Affiliations: 1) Depatment of Genetics, Stanford University, Stanford, CA; 2) Braun School of Public Health and Community Medicine, Hebrew University of Jerusalem, Ein Kerem, Israel; 3) Department of Biology, Stanford University, Stanford, CA
Keywords: Theory & Method Development
By providing additional opportunities for coalescence within families, the presence of consanguineous unions in a population reduces coalescence times relative to non-consanguineous populations. First-cousin consanguinity can take one of four forms differing in the sexes of the siblings whose offspring join in a consanguineous union: patrilateral parallel, patrilateral cross, matrilateral parallel, and matrilateral cross. Considering populations with each of the four types of consanguinity individually, as well as a population with a mixture of the four types, we examine coalescent models of consanguinity. We previously computed, for first-cousin consanguinity models, the mean coalescence time for X-chromosomal loci and the limiting distribution of coalescence times for autosomal loci. Here, we use the separation-of-time-scales approach to obtain the limiting distribution of coalescence times for X-chromosomal loci. This limiting distribution has an instantaneous coalescence probability that depends on the probability that a union is consanguineous; lineages that do not coalesce instantaneously coalesce according to an exponential distribution. The computations of coalescence time distributions are useful for understanding features of runs of homozygosity (ROH) and identity by descent (IBD): as coalescence times decrease in a population, ROH and IBD segments increase in length. We apply our calculations for X-chromosomal coalescence times alongside the analogous calculation on the autosomes to develop theory for the expected fractions of the X chromosome and of the autosomal genome that lie within ROH and IBD, expressing these fractions as functions of the rate and type of consanguinity. The results can inform the understanding of haplotype sharing patterns in highly consanguineous populations.