Table 4 Parameterization of one-locus models (9), (10), (11), (12) when m ≥ 3.

Allele

${\alpha }_m^{*}=0$

$\begin{array}{c}\mu ={\mu }^{*}=\left(G_{jm}+G_{km}\right)-G_{jk},j\ne k\ne m\\ {\alpha }_j={\alpha }_j^{*}=G_{jk}-G_{km},j=1,\dots ,m-1;j\ne k,m\\ {\delta }_j={\delta }_j^{*}=\left(G_{jj}-G_{jk}\right)-\left(G_{jl}-G_{kl}\right),j=1,\dots ,m;k\ne j\ne l\end{array}$

F_∞

$2{\alpha }_m^{*}+{\delta }_m^{*}=0$

$\begin{array}{c}\tau ={\mu }^{*}+\frac{1}{2}\sum _{j=1}^{m-1}\left(2{\alpha }_j^{*}+{\delta }_j^{*}\right)=G_{mm}+\frac{1}{2}\sum _{j=1}^{m-1}\left(G_{jj}-G_{mm}\right)\\ a_j=\frac{1}{2}\left(2{\alpha }_j^{*}+{\delta }_j^{*}\right)=\frac{G_{jj}-G_{mm}}{2},j=1,\dots ,m-1\\ d_j=-\frac{{\delta }_j^{*}}{2}=-\frac{\left(G_{jj}-G_{jk}\right)-\left(G_{jl}-G_{kl}\right)}{2},j=1,\dots ,m;j\ne k\ne l\end{array}$

Allele-count

${\alpha }_m^{*}=0$

$\begin{array}{c}{\pi }_0={\mu }^{*}=\left(G_{jm}+G_{km}\right)-G_{jk},j\ne k\ne m\\ {\pi }_j={\alpha }_j^{*}=G_{jk}-G_{km},j=1,\dots ,m-1;k\ne j,m\\ {\eta }_j=2{\alpha }_j^{*}+{\delta }_j^{*}=\left(G_{jj}-G_{jm}\right)+\left(G_{jk}-G_{km}\right),j=1,\dots ,m-1;k\ne j,m\\ {\eta }_m={\delta }_m^{*}=\left(G_{mm}-G_{jm}\right)-\left(G_{km}-G_{jk}\right),j\ne k\ne m\end{array}$

Allele-count

$2{\alpha }_m^{*}+{\delta }_m^{*}=0$

$\begin{array}{c}{{\pi }^{\prime }}_0={\mu }^{*}=G_{mm}\\ {{\pi }^{\prime }}_j={\alpha }_j^{*}=\frac{\left(G_{jm}-G_{mm}\right)+\left(G_{jk}-G_{km}\right)}{2},j=1,\dots ,m-1;k\ne j,m\\ {{\pi }^{\prime }}_m=-\frac{{\delta }_m^{*}}{2}=-\frac{\left(G_{mm}-G_{jm}\right)-\left(G_{km}-G_{jk}\right)}{2},j\ne k\ne m\\ {{\eta }^{\prime }}_j=2{\alpha }_j^{*}+{\delta }_j^{*}=G_{jj}-G_{mm},j=1,\dots ,m-1\end{array}$