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Table 4 Bias in estimation of σ² Av ,exp and correlation between mean and residual variance for a simulated trait *

From: Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

Observed pedigree

Model

rmv

σ²Av,exp = 0.01

σ²Av,exp = 0.09

σ²Av,exp = 0.25

Bias (%)

rˆmv

Bias (%)

rˆmv

Bias (%)

rˆmv

HOM

−0.5

−37.2

−0.13

−55.4

−0.26

−58.5

−0.32

(16.2)

(0.03)

(5.2)

(0.02)

(2.7)

(0.02)

HET

−0.5

1842.4

−0.15

302.8

−0.29

169.9

−0.35

(101.5)

(0.02)

(20.2)

(0.02)

(51.8)

(0.02)

HOM

0

−35.4

0.02

−53.7

0.01

−55.1

0.02

(12.9)

(0.02)

(5.2)

(0.02)

(3.3)

(0.02)

HET

0

1957.8

0.00

291.2

0.01

142.4

0.02

(160.3)

(0.02)

(17.3)

(0.02)

(10.1)

(0.02)

HOM

0.5

−44.5

0.11

−61.9

0.21

−56.4

0.30

(18.1)

(0.02)

(4.8)

(0.02)

(2.7)

(0.02)

HET

0.5

1820.0

0.13

311.4

0.26

131.5

0.34

(184.4)

(0.02)

(24.8)

(0.02)

(8.9)

(0.02)

Simulated pedigree

Model

r mv

σ² Av ,exp  = 0.01

σ² Av ,exp  = 0.09

σ² Av ,exp  = 0.25

Bias (%)

rˆ mv

Bias (%)

rˆ mv

Bias (%)

rˆ mv

HOM

−0.5

68.30

−0.05

−45.74

−0.20

−53.37

−0.26

(40.80)

(0.02)

(5.62)

(0.01)

(3.35)

(0.02)

HET

−0.5

2993.04

−0.08

389.63

−0.23

133.73

−0.30

(156.76)

(0.02)

(18.90)

(0.01)

(13.85)

(0.02)

HOM

0

56.29

−0.03

−51.58

−0.02

−50.35

0.01

(42.09)

(0.02)

(5.07)

(0.02)

(3.46)

(0.02)

HET

0

3062.76

0.02

361.38

0.01

136.38

−0.02

(131.99)

(0.02)

(18.28)

(0.01)

(7.71)

(0.02)

HOM

0.5

11.47

0.05

−47.80

0.21

−52.36

0.27

(34.49)

(0.02)

(5.99)

(0.01)

(3.90)

(0.01)

HET

0.5

2684.63

0.08

363.39

0.23

108.27

0.31

(184.43)

(0.01)

(19.62)

(0.01)

(16.81)

(0.01)

  1. * Results obtained after analyses of log squared estimated residuals under different scenarios, given as mean (s.e.) of 20 replicates. Each scenario is characterized by the simulated values for additive genetic variance on residual variance (σ²Av,exp), according to the model postulated by [15] and for the additive genetic correlation between the mean and the residual variance of the trait. Homoscedastic (HOM) or heterogeneous residual variances among sire families (HET) were assumed in the model for the mean of the trait (first step of analyses); simulations employed either the observed pedigree structure or a simulated pedigree; bias (%) = relative bias, computed as deviation between the estimated and the simulated value for σ²Av,exp, as percentage of the simulated parameter; rmv = simulated value for additive genetic correlation between the mean and the residual variance of the simulated trait; rˆmv = Pearson’s correlation between sire EBV for mean and for residual variance.