Fig. 2: Imputation of missing parental genotypes.

a, Imputation from sibling pairs (Fig. 1e). Given knowledge of the IBD state of the siblings’ alleles (alleles coded by ‘0’ and ‘1’), the sum of the maternal and paternal genotypes can be imputed \(\left( {\hat g_{{{{\mathrm{par(i)}}}}}} \right)\). If the siblings do not share any alleles IBD, then all four parental alleles are observed (IBD0). If the siblings share one allele IBD, then three parental alleles are observed (IBD1). If the siblings share both alleles IBD, then two parental alleles are observed (IBD2). When parental alleles are unobserved, we impute them with the frequency of allele 1, f. The IBD state between siblings changes with the recombination events that occurred during meiosis in the parents and can be inferred (Methods and Supplementary Note Section 9). b, Shows how phased data can be used to determine which allele is shared between two individuals who share one allele IBD at a SNP where both are heterozygous. This applies to sibling pairs in IBD1 and parent–offspring pairs, who always shared one allele IBD. A neighboring SNP that has been phased with the target SNP and is homozygous for one individual and heterozygous for the other is used to resolve the uncertainty. For the individual on the left, the 0 allele must be the allele shared with the other individual at the neighboring SNP; thus, through the phased haplotype ‘1-0’ (hap1), it is determined that the 1 allele is the shared allele at the target SNP.