.17 0.06
0.6 10 1.215 0.823 0.008 0.025 1.74 3.84 0.32 ± 0.03 0.21 ± 0.03 0.002 ± 0.001 0.43 ± 0.04 0.25 ± 0.16 0.8
0.8 10 1.218 0.821 0.008 0.025 1.73 3.83 0.32 ± 0.03 0.21 ± 0.03 0.002 ± 0.001 0.43 ± 0.04 0.27 ± 0.16 2.64
1 10 1.226 0.816 0.006 0.026 1.73 3.83 0.32 ± 0.03 0.21 ± 0.03 0.001 ± 0.001 0.43 ± 0.04 0.32 ± 0.18 5.64
Custom 10 1.231 0.823 0.006 0.024 2.03 4.16 0.30 ± 0.02 0.20 ± 0.02 0.001 ± 0.001 0.39 ± 0.04 0.28 ± 0.18 10.7
1σ2a, additive genetic variance; σ2pe, permanent environmental variance; σ2s, variance due to social genetic effects; sas, covariance between additive and social genetic effects; σ2e, residual variance; σ2p, phenotypic variance; h2 = σ2a/σ2p; pe2 = σ2pe/σ2p; s2 = σ2s/σ2p; T2 = [σ2a + (6 − 1) 2σ2s]/σ2p; ras, correlation between additive and social genetic effects; ΔAIC, change in Akaike’s information criteria from the best (minimum) model AIC.
2Variances and parameter estimates presented for group size class ≤4 only; entries of 0.00 indicate that the value was ≤0.01.