Supplementary Material for: Pedigree-Free Descent-Based Gene Mapping from Population Samples

Segments of the genome inherited from a common ancestor by related individuals are said to be identical by descent (IBD). Modern genetic marker data provide information to infer such segments among multiple related members of a population, even when pedigree relationships are unknown. Previous methods have been proposed for the detection of pairwise IBD, but the computation of probabilities of trait data under many trait models requires an IBD estimate jointly consistent among individuals and slowly varying across genome locations; we refer to such an estimate as an ‘IBD graph'. In this paper, we develop a novel method that builds IBD graphs sequentially among related individuals from a population sample using either phased or unphased genetic marker data. We show how IBD graphs realized conditionally on marker data provide a form of linkage mapping score, analogous to a LOD score, and propose a permutation approach to normalize this mapping score. Using a simulated quantitative trait dependent on the (unobserved) genotype at a major locus, we apply the approach to two samples containing both closely and remotely related individuals, among whom there are complex patterns of IBD. We compare the results of our approach with an alternate approach based on the estimation of local kinship. We show that pairwise estimates derived from a joint IBD graph give significant improvements in LOD score estimation over estimates derived from an intrinsically pairwise approach.