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Table 1 Variance component estimates based on models including or not inbreeding and non-additive genetic effects

From: Investigating the impact of non-additive genetic effects in the estimation of variance components and genomic predictions for heat tolerance and performance traits in crossbred and purebred pig populations

Trait

Modela

\(\widehat{{\sigma }_{a}^{2}}\)

\(\widehat{{\sigma }_{d}^{2}}\)

\(\widehat{{\sigma }_{aa}^{2}}\)

\(\widehat{{\sigma }_{ad}^{2}}\)

\(\widehat{{\sigma }_{dd}^{2}}\)

\(\widehat{{\sigma }_{e}^{2}}\)

T1

MA

0.0477 ± 0.0214

-

-

-

-

1.4103 ± 0.0418

MAI

0.0463 ± 0.0214

-

-

-

-

1.4117 ± 0.0418

MAE

0.0190 ± 0.0229

-

0.1864 ± 0.0942

-

-

1.2540 ± 0.0871

MAIE

0.0169 ± 0.0229

-

0.1880 ± 0.0945

-

-

1.2545 ± 0.0871

MAD

0.0477 ± 0.0214

8.92 × 10−8 ± 0.0000

-

-

-

1.4103 ± 0.0418

MAID

0.0463 ± 0.0214

8.93 × 10−8 ± 0.0000

-

-

-

1.4117 ± 0.0418

MADE1

0.0190 ± 0.0229

8.42 × 10−8 ± 0.0000

0.1864 ± 0.0956

-

-

1.2542 ± 0.0890

MAIDE1

0.0169 ± 0.0229

9.89 × 10−8 ± 0.0000

0.1880 ± 0.0959

-

-

1.2547 ± 0.0890

MADE2

0.0190 ± 0.0229

9.10 × 10−8 ± 0.0000

0.1864 ± 0.0942

9.96 × 10−7 ± 0.0000

-

1.2542 ± 0.0870

MAIDE2

0.0169 ± 0.0229

9.11 × 10−8 ± 0.0000

0.1880 ± 0.0945

1.03 × 10−6 ± 0.0000

-

1.2547 ± 0.0870

MADE3

0.0190 ± 0.0232

8.54 × 10−8 ± 0.0000

0.1864 ± 0.1030

4.67 × 10−7 ± 0.0000

1.16 × 10−6 ± 0.0000

1.2542 ± 0.2248

MAIDE3

0.0169 ± 0.0232

8.45 × 10−8 ± 0.0000

0.1880 ± 0.1033

4.33 × 10−7 ± 0.0000

1.22 × 10−6 ± 0.0000

1.2547 ± 0.2249

T2

MA

0.2945 ± 0.0339

-

-

-

-

0.7975 ± 0.0277

MAI

0.2946 ± 0.0340

-

-

-

-

0.7978 ± 0.0277

MAE

0.2276 ± 0.0355

-

0.2643 ± 0.0766

-

-

0.5943 ± 0.0617

MAIE

0.2263 ± 0.0356

-

0.2665 ± 0.0768

-

-

0.5934 ± 0.0618

MAD

0.2927 ± 0.0339

0.0221 ± 0.0240

-

-

-

0.7766 ± 0.0350

MAID

0.2926 ± 0.0340

0.0224 ± 0.0238

-

-

-

0.7767 ± 0.0350

MADE1

0.2266 ± 0.0354

0.0201 ± 0.0237

0.2625 ± 0.0768

-

-

0.5768 ± 0.0639

MAIDE1

0.2250 ± 0.0355

0.0209 ± 0.0238

0.2651 ± 0.0768

-

-

0.5750 ± 0.0640

MADE2

0.2267 ± 0.0354

0.0201 ± 0.0237

0.2625 ± 0.0768

9.23 × 10−7 ± 0.0000

-

0.5768 ± 0.0639

MAIDE2

0.2250 ± 0.0355

0.0209 ± 0.0238

0.2651 ± 0.0768

9.20 × 10−7 ± 0.0000

-

0.5750 ± 0.0640

MADE3

