Therefore, we created a complete IBD dictionary by identifying IBD segments between each pair of the 2x1,415 = 2,830 haplotypes in the sample (81 Text).

Our HMM is the haplotype analogue of the genotype HMM used for phasing, and is similar to the HBD-HMM developed previously [18].

A total of 97,821,947 IBD segments were identified among the 1,415 Hutterites (~1.1 segment per haplotype pair on average, because there are 2830x2829/2 = 4,003,035 individual pairs and 22 chromosomes).

We organize IBD segments in an IBD segment index data structure, which consists of a set of IBD cliques at each SNV and allows a quick O(1)time queries of whether a pair of haplotypes is IBD at a certain SNV.

2) whose nodes are the 2,830 haplotypes of the 1,415 Hutterites, an edge indicates the two haplotypes are IBD, and the edge weight is the HMM posterior probability of IBD (81 Text, Eq.

Large weights are thus given to haplotype pairs that have a higher probability of being IBD.

LD-based imputation methods require a reference panel of genotype training data, usually from unrelated individuals, to infer local haplotype structure, and sharing of hap-lotype stretches are used for filling in missing genotypes [8—11].

We first phased the SNV genotypes using pedigree-based phasing algorithms [16,17] and determined IBD segments between each pair of haplotypes using a Hidden-Markov Model [18].

To improve the call rate, the missing genotypes were imputed using the LD-based IMPUTE2 program [11], with the phased haplotypes of the 98 whole genome sequenced Hutterites as the reference panel.

The first four require only the framework SNVs: (i) phasing; (ii) identifying IBD segments among all haplotype pairs; (iii) indexing IBD segments into a dictionary of IBD cliques; and (iV) assigning parental origin to haplotypes .