Page 27 - Linear Models for the Prediction of Animal Breeding Values

Correlated response (CR) in trait x as a result of direct selection on y (Falconer
and Mckay, 1996) is:
x y axy y
CRx = ih h r s

Example 1.5
Suppose the standard deviation for growth rate (GR) (g/day) to 400 days in a popula-
tion of beef cattle was 80, with a heritability of 0.43. The standard deviation for lean
growth rate (LGR) (g/day) for the same population was 32, with a heritability of
0.45. If the genetic correlation between both traits is 0.95 and the population mean
for growth rate is 887 g/day, predict the breeding value for LGR for an animal with
a GR of 945 g/day.
Using Eqn 1.10:

a ˆ = b(945 − 887)
LGR
with:
b = cov(GR, LGR)/var(GR)
From Eqn 1.13:
b = (0.95(0.656)(0.671)(32))/80 = 0.167
a ˆ = 0.167(945 − 887) = 9.686
LGR
The accuracy of the prediction is:
r =0.95( 0 43) = . 0 623
.

1.7 Selection Index

The selection index is a method for estimating the breeding value of an animal com-
bining all information available on the animal and its relatives. It is the best linear
prediction of an individual breeding value. The numerical value obtained for each
animal is referred to as the index (I) and it is the basis on which animals are ranked
for selection. Suppose y , y and y are phenotypic values for animal i and its sire and
1 2 3
dam, then the index for this animal using this information would be:
I = aˆ = b (y − m ) + b (y − m ) + b (y − m ) (1.15)
i i 1 1 1 2 2 2 3 3 3
where b , b , b are the factors by which each measurement is weighted. The deter-
1 2 3
mination of the appropriate weights for the several sources of information is the main
concern of the selection index procedure. In Eqn 1.15, the index is an estimate of the
true breeding value of animal i.
Properties of a selection index are:
1. It minimizes the average square prediction error, that is, it minimizes the average
2
of all (a − aˆ ) .
i i
2. It maximizes the correlation (r ) between the true breeding value and the index.
a,a ˆ
The correlation is often called the accuracy of prediction.
3. The probability of correctly ranking pairs of animals on their breeding value is
maximized.

Genetic Evaluation with Different Sources of Records 11