0.2267 ± 0.0354

0.0201 ± 0.0237

0.2625 ± 0.0768

9.23 × 10−7 ± 0.0000

1.20 × 10−6 ± 0.0000

0.5768 ± 0.0639

MAIDE3

0.2250 ± 0.0355

0.0209 ± 0.0238

0.2651 ± 0.0768

9.20 × 10−7 ± 0.0000

1.20 × 10−6 ± 0.0000

0.5750 ± 0.0640

T3

MA

0.1881 ± 0.0257

-

-

-

-

0.7151 ± 0.0227

MAI

0.1869 ± 0.0256

-

-

-

-

0.7158 ± 0.0227

MAE

0.1049 ± 0.0239

-

0.3895 ± 0.0625

-

-

0.4094 ± 0.0494

MAIE

0.1033 ± 0.0238

-

0.3901 ± 0.0625

-

-

0.4097 ± 0.0494

MAD

0.1857 ± 0.0257

0.0186 ± 0.0207

-

-

-

0.6982 ± 0.0291

MAID

0.1845 ± 0.0256

0.0194 ± 0.0209

-

-

-

0.6982 ± 0.0292

MADE1

0.1048 ± 0.0239

1.10 × 10−7 ± 0.0000

0.3891 ± 0.0632

-

-

0.4090 ± 0.0506

MAIDE1

0.1032 ± 0.0238

1.43 × 10−7 ± 0.0000

0.3897 ± 0.0632

-

-

0.4093 ± 0.0506

MADE2

0.1133 ± 0.0243

2.61 × 10−7 ± 0.0000

0.2550 ± 0.0704

0.4553 ± 0.1227

-

0.0802 ± 0.0991

MAIDE2

0.1118 ± 0.0243

3.08 × 10−7 ± 0.0000

0.2561 ± 0.0705

0.4536 ± 0.1229

-

0.0818 ± 0.0986

MADE3

0.1139 ± 0.0242

1.89 × 10−7 ± 0.0000

0.2656 ± 0.0695

0.0841 ± 0.2002

0.4381 ± 0.1849

1.19 × 10−4 ± 0.0000

MAIDE3b

-

-

-

-

-

-

T4

MA

1.7199 ± 0.1708

-

-

-

-

3.4330 ± 0.1147

MAI

1.7206 ± 0.1710

-

-

-

-

3.4340 ± 0.1148

MAE

1.5743 ± 0.1846

-

0.4672 ± 0.2938

-

-

3.0851 ± 0.2441

MAIE

1.5738 ± 0.1845

-

0.4727 ± 0.2936

-

-

3.0819 ± 0.2444

MAD

1.7172 ± 0.1710

0.0576 ± 0.0847

-

-

-

3.3777 ± 0.1378

MAID

1.7178 ± 0.1711

0.0585 ± 0.0848

-

-

-

3.3779 ± 0.1379

MADE1

1.5794 ± 0.1849

0.0351 ± 0.0835

0.4445 ± 0.2983

-

-

3.0682 ± 0.2476

MAIDE1

1.5790 ± 0.1851

0.0355 ± 0.0826

0.4494 ± 0.2976

-

-

3.0649 ± 0.2480

MADE2

1.5794 ± 8.5400

0.0351 ± 0.4200

0.4445 ± 0.2983

3.10 × 10−7 ± 0.0000

-

3.0681 ± 0.2476

MAIDE2

1.5790 ± 0.1851

0.0355 ± 0.0826

0.4494 ± 0.2976

3.10 × 10−7 ± 0.0000

-

3.0649 ± 0.2480

MADE3

1.5794 ± 0.1849

0.0351 ± 0.0835

0.4445 ± 0.2983

4.91 × 10−7 ± 0.0000

6.38 × 10−6 ± 0.0000

3.0681 ± 0.2476

MAIDE3

1.5790 ± 0.1851

0.0355 ± 0.0826

0.4494 ± 0.2976

4.90 × 10−7 ± 0.0000

6.37 × 10−6 ± 0.0000

3.0649 ± 0.2480

T5

MA

1,310.6200 ± 122.0317

-

-

-

-

2,190.1200 ± 74.7226

MAI

1,313.0200 ± 122.1414

-

-

-

-

2,186.8400 ± 74.6617

MAE

1,146.0400 ± 129.7894

-

539.2420 ± 202.7226

-

-

1,786.3800 ± 163.5879

MAIE

1,149.1100 ± 129.8429

-

535.6400 ± 202.8939

  

