An improved transmissibility model to detect transgenerational transmitted environmental effects

Table 1 Description of the sets of parameters used in the simulations

Parameters	Set 1	Set 2	Set 3	Set 4
\({\omega }_{s}\)	0.40	0.40	0.40	0.20
\({\omega }_{d}\)	0.25	0.25	0.25	0.50
\(r\) \(\left(\rho \right)\)	0.544 (0.70)	0.389 (0.50)	0.233 (0.30)	0.213 (0.30)

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
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
\({\delta }_{i}=\left(1-{\omega }_{s}^{2}-{\omega }_{d}^{2}\right)\) 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. \(\rho =\frac{r}{1-{\omega }_{s}^{2}-{\omega }_{d}^{2}}\)

ISSN: 1297-9686