. Author manuscript; available in PMC: 2023 Oct 1.

Published in final edited form as: Theor Popul Biol. 2022 Aug 13;147:1–15. doi: 10.1016/j.tpb.2022.07.002

Table B1:

Constants used in matrix exponentiation for consanguinity models.

Type of consanguineous mating	Chromosome	Section	Quantity k satisfying Gⁿ = kⁿ⁻¹G for generator matrix G (Eq. B2)
Sibling	X	3.1	$- \frac{4 - c_{0}}{3 (4 - 3 c_{0})}$
Patrilateral-parallel first-cousin	X	3.2.1	$- \frac{1}{3}$
Patrilateral-cross first-cousin	X	3.2.2	$- \frac{1}{3}$
Matrilateral-parallel first-cousin	X	3.2.3	$- \frac{16 + c_{1}}{3 (16 - 5 c_{1})}$
Matrilateral-cross first-cousin	X	3.2.4	$- \frac{8 - c_{1}}{3 (8 - 3 c_{1})}$
Bilateral-parallel first-cousin	X	3.2.5	$- \frac{16 + c_{1}}{3 (16 - 5 c_{1})}$
Bilateral-cross first-cousin	X	3.2.6	$- \frac{8 - c_{1}}{3 (8 - 3 c_{1})}$
Superposition of unilateral first-cousin	X	3.2.7	$- \frac{16 + c_{m p} - 2 c_{m c}}{3 (16 - 5 c_{m p} - 6 c_{m c})}$
First-cousin	Autosomes	Appendix C	$- \frac{4}{16 - 3 c_{1}}$

Note that c_mp and c_mc in Section 3.2.7 have the same meaning as c₁ in Sections 3.2.3 and 3.2.4, respectively.