Exponential Distributed IBD Lengths

The lengths of an IBD segment are exponentially distributed with a mean of $100/(2g)$ cM (centiMorgans), where $g$ is the number of generations which separate the two haplotypes that share a segment from their common ancestor (17,31,16,19,18). We follow Ulgen and Li (32), who recommend to use a cM-to-Mbp ratio of 1. However, the recombination rate, the cM-to-Mbp ratio, varies from 0 to 9 along a chromosome (33). An average IBD segment length of 10 kbp corresponds to a most recent common ancestor 5,000 generations or 100 thousand years ago (kya) using 20 years per generation, and 20 kbp corresponds to 2,500 generations or 50 kya. Therefore, individuals sharing short IBD segments provide insight into the origin and migration of modern humans.

Age estimations of the IBD segments should be considered with care. Computing the time since the last common ancestor depends on many assumptions like the time span of a generation, the ratio of centiMorgans and megabases which we assumed to be 1, and the distribution of IBD lengths.