Page 324 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Delete animal 5 from AN ; animals 4 and 3 left in AN .
5 5
Next animal in AN :
5
j = max(AN ) = 4
5
Add sire of 4 (animal 1) to AN :
5
l = l + 0.5l = 0.25
51 51 54
2
2
a = a + l D = 0.5 + (0.5) (0.75) = 0.6875
55 55 54 44
Delete animal 4 from AN ; animals 3 and 1 left in AN .
5 5
Next animal in AN :
5
j = max(AN ) = 3
5
Since animal 1, the sire of j, is already in AN , add only the dam of 3 (animal 2) to AN :
5 5
l = l + 0.5l = 0.25 + (0.5)0.5 = 0.5
51 51 53
l = l + 0.5l = 0 + (0.5)0.5 = 0.25
52 52 53
a = a + l D = 0.6875 + (0.5) 0.5 = 0.8125
2
2
55 55 53 33
Delete animal 3 from AN ; animals 1 and 2 left in AN .
5 5
Next animal in AN :
5
j = max(AN ) = 2
5
Both parents are unknown:
2
a = a + l D = 0.8125 + (0.25) 1 = 0.875
2
55 55 52 22
Delete animal 2 from AN ; animal 1 left in AN .
5 5
Next animal in AN :
5
j = max(AN ) = 1
5
Both parents are unknown:
2
2
a = a + l D = 0.875 + (0.5) 1 = 1.125
55 55 51 11
Delete 1 from AN ; AN is empty.
5 5
F = 1.125 − 1 = 0.125
5
which is the same inbreeding coefficient as that obtained for animal 5 in Section 2.2.
B.2 Modified Meuwissen and Luo Algorithm
The approach of Meuwissen and Luo given above was modified by Quaas (1995) to
improve its efficiency. The disadvantage of the above method is that, while calculating
a row of L at a time (Henderson, 1976), it is accumulating diagonal elements of A, as
in Quaas (1976), and this necessitates tracing the entire pedigree for i, but what is really
needed is only the common ancestors. Thus a more efficient approach is to accumulate
a as S l l D (Henderson (1976) and calculate F as 0.5a = S l l (0.5D ).
s id i k s ik d ik kk i s id i k s ik d ik kk
Instead of computing the ith row of L, only the non-zero elements in the rows for the
sire and dam of i are calculated. Quaas (1995) suggested setting up a separate ancestor
list (AS ) for s and another (AD ) for d ; then F = 0.5a = S e U l l (0.5D ).
s i i d i i i s id i k s i d i s ik d ik kk

308 Appendix B