Page 26 - Linear Models for the Prediction of Animal Breeding Values

Example 1.4
Suppose that the EBVs for the sire and dam of a heifer are 180 and 70 kg for yearling
body weight, respectively. Given that the accuracy of the proofs are 0.97 for the sire
and 0.77 for the dam, predict the breeding value of the heifer and its accuracy for
body weight at 12 months of age.
From Eqn 1.9:

a ˆ = 0.5(180 + 70) = 125 kg
heifer
The accuracy is:
2
7
.
r ˆ aa = 05 . 2 + 0 . ) = 062
. ( 097
7
,
1.6 Breeding Value Prediction for One Trait from Another
The breeding value of one trait may be predicted from the observation on another
trait if the traits are genetically correlated. If y is the observation on animal i from
one trait, its breeding value for another trait x is:
a = b(y − m) (1.10)
ˆ
ix
with:
b = cov(a , measurement on y)/var(measurement on y) (1.11)
x
The genetic correlation between traits x and y (r ) is:
axy
r = cov(a , a )/(s s )
axy x y ax ay
Therefore:
cov(a , a ) = r (1.12)
x y axy ax ay
s s
Substituting Eqn 1.12 into Eqn 1.11:
b = r 2 (1.13)
axy ay ax y
s s /s
If the additive genetic standard deviations for x and y in Eqn 1.13 are expressed
as the product of the square root of their individual heritabilities and phenotypic
variances, then:

b = r 2
axy y x x y y
s s h h /s
= r (1.14)
axy x y x y
h h s /s
The weight depends on the genetic correlation between the two traits, their heritabilities
and phenotypic standard deviations.
The accuracy of the predicted breeding value is:
r
x
ax,ay = cov(a , measurement on y)/s s
ax y
= r s s /(s s )
axy ay ax ax y
= r h
axy y
The accuracy depends on the genetic correlation between the two traits and heritability
of the recorded trait.
10 Chapter 1