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

Table 3 Variance components for test-day production traits and SCS in the real dataset

Trait	Model	\(\sigma _{{\mathbf{a}}}^{2}\)	\(\sigma _{{\mathbf{v}}}^{2}\)	\(\sigma _{{{\mathbf{PE}}}}^{2}\)	\({\mathbf{\sigma }}_{{\mathbf{e}}}^{2}\)	\({\mathbf{QTL}} - {\mathbf{h}}^{2}\)	\({\mathbf{h}}^{2}\)(SE) (polygenic + QTL)	LRT p (λ)
MY (kg)	Basic (univariate)	5.919		5.007	14.862		0.230 (0.025)	1 (− 0.1e−03)
	QTL (univariate)	5.919	0.778e−05	5.007	14.862	0.302e−06	0.230 (0.027)	1 (− 0.1e−03)
	Basic (bivariate)	6.000		4.922	14.867		0.233 (0.025)
	QTL (bivariate)	6.012	0.816e−04	4.914	14.867	0.316e−05	0.233 (0.027)
F (%)	Basic (univariate)	0.109		0.014	0.283		0.268 (0.018)	0.597 (0.279)
	QTL (univariate)	0.106	0.002	0.015	0.283	0.005	0.267 (0.022)	0.597 (0.279)
	Basic (bivariate)	0.109		0.014	0.283		0.269 (0.019)
	QTL (bivariate)	0.109	0.460e−03	0.014	0.283	0.001	0.268 (0.020)
P (%)	Basic (univariate)	0.033		0.006	0.040		0.414 (0.025)	0.047 (3.941)
	QTL (univariate)	0.030	0.002	0.006	0.040	0.023	0.411 (0.033)	0.047 (3.941)
	Basic (bivariate)	0.032		0.006	0.040		0.410 (0.026)
	QTL (bivariate)	0.032	0.245e−04	0.006	0.040	0.313e−03	0.410 (0.028)
SCS	Basic (univariate)	0.224		0.636	1.543		0.093 (0.019)	0.405 (0.692)
	QTL (univariate)	0.211	0.008	0.639	1.543	0.004	0.091 (0.020)	0.405 (0.692)
	Basic (bivariate)	0.236		0.626	1544		0.098 (0.019)
	QTL (bivariate)	0.233	0.576e−03	0.626	1.544	0.240e−03	0.097 (0.022)

Corresponding variance components for the polledness trait from the bivariate models are included in Additional file 5
MY: milk yield; F: fat, P: protein; SCS: somatic cell score
\(\sigma _{{\mathbf{a}}}^{2}\) = additive genetic variance based on \(A\); \(\sigma _{{\mathbf{v}}}^{2}\) = 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 \(\sigma _{{\mathbf{v}}}^{2} + \sigma _{{\mathbf{a}}}^{2} /\sigma _{{\text{a}}}^{2} + \sigma _{{\mathbf{v}}}^{2} + \sigma _{{{\mathbf{PE}}}}^{2} + \sigma _{{\mathbf{e}}}^{2}\); LRT p (λ) = p- and lambda values from likelihood ratio tests

ISSN: 1297-9686