With a phenotypic variance of 1 and individual-level genetic effects gk = Wbk, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_k^2 = \sigma _{g_k}^2 = M\sigma _{b_k}^2$$\end{document}hk2=σgk2=Mσbk2 and the squared correlation between the true, gk, and estimated BLUP effects, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}$$\end{document}g^BLUPk, is:17\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{{\bf{g}}_k,\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}}^2 = R_k^2{\mathrm{/}}h_k^2$$\end{document}Rgk,g^BLUPk2=Rk2∕hk2Rearranging Eq. (17) gives \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_k^2 = h_k^2R_{{\bf{g}}_k,\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}}^2 = h_k^2\frac{{{\mathrm{cov}}\left( {{\bf{g}}_k,\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right)^2}}{{{\mathrm{var}}\left( {{\bf{g}}_k} \right){\mathrm{var}}\left( {\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right)}}$$\end{document}Rk2=hk2Rgk,g^BLUPk2=hk2covgk,g^BLUPk2vargkvarg^BLUPk, which given the BLUP properties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{cov}}\left( {{\bf{g}}_k,\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right) = {\mathrm{var}}\left( {\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right)$$\end{document}covgk,g^BLUPk=varg^BLUPk and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_k^2 = \sigma _{g_k}^2$$\end{document}hk2=σgk2 with a phenotypic variance of 1, reduces to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_k^2 = {\mathrm{cov}}\left( {{\bf{g}}_k,\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right)$$\end{document}Rk2=covgk,g^BLUPk = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{var}}\left( {\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right) = M{\mathrm{var}}\left( {\widehat {\bf{b}}_{{\mathrm{BLUP}}_k}} \right)$$\end{document}varg^BLUPk=Mvarb^BLUPk. Therefore:18\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{var}}\left( {\widehat {\bf{b}}_{{\mathrm{BLUP}}_k}} \right) = \frac{{{\mathrm{var}}\left( {\widehat {\bf{g}}_{{\mathrm{BLUP}}_k}} \right)}}{M} = \frac{{R_k^2}}{M}$$\end{document}varb^BLUPk=varg^BLUPkM=Rk2M