Towards genetic improvement of social behaviours in livestock using large-scale sensor data: data simulation and genetic analysis

Table 1 Simulated genetic variances (\({{{\sigma}}}_{{{A}}}^{2}\))^a required to obtain a certain observed-scale heritability (\({{{h}}}_{{{o}}}^{2}\))^b

\({h}_{o}^{2}\)	\({h}_{u}^{2}\)	\({\sigma }_{A}^{2}\)	\(\overline{p }({A}_{\alpha }={\mu }_{\alpha }-2{\sigma }_{{A}_{\alpha }})^\text{c}\)	\(\overline{p }({A}_{\alpha }={\mu }_{\alpha }+2{\sigma }_{{A}_{\alpha }})^\text{c}\)	Accuracy LMM^d
0.05	0.0036	0.012	0.008	0.012	0.173
0.1	0.0111	0.038	0.006	0.015	0.195
0.2	0.0429	0.170	0.004	0.022	0.241

^aVariances were the same for genetic effect and permanent environmental effect, as well as for both traits, so these input values are for all four variances
^b \({h}_{o}^{2}\) is the observed-scale heritability of the mean of 2500 binary observations with on average 25 successes, based on a linear mixed model
^cInteraction probability of the top and bottom ranking individuals for the performer effect. These values are calculated assuming that an individual whose value for trait \(\alpha\) is \({P}_{\alpha }={\mu }_{\alpha }\pm 2{\sigma }_{{A}_{\alpha }}\) interacts with an average pen mate (\({P}_{\beta }={\mu }_{\beta }\)). The interaction probability for such a combination is \(p=\) logistic (\({\mu }_{\alpha }\pm 2{\sigma }_{{A}_{\alpha }}+{\mu }_{\beta }\)). The mean interaction probability was 1% (\({\mu }_{\alpha }={\mu }_{\beta }=1/2logi{stic}^{-1}\left(0.01\right)\))
^dAccuracy of the EBV for the performer effect based on the simple LMM, computed as the correlation between true and estimated breeding values

ISSN: 1297-9686