Page 325 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Similar to the approach of Meuwissen and Luo (1992), the two lists can be set
up simultaneously while processing the ith animal by continually adding the parents
of the next youngest animal in either list to the appropriate list. If the next youngest
in each list is the same animal, say k, then it is a common ancestor and F is updated
i
as F = F + l l (0.5D ). When ancestors of one of the parents have been processed,
i i s ik d ik kk
the procedure can be stopped, and it is not necessary to search both lists completely.
The algorithm for this methodology is:
F = −1
0
For i =1, N:
F = 0
i
If s is known, add s to AS , l = 1.
i i s i s is i
If d is known, add d to AD , l = 1.
i i d i d id i
Do while AS not empty and AD not empty.
s i ˆ d i
j = max(AS ), k = max(AD )
s i d i
If j > k then (next youngest j is in AS ):
s i
If s is known, add s to AS ; l = l + 0.5l
j j s i s is j s is j s ij
If d is known, add d to AS ; l = l + 0.5l
j j s i s id j s id j s ij
Delete j from AS
s i
Else if k > j then (next youngest k is in AD ):
d i
If s is known, add s to AD ; l = l + 0.5l
k k d i d is k d is k d ik
If d is known, add d to AD ; l = l + 0.5l
k k d i d id k d id k d ik
Delete k from AD
di
Else (next youngest ancestor j = k is a common ancestor):
If s is known, add s to AS ; l = l + 0.5l
j j s i s is j s is j s ij
add s to AD ; l = l + 0.5l
j d i d is j d is j d ij
If d is known, add d to AS ; l = l + 0.5l
j j s i s id j s id j s ij
add d to AD ; l = l + 0.5l
j d i d id j d id j d ij
F = F + l l 0.5(D )
i i s ij d ij jj
Delete j from AN and AD
ˆ s i d i
End if
End while
End do
B.2.1 Illustration of the algorithm

Using the pedigree in Table 2.1, the algorithm is illustrated for animal 5, which is inbred.
For animal 5:
F = 0
5
Both parents known, s = 4 and d = 3.

Add 4 to AD ; l = 0.5
4 44
Add 3 to AD ; l = 0.5
3 33
Appendix B 309