# Table 3 Expectation of elements involved in precision formulae when a uniform $$( f ( p ) = 1 )$$ or a U shaped distribution of allelic frequencies is assumed $$\left( {f( p) = {k \mathord{\left/ {\vphantom {k {2p\left( {1\text{ - }p} \right)}}} \right. \kern-0pt} {2p\left( {1-p} \right)}}} \right)$$
E[ρ m ] $$1 - 2\frac{h}{\omega }\theta$$ $$\frac{k}{\omega }\theta$$
E[ρ 2 m ] $$\left( {\frac{4\theta }{\omega } + \frac{2}{h}} \right)\left( {\frac{1 + h}{1 + 4h}} \right)^{2} - \frac{4\theta h}{\omega }$$ $$\frac{k}{{\omega^{2} }}\left[ {\theta \left( {\omega - \frac{2h}{\omega }} \right) - 1} \right]$$
E[ρ 2 m /σ 2 m ] $$\frac{1}{{\omega^{2} }}\left[ {\theta \left( {\omega - \frac{2h}{\omega }} \right) - 1} \right]$$ $$\frac{k}{{2\omega^{3} }}\left\{ {2\theta + \frac{\omega }{h}} \right\}$$
1. A large effective size $$N_{e}$$ of the population was assumed to make 1/N e negligible $$\theta = \log \left( {\left| {\frac{1 + \omega }{1 - \omega }} \right|} \right),\omega = \sqrt {1 + 4h}$$ $$h = {{{{\uplambda }}_{{{\upbeta }}} } \mathord{\left/ {\vphantom {{{{\uplambda }}_{{{\upbeta }}} } {2n_{r} }}} \right. \kern-0pt} {2n_{r} }}, {{\uplambda }}_{{{\upbeta }}} = {{\sigma_{e}^{2} } \mathord{\left/ {\vphantom {{\sigma_{e}^{2} } {\sigma_{{{\upbeta }}}^{2} }}} \right. \kern-0pt} {\sigma_{{{\upbeta }}}^{2} }}$$