Page 34 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

in Example 1.6, construct an index to select fast-growing lean beef calves using
Eqn 1.22. Repeat the analysis using Eqn 1.23.
Using Eqn 1.22, index equations are:

1 11 w g ⎤
⎡ 1 b ⎤ ⎡ p p ⎤ − 1 ⎡ w g+
=
⎢ ⎥ ⎢ 11 12 ⎥ ⎢ 2 12 ⎥
2 b ⎣ ⎦ ⎣ p 21 p ⎦ ⎣ w g+ 2 22 2
1 21 w g ⎦
22
Inserting the appropriate values:
- 1
é 1 b ù é 6400.00 - 57.60ù é 1.5(2752)+0.55(62.064)ù
ê ú ê ú ê ú
=
2 b ë û ë - 57.60 51.84 û ë 1.5(62.064+0.5(15.552) û
Solutions for b and b from the above equations are 0.674 and 2.695, respectively.
1 2
The index therefore is:
) + 2.694(LP − m )
I = 0.674(ADG − m ADG LP
Applying Eqn 1.23, the sub-index for ADG is the same as that calculated in
Example 1.6 with b = 0.445 and b = 1.692.The sub-index for LP is:
1 2
b p + b p = g
1 11 2 12 12
b p + b p = g
1 21 2 22 22
which gives:
⎡ 1 b ⎤ ⎡ 6400.00 − 57.60⎤ − 1 ⎡ ⎡ 62.064⎤
=
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
2 b ⎣ ⎦ ⎣ − 57.60 51.84 ⎦ ⎣ 15.552 ⎦
The solutions are b = 0.0125 and b = 0.314. Multiplying the sub-indices by their
1 2
respective weights gives:
I ) + 1.692(1.5)(LP − m )
ADG = 0.445(1.5)(ADG − m ADG LP
) + 2.538(LP − m )
ADG LP
= 0.668(ADG − m
and:
) + 0.314(0.5)(LP − m )
LP ADG LP
I = 0.0125(0.5)(ADG − m
) + 0.157(LP − m )
ADG LP
= 0.006(ADG − m
Summing the b terms from the two sub-indices, the final b terms are:
b = 0.668 + 0.006 = 0.674
1
b = 2.538 + 0.157 = 2.695
2
Therefore the final index is:
) + 2.695(LP − m )
ADG LP
I = 0.675(ADG − m
which is the same as calculated using Eqn 1.22.
1.7.4 Overall economic indices using predicted genetic merit

Overall economic indices that combine (PTAs) or estimated breeding values (EBVs)
calculated by best linear unbiased prediction (BLUP, see Chapter 3) have become

18 Chapter 1