Page 98 - Applied Probability

5. Genetic Identity Coefficients
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TABLE 5.1. Condensed Coefficients of Identity
Relationship
0
Parent–Offspring
1
0
1
1
Half Siblings ∆ 7 ∆ 8 ∆ 9 Φ 1 4 1
0
2 2 8
Full Siblings 1 1 1 1
4 2 4 4
First Cousins 0 1 3 1
4 4 16
Double First Cousins 1 6 9 1
16 16 16 8
Second Cousins 0 1 15 1
16 16 64
Uncle–Nephew 0 1 1 1
2 2 8
algorithm produces the kinship coefficient for every possible pair in a pedi-
gree. These coefficients can be arranged in a symmetric matrix Φ with Φ ij
as the entry in row i and column j. To compute Φ, we first number the
people in the pedigree in such a way that every parent precedes his or her
children. Any person should have either both or neither of his or her par-
ents present in the pedigree. To avoid ambiguity, it is convenient to assume
that all pedigree founders are non-inbred and unrelated.

1 2

3 4

5 6

FIGURE 5.1. A Brother–Sister Mating

The matrix Φ is constructed starting with the 1×1 submatrix in its upper
left corner. This submatrix is iteratively expanded by adding a partial row
and column as each successive pedigree member is encountered. To make
this precise, consider the numbered individuals in sequence. If the current