is homozygous. For example, let B be a member of Group 1 and apart from H1, let H3 be the other haplotype she carries. Treating B as the proband, one group of her surrogate parents includes everyone in Group 1 but her plus A, while the other group includes individuals carrying H3. Suppose a member of this latter group is homozygous for the major allele, this would imply that H3 has the major allele which in turn implies that H1 has the minor allele. In general, consider a SNP that is heterozygous (1,2) for A and all of his surrogate relatives with a Erdös distance of K or less. If a surrogate relative C with Erdös distance K+1 is homozygous (1,1) , then the haplotype of A through which she is linked to C by the shortest path has allele 2 if K is odd, and allele 1 if K is even.
