Page 160 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

For cow 8 with ten TD records and no progeny, Eqn 9.4 is:
é ˆ u ù é 0.3893 - 0.0844 0.1763ù é 0.3967ù
ê 0 ú = - ú ê ú
ê
ê ˆ u 1ú ê 0.0604 0.5903 0.0353 ú ê 0.0228 ú
ê ˆ u ë 2û ú ê ë 0 0.1576 0.0425 0.6379ú - ê 0.1787ú û
û ë
( W 1 ) ( PA)
é 0.6107 0.0844 - 0.1763ù é 0.2102ù
ê ú ê ú
+ ê 0.0604 0..4097 - 0.0353 ú ê 0.0574 ú
û ë
ë - ê 0.1576 - 0.0425 0.3621ú ê 0.18893ú û
(W 2 ) (YD 8 )

and:

⎡ 0 ˆ u ⎤ ⎡ 0.1210⎤ ⎡ 0.09998⎤ ⎡ 0.2208⎤
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎥ ⎢
⎥ ⎢
⎥ ⎢
⎢ 1 ˆ u = − 0.0168 + 0.0295 = 0.0127 ⎥
⎢ 2 ˆ u ⎣ ⎥ ⎢ − 0.0505⎥ ⎢ 0.0330⎥ ⎢ − 0.0175⎥ ⎦
⎦ ⎣
⎦ ⎣
⎦ ⎣
Considering cow 4, with ten TD records and a progeny:
0 ˆ u ⎡ ⎤ ⎡ 0.3488 − 0.0684 0.1393⎤ − ⎡ 0.0655⎤ ⎡ 0.5640 0.0856 −0.1741⎤
⎢ ⎥ = − ⎥ ⎢ ⎥ ⎥ ⎢ ⎥
⎢
1 ˆ u
⎢ ⎥ ⎢ 0.0490 0.5132 0.02884 ⎥ ⎢ 0.0123 + 0.0613 0.3585 −0.0355 ⎥
⎥ ⎢
⎢ ⎥ ⎢ ⎣ 0.1245 0.0343 0.5451⎥ − ⎢ 0.0343⎥ ⎢ −0.1557 −0.0428 0.3186⎥ ⎦
⎣
⎦ ⎣
⎦ ⎣
ˆ u2⎦
8
(W ) (PA ) (W )
1 2
⎡ 0.2711⎤ ⎡ 0.0872 −0.0171 0.0348⎤ ⎡ 1 . 5725⎤
⎢ − ⎥ ⎢ ⎥ ⎢ ⎥
⎥ ⎥ ⎢
⎢ 0.0508 + −0.0123 0.1283 0.0071 ⎥ ⎢ 0.0057 ⎥
⎢
⎦ ⎣
⎣ − ⎢ 0.6412⎥ ⎢ 0.0311 0.0086 0.11363⎥ − 0.6948 ⎦ ⎥
⎦ ⎣
(YD ) (W ) (PC )
3
ˆ 0 u ⎡ ⎤ ⎡ −0.0285⎤ ⎡ 0.2602⎤ ⎡ 0.1128⎤ ⎡ 0.3445⎤
⎢ ⎥ ⎢ ⎥ ⎢ 0.0212 + − ⎥ ⎢ ⎥
⎥ ⎢
ˆ 1 u
⎢ ⎥ = ⎢ 0 0.0086 + ⎥ ⎢ 0.0235 = 0.0063 ⎥
⎥ ⎢
⎥ ⎢
⎢ ⎥ ⎣ − ⎢ 0.0264⎥ ⎢ − 0.2443⎥ ⎢ − 0.0457⎥ ⎢ ⎢ − 0.3164⎥ ⎦
ˆ 2 u ⎣ ⎦
⎦ ⎣
⎦ ⎣
⎦ ⎣
Equation 9.4 is useful in explaining the evaluations for animals in terms of con-
tributions from different sources of information, and how these contributions vary
with different DIM could also be examined. However, Eqn 9.4 relates to random
regression coefficients. Usually, the EBV at a particular stage of the longitudinal scale,
such as 305 days for milk yield or body weight at 1 year of age, is published. Therefore,
the interest might be in calculating the contributions from the various sources of infor-
mation to the published EBV. Using milk yield as an example, the contribution to
305-day estimated BV from various sources of information can be calculated as:
u ˆ = V PA + V YD + V PC
(305)anim 1 2 3
*
u ˆ = PA + YD + PC * (9.5)
*
(305)anim
144 Chapter 9