Page 48 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

-1
Without inbreeding, d = 16 .
ii 11
If only the maternal grandsire (k) of animal i is known, add:
−1
d to the (i,i) element
ii
−1
−d /4 to the (k,i) and (i,k) elements
ii
−1
d /16 to the (k,k) element
ii
Without inbreeding, d -1 = 16 .
ii 15
If only the sire (s) of animal i is known, add:
−1
d to the (i,i) element
ii
−1
−d /2 to the (s,i) and (i,s) elements
ii
−1
d /4 to the (s,s) element
ii
4
Without inbreeding, d -1 = in this situation, as in Section 2.4.1.
ii 3
When s and k are unknown, add:
−1
d to the (i,i) element
ii
−1
and d = 1.
ii
2.6 An Example of the Inverse of a Sire and Maternal Grandsire
Relationsip Matrix
A pedigree consisting of sires and maternal grandsires set up from the pedigree in
Table 2.1 is:
Sire Sire of sire Maternal grandsire of sire
1 Unknown Unknown
4 1 Unknown
5 4 1

Recoding sires 1 to n, the pedigree becomes:

1 Unknown Unknown
2 1 Unknown
3 2 1
⎡ 1.0 0.5 0.5 ⎤
⎢ ⎥
Using Eqns 2.6 and 2.7, A = 0.5 1.0 0.625
⎢ ⎥
⎢ ⎣ 0.5 0.625 1.125⎥ ⎦
Note that the relationship among sires is the same as in A calculated from the full
pedigree in Section 2.2.
⎡ 1.0 0.0 0.0⎤
−1
The T matrix for the pedigree is: T −1 = ⎢ ⎢ −0.5 1.0 0.0 ⎥ ⎥
⎢ ⎣ −0.25 −0.5 1.0⎥ ⎦

32 Chapter 2