Page 135 - Applied Probability

7. Computation of Mendelian Likelihoods

2
1
O
119
3 4
A

5
O
FIGURE 7.1. A Pedigree Partially Typed at the ABO Locus
through the pedigree, requiring multiple visits to each nuclear family. For
pedigrees that are graphically trees, that is, have no loops or cycles, the
algorithm is guaranteed to eliminate all superfluous genotypes for each
person [19]. O’Connell and Weeks present a generalization of the algorithm
that is optimal even in the exceptional cases [5].

TABLE 7.1. Genotype Sets for a Genotype Elimination Example

After After Applying After Applying
Person Applying (A) (B) to {3, 4, 5} (B) to {1, 2, 3}
{A/A, A/O, O/A,
1 All 9 genotypes All 9 genotypes
A/B, B/A}
2 {O/O} {O/O} {O/O}

3 {A/A, A/O, O/A} {A/O, O/A} {O/A}

{A/O, O/A, B/O, {A/O, O/A, B/O,
4 All 9 genotypes
O/B, O/O} O/B, O/O}
5 {O/O} {O/O} {O/O}

Allele consolidation is another tactic that reduces ranges of summation.
At a highly polymorphic, codominant marker locus, most pedigrees will
segregate only a subset of the possible alleles. If a person i is untyped, then
the range of summation for his or her genotypes may involve genotypes
composed of alleles not actually seen within the pedigree. These unseen
genotypes can be consolidated by consolidating unseen alleles. In most ap-