1,786.0400 ± 163.7067

MAD

1,303.6700 ± 121.8383

171.8660 ± 65.5977

-

-

-

2,022.8200 ± 90.7908

MAID

1,305.2600 ± 121.8730

158.4950 ± 65.4938

-

-

-

2,033.7900 ± 90.9973

MADE1

1,168.3800 ± 130.5453

151.9660 ± 64.9427

451.3190 ± 205.1450

-

-

1,703.5000 ± 167.0098

MAIDE1

1,167.8900 ± 130.4905

138.0280 ± 64.4991

457.6490 ± 205.2238

-

-

1,710.3400 ± 167.0254

MADE2

1,168.3800 ± 130.5453

151.9660 ± 64.9427

451.3180 ± 205.1445

0.0012 ± 0.0000

-

1,703.4900 ± 167.0088

MAIDE2

1,167.8900 ± 130.4905

138.0280 ± 64.4991

457.6490 ± 205.2238

0.0012 ± 0.0000

-

1,710.3400 ± 167.0254

MAIDE3

1,167.8800 ± 130.9283

138.0280 ± 65.7276

457.6430 ± 231.1328

0.0012 ± 0.0000

0.0036 ± 0.0000

1,710.3200 ± 337.3412

  1. \(\widehat{{\sigma }_{a}^{2}}\): additive genetic variance estimate
  2. \(\widehat{{\sigma }_{d}^{2}}\): dominance variance estimate
  3. \(\widehat{{\sigma }_{aa}^{2}}\): additive-by-additive epistatic variance estimate
  4. \(\widehat{{\sigma }_{ad}^{2}}\): additive-by-dominance epistatic variance estimate
  5. \(\widehat{{\sigma }_{dd}^{2}}\): dominance-by-dominance epistatic variance estimate
  6. \(\widehat{{\sigma }_{e}^{2}}\): residual variance estimate
  7. aMA: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{Za}+\varvec{\upepsilon }\) ; MAI: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{fb}+\textbf{Za}+\varvec{\upepsilon }\); MAE: \(\textbf{y}=\textbf{X}\varvec{\upbeta}+\textbf{Za}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\varvec{\upepsilon }\); MAIE: \(\textbf{y}=\textbf{X}\varvec{\upbeta}+\textbf{fb}+\textbf{Za}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\varvec{\upepsilon }\); MAD: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{Za}+\textbf{Zd}+\varvec{\upepsilon }\); MAID: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{fb}+\textbf{Za}+\textbf{Zd}+\varvec{\upepsilon }\); MADE1: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\varvec{\upepsilon }\); MAIDE1: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{fb}+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\varvec{\upepsilon }\); MADE2: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\textbf{Z}{\varvec{e}}_{\textbf{ad}}+\varvec{\upepsilon }\); MAIDE2: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{fb}+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\textbf{Z}{\varvec{e}}_{\textbf{ad}}+\varvec{\upepsilon }\); MADE3: \(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\textbf{Z}{\varvec{e}}_{\textbf{ad}}+\textbf{Z}{\varvec{e}}_{\textbf{dd}}+\varvec{\upepsilon }\); MAIDE3:\(\textbf{y}=\textbf{X}\varvec{\upbeta }+\textbf{fb}+\textbf{Za}+\textbf{Zd}+\textbf{Z}{\varvec{e}}_{\textbf{aa}}+\textbf{Z}{\varvec{e}}_{\textbf{ad}}+\textbf{Z}{\varvec{e}}_{\textbf{dd}}+\varvec{\upepsilon }\)
  8. bModel MAIDE3 did not converge for T3.
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