Page 19 - Linear Models for the Prediction of Animal Breeding Values

where b is the regression of true breeding value on phenotypic performance and m, as
indicated earlier, is the mean performance of animals in the same management group
and is assumed to be known. Thus:
b = cov(a, y)/var(y) = cov(a, a + e)/var(y)
2 2
a
= s /s y
= h 2
2
The prediction is simply the adjusted record multiplied by the heritability (h ). The
correlation between the selection criterion, in this case the phenotypic value, and the
true breeding value is known as the accuracy of prediction. It provides a means of
evaluating different selection criteria because the higher the correlation, the better
the criterion as a predictor of breeding value. In some cases, the accuracy of evalu-
2
ations is reported in terms of reliability or repeatability (r ), which is the squared
correlation between the selection criterion and the true breeding value. With a single
record per animal, the accuracy is:
r = cov(a, y)/(s s )
a,y a y
2
= s /(s s )
a a y
= h
2
and reliability equals h .
Expected response (R) to selection on the basis of a single record per individual
(Falconer and Mackay, 1996) is:
2 2
a,y y
R = ir s = ih s y
where i, the intensity of selection, refers to the superiority of selected individuals
above population average expressed in phenotypic standard deviation.
ˆ
The variance of EBV (var(a)) is:
i
2
ˆ
var(a) = var(by) = var(h y)
i
4 2
= h s y
2 2 2 2 2
y
= r a,y h s = r a,y s a (1.4)
Example 1.1
Given that the yearling weight of a heifer is 320 kg in a herd with a mean of 250 kg,
predict her breeding value and its accuracy if the heritability of yearling weight is 0.45.
From Eqn 1.3:
aˆ = 0.45(320 − 250) = 31.50 kg
and:
r ay = . 045 = . 0 67
,

1.3.2 Repeated records

When multiple measurements on the same trait, such as milk yield in successive
lactations, are recorded on an animal, its breeding value may be predicted from the

Genetic Evaluation with Different Sources of Records 3