Table 4. Population-level estimates for private alleles.

Quantity	Observation or estimate
Private allele frequency	${\stackrel{\sim }{p}}_1$ in population 1, zero in populations $2,3,\dots ,r$
Sample matching proportions	${\stackrel{\sim }{M}}_W^1=1-2{\stackrel{\sim }{p}}_1\left(1-{\stackrel{\sim }{p}}_1\right)2n_i/(2n_i-1)$
	${\stackrel{\sim }{M}}_W^i=1,\hspace{1em}i\ne 1$
	${\stackrel{\sim }{M}}^W=1-2{\stackrel{\sim }{p}}_1\left(1-{\stackrel{\sim }{p}}_1\right)2n_1/[r\left(2n_1-1\right)]$
	${\stackrel{\sim }{M}}_B^{1i}=1-{\stackrel{\sim }{p}}_1,\hspace{1em}i\ne 1$
	${\stackrel{\sim }{M}}_B^{i{i}^{\prime }}=1,\hspace{1em}i,i^{\prime }\ne 1,i\ne i^{\prime }$
	${\stackrel{\sim }{M}}^B=1-2{\stackrel{\sim }{p}}_1/r$
β estimates	$F_{\mathrm{ST}}^1={\widehat{\beta }}_{\mathrm{WT}}^1=1-r\left(1-{\stackrel{\sim }{p}}_1\right)2n_1/(2n_{\mathrm{i}}-1)\approx 1-r\left(1-{\stackrel{\sim }{p}}_1\right)$
	$F_{\mathrm{ST}}^i={\widehat{\beta }}_{\mathrm{WT}}^i=1,\hspace{1em}i\ne 1$
	$F_{\mathrm{ST}}={\widehat{\beta }}_{\mathrm{WT}}=(2n_1-{\stackrel{\sim }{p}}_1-1)/(2n_1-1)\approx {\stackrel{\sim }{p}}_1$
	${\widehat{\beta }}_{\mathrm{WT}}^{1i}=1-r/2,i\ne 1$
	${\widehat{\beta }}_{\mathrm{WT}}^{i{i}^{\prime }}=1,\hspace{1em}i,i^{\prime }\ne 1$