Rapidly registering identity-by-descent across ancestral recombination graphs

The genomes of remotely related individuals occasionally contain long segments that are identical by descent (IBD). Sharing of IBD segments has many applications in population and medical genetics, and it is thus desirable to study their properties in simulations. However, no current method provides a direct, efficient means to extract IBD segments from simulated genealogies. Here, we introduce computationally efficient approaches to extract ground-truth IBD segments from a sequence of genealogies, or equivalently, an ancestral recombination graph. Specifically, we use a two-step scheme, where we first identify putative shared segments by comparing the common ancestors of all pairs of individuals at some distance apart. This reduces the search space considerably, and we then proceed by determining the true IBD status of the candidate segments. Under some assumptions and when allowing a limited resolution of segment lengths, our run-time complexity is reduced from O(n³ log n) for the naïve algorithm to O(n log n), where n is the number of individuals in the sample.