The effect of consanguinity on coalescence times on the X chromosome

Consanguineous unions increase the frequency at which identical genomic segments are inherited along separate paths of descent, decreasing coalescence times for pairs of alleles drawn from an individual who is the offspring of a consanguineous pair. For an autosomal locus, it has recently been shown that the mean time to the most recent common ancestor (T_MRCA) for two alleles in the same individual and the mean T_MRCA for two alleles in two separate individuals both decrease with increasing consanguinity in a population. Here, we extend this analysis to the X chromosome, considering X-chromosomal coalescence times under a coalescent model with diploid, male-female mating pairs. We examine four possible first-cousin mating schemes that are equivalent in their effects on autosomes, but that have differing effects on the X chromosome: patrilateral-parallel, patrilateral-cross, matrilateral-parallel, and matrilateral-cross. In each mating model, we calculate mean T_MRCA for X-chromosomal alleles sampled either within or between individuals. We describe a consanguinity effect on X-chromosomal T_MRCA that differs from the autosomal pattern under matrilateral but not under patrilateral first-cousin mating. For matrilateral first cousins, the effect of consanguinity in reducing T_MRCA is stronger on the X chromosome than on the autosomes, with an increased effect of parallel-cousin mating compared to cross-cousin mating. The theoretical computations support the utility of the model in understanding patterns of genomic sharing on the X chromosome.