Page 229 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Table 12.1. List of filled sire × dam subclasses and ancestor subclasses.
Sire ×
dam
subclass Pass Counts from
subclass progeny Known parent
Φ S D added subclasses Status ϕ subclasses

A 6 8 1 KN 1 2 3 6
B 6 5 1 1 KN 2 3 6
C 3 8 1 1 KN 3 6
D 3 4 1 KN 4
E 1 2 1 KN 5
F 4 8 2 1 UK
G 3 5 2 1 + 1 − 1 = 1 KN 6
H 6 1 2 1 UK
I 6 2 2 1 UK
J 4 5 2 1 + 1 − 1 = 1 UK
K 3 1 3 1 + 1 − 1 = 1 UK
L 3 2 3 1 + 1 − 1 = 1 UK
M 4 1 3 1 + 1 − 1 = 1 UK
N 4 2 3 1 + 1 − 1 = 1 UK
Φ, consecutive label for subclasses.
S, sire; D, dam; KN, known; UK, regarded as unknown.
ϕ, consecutive number for known subclasses.

determine whether ancestor subclasses are treated as known or unknown were
calculated as specified earlier. Subclasses of the types f and f received a count
S,SD SS,SD
of 1 and −1, respectively, from progeny subclass f . Thus subclass f received a
SD 3,5
count of 1 from each of its progeny subclasses, f and f , and a count of −1 from
3,8 6,5
f . Again, f received 1 each from f and f and −1 from f . Proceeding through
6,8 4,1 6,1 4,5 6,5
the ancestor subclasses (F to N), those with a count of 1 and with at least two prog-
eny subclasses known are regarded as unknown. Only the ancestor subclass f was
3,5
regarded as known because two of its progeny subclasses (f and f ) were known
3,8 6,5
although it had a count of 1.
Using rule 3, the contribution of subclass i regarded as known (subclasses 1 to 6
ii
−1
(see Table 12.1)) to F is then calculated as c c′r . For example, for the subclass f
i i 6,8
(subclass 1), three parent subclasses are known: 2, 3 and 6, which are of the subclass
type f , f and f , respectively. Therefore, b′ = [0.5 0.5 −0.25], c′ = [1 − b′] =
S,DD SS,D SS,DD 1 2 1
[1 −0.5 −0.5 0.25]. The matrix, F , the relationship among parent subclasses 2, 3 and
1
6 (see 12.14) is:
2 3 6
⎡ 1.00 0.25 0.50⎤
⎢ ⎥
F 1 = 0.25 1.00 0.50 ⎥
⎢
⎢ ⎣ 0.50 0.50 100⎥ ⎦
.

Non-additive Animal Models 213