Page 37 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

1.7.6 Index combining breeding values from phenotype
and genetic marker information
Consider a situation in which one or more genes affecting a trait with a large impact
on profit have been identified to be linked to a genetic marker (see Chapter 10). If genetic
prediction based only on marker information is available in addition to the conven-
tional BV estimated without marker information, then both sources of information can
be combined into an index (Goddard, 1999). It is also possible that the conventional
BV is based on a subset of traits in the breeding goal and marker information is avail-
able on other traits that are not routinely measured, such as meat quality traits.
A selection index could be used to combine both sources of information and the
increase in accuracy from including marker information could be computed
(Goddard, 1999). Given r as the accuracy of the conventional breeding BV and d as
the proportion of genetic variance explained by the marker information, then the
2
covariance between the two sources of information is dr . If m is the BV based on
marker information and a the BV from phenotypic information, then:
2
⎛ m⎞ ⎛ d dr ⎞
var ⎜ ⎟ = ⎜ ⎝ dr 2 r ⎠ ⎟
⎝ ⎠
2
a
2
Let g be the true breeding value to be predicted, then cov(g, m) = d and cov(g, a) = r .
The normal index equations are:
⎛ b ⎞ ⎛ d dr ⎞ − 1 ⎛ d ⎞
2
1
⎜ ⎝ b 2 ⎟ ⎠ = ⎜ ⎝ dr 2 r ⎠ ⎟ ⎜ r ⎝ 2 ⎟ ⎠
2
Solving the above equations gives the following index weights:
2
2
2
b = 1 − r /(1 − dr ) and b = 1 − d/(1 − dr )
1 2
2
The variance of the index = reliability (r ) is:
I
2
2
2
2
r = [(1 − r )d + (1 − d)r ]/(1 − dr )
I
2
The increase in reliability (r ) from incorporating marker information therefore is:
inc
2 2
2
2
2
2
r = (r − r ) = d/(1 − dr )[(1 − r ) ]
inc I
2
For example, given that r of the conventional BV is 0.34 and marker information
2
accounts for 25% of the genetic variance, then r is 0.459, an increase in reliability of
I
2
2
2
0.12. However, if r is 0.81, then r is 0.83 and r is only 0.02. Thus the usefulness
I inc
of marker information is greater when reliability is low, such as in traits of low herit-
ability and also traits that cannot be measured in young animals such as carcass traits
(Goddard and Hayes, 2002).
Genetic Evaluation with Different Sources of Records 21