An improved transmissibility model to detect transgenerational transmitted environmental effects

David, Ingrid; Ricard, Anne

doi:10.1186/s12711-023-00833-y

Genetics Selection Evolution

Table 3 Estimates (± sd) obtained with the transmissibility model and the transmissibility model with environment

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

Set	Simulated value		Scenario 1 (without a transmitted environmental effect)		Scenario 2 (with a transmitted environmental effect
Set	Simulated value		Trans	TransEnv	Trans	TransEnv
1	\({\sigma }_{e}^{2}\)	10	9.64 ± 1.71	9.62 ± 1.73	9.82 ± 1.43	9.68 ± 1.37
	\({\sigma }_{t}^{2}\)	5	5.33 ± 1.72	5.40 ± 1.75	4.91 ± 1.43	5.29 ± 1.46
	\({\omega }_{s}\)	0.40	0.39 ± 0.08	0.39 ± 0.08	0.40 ± 0.07	0.38 ± 0.07
	\({\omega }_{d}\)	0.25	0.25 ± 0.08	0.24 ± 0.08	0.27 ± 0.09	0.24 ± 0.07
	\(r\) \((\rho )\)	0.544 (0.70)	–	0.08 ± 0.15 (0.10 ± 0.20)	–	0.53 ± 0.18 (0.68 ± 0.25)
2	\({\sigma }_{e}^{2}\)	10	9.64 ± 1.71	9.62 ± 1.73	9.79 ± 1.47	9.69 ± 1.50
	\({\sigma }_{t}^{2}\)	5	5.33 ± 1.72	5.40 ± 1.75	5.01 ± 1.49	5.29 ± 1.58
	\({\omega }_{s}\)	0.40	0.39 ± 0.08	0.39 ± 0.08	0.40 ± 0.07	0.39 ± 0.07
	\({\omega }_{d}\)	0.25	0.25 ± 0.08	0.24 ± 0.08	0.26 ± 0.09	0.25 ± 0.08
	\(r\) \((\rho )\)	0.389 (0.50)	–	0.08 ± 0.15 (0.10 ± 0.20)	–	0.39 ± 0.20 (0.51 ± 0.27)
3	\({\sigma }_{e}^{2}\)	10	9.76 ± 1.73	9.73 ± 1.75	9.83 ± 1.54	9.76 ± 1.55
	\({\sigma }_{t}^{2}\)	5	5.16 ± 1.79	5.23 ± 1.80	5.00 ± 1.59	5.18 ± 1.65
	\({\omega }_{s}\)	0.40	0.39 ± 0.08	0.39 ± 0.08	0.40 ± 0.08	0.39 ± 0.08
	\({\omega }_{d}\)	0.25	0.25 ± 0.08	0.24 ± 0.07	0.25 ± 0.08	0.24 ± 0.08
	\(r\) \((\rho )\)	0.233 (030)		0.07 ± 0.15 (0.09 ± 0.20)		0.24 ± 0.19 (0.32 ± 0.26)
4	\({\sigma }_{e}^{2}\)	10	9.86 ± 1.37	9.88 ± 1.36	9.95 ± 1.26	9.90 ± 1.27
	\({\sigma }_{t}^{2}\)	5	5.07 ± 1.39	5.09 ± 1.39	4.89 ± 1.29	5.05 ± 1.32
	\({\omega }_{s}\)	0.20	0.20 ± 0.08	0.20 ± 0.08	0.20 ± 0.08	0.20 ± 0.08
	\({\omega }_{d}\)	0.50	0.49 ± 0.09	0.49 ± 0.09	0.50 ± 0.09	0.49 ± 0.09
	\(r\) \((\rho )\)	0.213 (0.30)	–	0.07 ± 0.13 (0.11 ± 0.20)	–	0.23 ± 0.17 (0.34 ± 0.26)

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. \(\rho =\frac{r}{1-{\omega }_{s}^{2}-{\omega }_{d}^{2}}\)
Trans transmissibility model, TransEnv transmissibility model with environment

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ISSN: 1297-9686

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