Table 1:

Recursions for autosomal and X-chromosomal admixture. The table shows the probability of parental pairings and the admixture fractions for each of the nine possible pairings for a randomly chosen female and a randomly chosen male from the admixed population at generation g.

Case	Female parent’s population	Male parent’s population	Probability	Admixture in males		Admixture in females
				$H_{1,g,m}^A$	$H_{1,g,m}^X$	$H_{1,g,f}^A$	$H_{1,g.f}^X$
1	S1	S1	$s_{1,g-1}^f{s}_{1,g-1}^m+c_{11,g}$	1	1	1	1
2	S1	H	$s_{1,g-1}^f{h}_{g-1}^m+c_{1h,g}$	$\frac{1+H_{1,g-1,m}^A}{2}$	1	$\frac{1+H_{1,g-1,m}^A}{2}$	$\frac{1+H_{1,g-1,m}^X}{2}$
3	S1	S2	$s_{1,g-1}^f{s}_{2,g-1}^m+c_{12,g}$	½	1	½	½
4	H	S1	$h_{g-1}^f{s}_{1,g-1}^m+c_{h1,g}$	$\frac{1+H_{1,g-1,f}^A}{2}$	$H_{1,g-1,f}^X$	$\frac{1+H_{1,g-1,f}^A}{2}$	$\frac{1+H_{1,g-1,f}^X}{2}$
5	H	H	$h_{g-1}^f{h}_{g-1}^m+c_{hh,g}$	$\frac{H_{1,g-1,f}^A+H_{1,g-1,m}^A}{2}$	$H_{1,g-1,f}^X$	$\frac{H_{1,g-1,f}^A+H_{1,g-1,m}^A}{2}$	$\frac{H_{1,g-1,f}^X+H_{1,g-1,m}^X}{2}$
6	H	S2	$h_{g-1}^f{s}_{2,g-1}^m+c_{h2,g}$	$\frac{{\text{H}}_{1,9}^{\text{A}}-1,\text{f}}{2}$	$H_{1,g-1,f}^X$	$\frac{H_{1,g-1,f}^A}{2}$	$\frac{H_{1,g-1,f}^X}{2}$
7	S2	S1	$s_{2,g-1}^f{s}_{1,g-1}^m+c_{21,g}$	½	0	½	½
8	S2	H	$s_{2,g-1}^f{h}_{g-1}^m+c_{2h,g}$	$\frac{H_{1,g-1,m}^A}{2}$	0	$\frac{H_{1,g-1,m}^A}{2}$	$\frac{H_{1,g-1,m}^X}{2}$
9	S2	S2	$s_{2,g-1}^f{s}_{2,g-1}^m+c_{22,g}$	0	0	0	0