Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population

Recent modeling studies interested in runs of homozygosity (ROH) and identity by descent (IBD) have sought to connect these properties of genomic sharing to pairwise coalescence times. Here, we examine a variety of features of pairwise coalescence times in models that consider consanguinity. In particular, we extend a recent diploid analysis of mean coalescence times for lineage pairs within and between individuals in a consanguineous population to derive the variance of coalescence times, studying its dependence on the frequency of consanguinity and the kinship coefficient of consanguineous relationships. We also introduce a separation-of-time-scales approach that treats consanguinity models analogously to mathematically similar phenomena such as partial selfing, using this approach to obtain coalescence-time distributions. This approach shows that the consanguinity model behaves similarly to a standard coalescent, scaling population size by a factor 1 - 3c, where c represents the kinship coefficient of a randomly chosen mating pair. It provides the explanation for an earlier result describing mean coalescence time in the consanguinity model in terms of c. The results extend the potential to make predictions about ROH and IBD in relation to demographic parameters of diploid populations. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

Recent modeling studies have investigated the connection between runs of homozygosity (ROH), identity by descent (IBD), and pairwise coalescence times. The study examines various features of pairwise coalescence times in consanguinity models and introduces a separation-of-time-scales approach to analyze coalescence-time distributions. The results suggest that the consanguinity model behaves similarly to a standard coalescent, providing potential for predicting ROH and IBD in diploid populations based on demographic parameters.