Connecting IBD tracts and runs of homozygosity: A coalescent framework for inferring effective population size

arXiv:2605.03498v1 Announce Type: new
Abstract: Identity by descent (IBD) tracts and runs of homozygosity (ROH) are related concepts that refer to the autozygosity in chromosome segments. However the formal relationship between their length distributions remains to be established. Here we present a coalescent framework that unifies these two concepts within a single analytical development. Starting from a Wright-Fisher model, we derive closed-form probability density functions for IBD tract lengths and extend these to the observable distribution of ROH lengths. This is achieved by explicitly modelling the displacement of ROH limits from true recombination breakpoints to the nearest heterozygous marker site. Mutation, gene conversion, finite marker density, and variable marker heterozygosity are incorporated as parameters in the theory that link IBD tracts to ROH. We show that the chromosome segment homozygosity (CSH) statistic emerges as a special case. This enables demographic information from IBD tracts and ROHs to be combined into a framework for inferring effective population size. Finally, we incorporate the quantitative genetic theory of background selection into the IBD length distribution, to show how selection introduces a systematic upward bias in apparent tract lengths. This demonstrates that no single Ne value can account for the entire IBD length distribution under selection. The application of this theory to the detection of selection signatures in the genome is illustrated using the example of the local selective sweep associated with lactase persistence in human populations.