Table 1. Notation.

Quantity	Notation
Allele	$A_{jk}^i$ for allele $k\in \left\{1,2\right\},$ individual $j\in \left\{1,2,\dots .n_i\right\},$ population $i\in \left\{1,2,\dots r\right\}$
Allelic indicator	$x_{jku}^i$ for allele $A_{jk}^i$ being of type u
Allele frequency	${\pi }_u$ expected value of $x_{jku}^i$ for all $i,j,k$
	$p_{iu}$ actual frequency for allele type u in population i
	${\stackrel{\sim }{p}}_{iu}$ observed frequency for allele type u in sample from population i
Theta	${\theta }_{jk,j^{\prime }{k}^{\prime }}^{i{i}^{\prime }}$ is probability of ibd between allele k in individual j from population i and allele $k^{\prime }$ in individual $j^{\prime }$ from population $i^{\prime }$
Inbreeding coefficient	$F_j^i$ is the ibd probability for the two alleles for individual j in population i: $F_j^i=\frac{1}{2}{\displaystyle {\sum }_{k=1}^2{\displaystyle {\sum }_{k^{\prime }=1,k^{\prime }\ne k}^2{\theta }_{jk,j{k}^{\prime }}^{ii}}}$
Coancestry coefficient	Coancestry ${\theta }_{j{j}^{\prime }}^i$ is the ibd probability for a pair of alleles drawn from individuals $j,j^{\prime }$ in population i: ${\theta }_{j{j}^{\prime }}^i=\frac{1}{4}{\displaystyle {\sum }_{k=1}^2{\displaystyle {\sum }_{k^{\prime }=1}^2{\theta }_{jk,j^{\prime }{k}^{\prime }}^{ii}}}.$ ${\theta }_S^i$ is the average of ${\theta }_{j{j}^{\prime }}^i$ for all pairs $j,j^{\prime }.$ ${\theta }^S$ is the average over populations of ${\theta }_S^i.$ For any two distinct alleles drawn from population i, the ibd probability is ${\theta }_W^i.$ The average over populations of ${\theta }_W^i$ is ${\theta }^W.$ ${\theta }^B$ is the average of ibd probabilities for alleles from different populations
Relative inbreeding	The relative inbreeding coefficient for individual j in population i is ${\beta }_j^i=\left(F_j^i-{\theta }_R\right)/\left(1-{\theta }_R\right):$ reference ${\theta }_R$ is ${\theta }_S^i$ or ${\theta }^B$
Relative coancestry	The relative coancestry coefficient for individuals $j,j^{\prime }$ in population i is ${\beta }_{j{j}^{\prime }}^i=\left({\theta }_{j{j}^{\prime }}^i-{\theta }_R\right)/\left(1-{\theta }_R\right):$ reference ${\theta }_R$ is ${\theta }_S^i$ or ${\theta }^B$
Population-specific $F_{\mathrm{ST}}$	${\beta }_{\mathrm{WT}}^i=\left({\theta }_W^i-{\theta }^B\right)/\left(1-{\theta }^B\right)$ is probability two alleles drawn from population i are ibd, relative to the probability an allele drawn from one population is ibd to an allele drawn from another population. ${\beta }_{\mathrm{ST}}^i=\left({\theta }_S^i-{\theta }^B\right)/\left(1-{\theta }^B\right)$ is for alleles drawn from two individuals in population i