Page 30 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

1.7.2 Examples of selection indices using different sources of information

Data available on correlated traits

Example 1.6
Assume the following parameters were obtained for average daily gain (ADG) from
birth to 400 days and lean per cent (LP) at the same age in a group of beef calves:

Heritability Standard deviation
ADG (g/day) 0.43 80.0
LP (%) 0.30 7.2
The genetic and phenotypic correlations (r and r ) between ADG and LP are 0.30
g p
and −0.10, respectively. Construct an index to improve growth rate in the beef calves.
Assuming ADG as trait 1 and LP as trait 2, then from the given parameters:
2
p 11 = 80 = 6400
7 2 =
p 22 = . 2 51 84
.
p 12 = rp ( p )( p ) =- . ( )( ( .
0 1 6400 51 84) =-57 6.
22
11
g = h 2 p ) = 0 43. (6400 ) = 2752
11 ( 11
)
.
g = h 2 (p ) = 030. (5184. ) = 15 552
22 22
g = rg g )(g ) = 62 064
.
12 ( 11 22
The index equations to be solved are:
⎡ b ⎤ ⎡ p 11 p ⎤ − 1 ⎡ g ⎤
1
12
11
=
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
2 b ⎣ ⎦ ⎣ p 21 p 22⎦ ⎣ g 21⎦
Inserting appropriate values gives:
é 1 b ù é 6400.00 - 57.60ù - 1 é 2752.000ù
=
ê ú ê ú ê ú
2 b ë û ë - 57.60 51.84 û ë 62.0664 û
The solutions are b = 0.445 and b = 1.692.
1 2
The index therefore is:
) + 1.692(LP − m )
I = 0.445(ADG − m ADG LP
and m are herd averages for ADG and LP. Using Eqn 1.21:
where m ADG LP
r = ( é 0 445. (2752 ) 1 692.+ (62 064. )) 2752/ ù = 0 695.
û
ë
Using single records on individual and relatives

Example 1.7
Suppose the ADG for a bull calf (y ) is 900 g/day and the ADG for his sire (y ) and dam
1 2
(y ) are 800 g/day and 450 g/day, respectively. Assuming all observations were obtained
3
14 Chapter 1