. Author manuscript; available in PMC: 2022 Aug 1.

Published in final edited form as: Theor Popul Biol. 2021 Apr 24;140:32–43. doi: 10.1016/j.tpb.2021.03.004

Table 1:

Large-N reduction factors of pairwise coalescence times due to various types of consanguinity.

	Autosomal			X-chromosomal
	Siblings	First cousins	Double first cousins	Siblings	First cousins
	Siblings	First cousins	Double first cousins	Siblings	Patrilateral-parallel, Patrilateral-cross	Matrilateral-parallel, Bilateral-parallel	Matrilateral-cross, Bilateral-cross
Kinship coefficient	$\frac{1}{4}$	$\frac{1}{16}$	$\frac{1}{8}$	$\frac{1}{2}$	0	$\frac{3}{16}$	$\frac{1}{8}$
T_m, T_f, U	1 −c₀	$1 - \frac{1}{4} c_{1}$	$1 - \frac{1}{2} c_{1}$	$\frac{1 - c_{0}}{1 - \frac{1}{4} c_{0}}$	1	$\frac{1 - \frac{1}{2} c_{1}}{1 + \frac{1}{16} c_{1}}$	$\frac{1 - \frac{1}{2} c_{1}}{1 - \frac{1}{8} c_{1}}$
**Vmm, Vmf, Vff**	$1 - \frac{3}{4} c_{0}$	$1 - \frac{3}{16} c_{1}$	$1 - \frac{3}{8} c_{1}$	$\frac{1 - \frac{3}{4} c_{0}}{1 - \frac{1}{4} c_{0}}$	1	$\frac{1 - \frac{5}{16} c_{1}}{1 + \frac{1}{16} c_{1}}$	$\frac{1 - \frac{3}{8} c_{1}}{1 - \frac{1}{8} c_{1}}$

These reduction factors give multipliers for the mean T_MRCA for a non-consanguineous population of 2N individuals: 4N for autosomes and 3N for X chromosomes. The kinship coefficient for a mating pair refers to the probability that two alleles sampled from the two individuals of the pair are identical by descent. Kinship coefficients are computed separately for autosomal loci and X-chromosomal loci. Note that T_m is used only in the autosomal case; for the X chromosome, two alleles cannot be in the same male.