Table 2.

Estimators of inbreeding.

Estimate	Calculationa	Expected Valueb
${\widehat{F}}_{{\mathrm{ROH}}_j}$	Proportion of homozygous blocks.	No explicit expression.
${\widehat{f}}_{{\mathrm{MLE}}_j}$	Maximization of likelihood for fj.	No explicit expression.
${\widehat{f}}_{{\mathrm{HOM}}_j}$	$1-\frac{{\sum }_l{X}_{jl}\left(2-X_{jl}\right)}{{\sum }_{l}2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}$	$\frac{f_j-\frac{1}{2n}\left(1+f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{HOM}}_W}$	$1-\frac{1}{n}{\sum }_{j=1}^n\frac{{\sum }_l{X}_{jl}\left(2-X_{jl}\right)}{{\sum }_{l}2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}$	$\frac{f_W-\frac{1}{2n}\left(1+f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{AS}}_j}$	$\frac{{\sum }_l\left({\tilde{A}}_{jl}-{\tilde{A}}_{Sl}\right)}{{\sum }_l\left(1-{\tilde{A}}_{Sl}\right)}$	fj
${\widehat{f}}_{{\mathrm{AS}}_W}$	$\frac{1}{n}{\sum }_{j=1}^n{\widehat{f}}_{{\mathrm{AS}}_j}$	fW
${\widehat{f}}_{{\mathrm{UNI}}_j}^w$	$\frac{{\sum }_l\left[X_{jl}^2-\left(1+2{\tilde{p}}_l\right)X_{jl}+2{\tilde{p}}_l^2\right]}{{\sum }_{l}2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}$	$\frac{f_j-2{\psi }_j-\frac{1}{2n}\left(3+4f_j-8{\psi }_j-f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{UNI}}_W}^w$	$\frac{1}{n}{\sum }_{j=1}^n{\widehat{f}}_{{\mathrm{UNI}}_j}^w$	$\frac{f_W-\frac{3}{2n}\left(1+f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{UNI}}_j}^u$	$\frac{1}{L}{\sum }_{l=1}^L\frac{X_{jl}^2-\left(1+2{\tilde{p}}_l\right)X_{jl}+2{\tilde{p}}_l^2}{2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}$	No explicit expression.
${\widehat{f}}_{{\mathrm{STD}}_j}^w$	$\frac{{\sum }_l{\left(X_{jl}-2{\tilde{p}}_l\right)}^2}{{\sum }_{l}2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}-1$	$\frac{f_j-4{\psi }_j-\frac{1}{2n}\left(3+4f_j-8{\psi }_j-f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{STD}}_W}^w$	$\frac{1}{n}{\sum }_{j=1}^n{\widehat{f}}_{{\mathrm{STD}}_j}^w$	$\frac{f_W-\frac{3}{2n}\left(1+f_W\right)}{1-\frac{1}{2n}\left(1+f_W\right)}$
${\widehat{f}}_{{\mathrm{STD}}_j}^u$	$\frac{1}{L}{\sum }_{l=1}^L\frac{{\left(X_{jl}-2{\tilde{p}}_l\right)}^2}{2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)}-1$	No explicit expression.

^aX_jl is the reference allele dosage for SNP l in individual j.

^a${\tilde{p}}_l=\frac{1}{2n}{\sum }_{j=1}^n{X}_{jl}$ is the sample allele frequency for SNP l.

^bFor weighted averages over large numbers of loci.