Table 4.

Estimates of SNP additive heritabilities of teat number when using 41,108 autosomal SNPs or every other (20,554) of the 41,108 SNPs

SNP set	Average ${\widehat{\text{h}}}_{\text{k}\mathrm{\alpha }}^2$ per SNP	Ratio	Total ${\widehat{\text{h}}}_{\mathrm{\alpha }\text{i}}^2$
20,554 SNPs	${\overline{\text{h}}}_{\mathrm{\alpha }1}^2=1.75\left({10}^{-5}\right)$	${\overline{\text{h}}}_{\mathrm{\alpha }1}^2/{\overline{\text{h}}}_{\mathrm{\alpha }2}^2=1.960$	${\widehat{\text{h}}}_{\mathrm{\alpha }1}^2=0.360$
20,554 SNPs with all 41,108 SNPs in the mixed model	${\overline{\text{h}}}_{\mathrm{\alpha }2}^2=8.93\left({10}^{-6}\right)$	${\overline{\text{h}}}_{\mathrm{\alpha }2}^2/{\overline{\text{h}}}_{\mathrm{\alpha }3}^2=0.998$	${\widehat{\text{h}}}_{\mathrm{\alpha }2}^2=0.184$
41,108 SNPs	${\overline{\text{h}}}_{\mathrm{\alpha }3}^2=8.95\left({10}^{-6}\right)$	${\overline{\text{h}}}_{\mathrm{\alpha }1}^2/{\overline{\text{h}}}_{\mathrm{\alpha }3}^2=1.955$	${\widehat{\text{h}}}_{\mathrm{\alpha }3}^2=0.368$

${\widehat{\text{h}}}_{\text{k}\mathrm{\alpha }}^2$ is the heritability of the $\text{k}$th SNP. ${\overline{\text{h}}}_{\mathrm{\alpha }\text{i}}^2={\sum }_{\text{k}=1}^{\text{mi}}{\widehat{\text{h}}}_{\text{ka}}^2/{\text{m}}_{\text{i}}$ is the average of SNP additive heritability of the $\text{i}$th SNP set, ${\widehat{\text{h}}}_{\mathrm{\alpha }\text{i}}^2={\sum }_{\text{k}=1}^{{\text{m}}_{\text{i}}}{\widehat{\text{h}}}_{\text{ka}}^2$ is the total additive heritability of all SNPs in the $\text{i}$th SNP set, where ${\text{m}}_{\text{i}}$ is the number of SNPs in the $\text{i}$th SNP set