A variance component estimation approach to infer associations between Mendelian polledness and quantitative production and female fertility traits in German Simmental cattle

Table 4 Variance components for fertility traits in the real dataset

Trait	Model	\(\sigma _{{\mathbf{a}}}^{2}\)	\(\sigma _{{\mathbf{v}}}^{2}\)	\(\sigma _{{{\mathbf{PE}}}}^{2}\)	\(\sigma _{{\mathbf{e}}}^{2}\)	\({\mathbf{QTL}} - {\mathbf{h}}^{2}\)	\({\mathbf{h}}^{2}\)(SE) (polygenic + QTL)	LRT p (λ)
NRR-56 (binary)	Basic (univariate)	0.075		0.409	3.290		0.020 (0.038)	1 (− 0.407)
	QTL (univariate)	0.047	0.018	0.416	3.290	0.005	0.017 (0.049)	1 (− 0.407)
	Basic (bivariate)	0.061		0.232	3.290		0.017 (0.030)
	QTL (bivariate)	0.061	0.531e−03	0.228	3.290	0.148e−03	0.017 (0.048)
DFS* (days)	Basic (univariate)	54.142		209.418	2098.704		0.023 (0.018)	0.663 (0.190)
	QTL (univariate)	39.286	12.249	210.966	2097.825	0.005	0.022 (0.024)	0.663 (0.190)
	Basic (bivariate)	45.011		220.952	2096.554		0.019 (0.016)
	QTL (bivariate)	38.886	0.825	220.753	2097.187	0.350e−03	0.017 (0.014)
DO (days)	Basic (univariate)	55.600		102.212	1931.358		0.027 (0.018)	0.434 (0.613)
	QTL (univariate)	26.347	25.290	102.586	1930.923	0.012	0.025 (0.027)	0.434 (0.613)
	Basic (bivariate)	46.174		112.101	1930.572		0.022 (0.016)
	QTL (bivariate)	31.215	11.429	110.559	1931.022	0.005	0.020 (0.024)

Corresponding variance components for the polled trait from the bivariate models are included in Additional file 5
NRR-56: non return rate 56; DFS: days to first service; DO: days open
\({\sigma}_{\mathbf{a}}^2\) = additive genetic variance based on \({\mathbf{A}}\); \({\sigma}_{{{\mathbf{v}}}}^2\) = additive genetic variance based on \({\mathbf{A}}_{{\mathbf{v}}}\); \(\sigma_{{{\text{PE}}}}^{2}\) = permanent environment variance; \(\sigma_{{\mathbf{e}}}^{2}\) = residual variance; \({\text{QTL}} - {\text{h}}^{2}\) = QTL heritability calculated as \(\sigma _{{\mathbf{v}}}^{2} /\sigma _{{\mathbf{a}}}^{2} + \sigma _{{\mathbf{v}}}^{2} + \sigma _{{{\mathbf{PE}}}}^{2} + \sigma _{{\mathbf{e}}}^{2}\); \({\text{h}}^{2}\) (SE) = overall heritability and standard error (in brackets) calculated as \(\sigma _{{\text{v}}}^{2} + \sigma _{{\mathbf{a}}}^{2} /\sigma _{{\mathbf{a}}}^{2} + \sigma _{{\mathbf{v}}}^{2} + \sigma _{{{\mathbf{PE}}}}^{2} + \sigma _{{\mathbf{e}}}^{2}\); LRT p (λ) = p- and lambda values from likelihood ratio tests
*Since the full bivariate model including \({\mathbf{A}}\) and \({\mathbf{A}}_{{\mathbf{v}}}\) for the trait DFS did not fully converge, we present the results for a model excluding \({\mathbf{A}}\) in the model for polledness.

ISSN: 1297-9686