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Table 2 Number of simulations over 100 rejecting the null hypothesis of no transmitted environmental effect

From: An improved transmissibility model to detect transgenerational transmitted environmental effects

Set

\({\omega }_{s}\)

\({\omega }_{d}\)

\(r\) \(\left(\rho \right)\)

Scenario 1 (without a transmitted environmental effect)

Scenario 2 (with a transmitted environmental effect)

LRT

T-test

LRT

T-test

1

0.40

0.25

0.544 (0.70)

7

15

94

26

2

0.40

0.25

0.389 (0.50)

7

15

75

24

3

0.40

0.25

0.233 (0.30)

4

11

46

22

4

0.20

0.50

0.213 (0.30)

2

18

45

23

Average percentage

5.00

14.75

65.00

23.75

  1. In Scenario 1, the model of simulation is: \({y}_{i}={\mathbf{x}}_{\mathbf{i}}{\varvec{\upbeta}}+{\theta }_{i}+{t}_{i}+{e}_{i},\) where \({\theta }_{i}=\sqrt{r}{\sigma }_{t}\) if animal \(i\) is in the particular environment, \({\theta }_{i}=\) 0 elsewhere; and \({t}_{i}\) is modeled as in the “classical” transmissibility model
  2. In Scenario 2: the model of simulation is: \({y}_{i}={\mathbf{x}}_{\mathbf{i}}{\varvec{\upbeta}}+{t}_{i}+{e}_{i},\) where \({t}_{i}={{\omega }_{s}t}_{si}+{{\omega }_{d}t}_{di}+{\theta }_{i}+{\xi }_{i}\), \({\theta }_{i}=\sqrt{r}{\sigma }_{t}\) if animal \(i\) is in the particular environment, \({\theta }_{i}=\) 0 elsewhere; \(\mathbf{\xi}\) are independently distributed with variance equal to \(\left({\delta }_{i}-r\right){\sigma }_{t}^{2}\) for animals that experience the particular environment, and \({\delta }_{i}{\sigma }_{t}^{2}\) elsewhere
  3. \({\delta }_{i}=\left(1-{\omega }_{s}^{2}-{\omega }_{d}^{2}\right)\) if both parents are known, \(\left(1-{\omega }_{d}^{2}\right)\) for animals of unknown sire; \(\left(1-{\omega }_{s}^{2}\right)\) for animals of unknown dam; and 1 for animals for which both parents are unknown. \(\rho =\frac{r}{1-{\omega }_{s}^{2}-{\omega }_{d}^{2}}\)
  4. LRT: likelihood ratio test comparing the transmissibility and the transmissibility model with environment; the null hypothesis is \(H0{:}r=0\)
  5. T-test: paired T-test comparing the average phenotype of the two lines \((E+,E-)\) in the last generation. The null hypothesis is \(H0{:}{\mu }_{E+}={\mu }_{E-}\)
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Genetics Selection Evolution

ISSN: 1297-9686