Page 18 - Linear Models for the Prediction of Animal Breeding Values

epistasis, which represent intra-locus and inter-loci interactions respectively, are
assumed to be of little significance and are included in the e term of the model as:
ij
y = m + g + e * (1.2)
ij i ai ij
*
with e being the sum of the random environmental effects, dominance and epistatic
ij
genetic values. Equation 1.2 constitutes the linear model usually employed in most
problems of breeding value prediction in animal breeding. Usually it is assumed that
y follows a multivariate normal distribution, implying that traits are determined by
infinitely many additive genes of infinitesimal effect at unlinked loci, the so-called
infinitesimal model (Fisher, 1918; Bulmer, 1980). Also, it is assumed that var(y), var(g)
*
*
*
and var(e ) are known and that there is no correlation between g and e (cov(g, e ) = 0)
*
*
nor is there any correlation among mates (cov(e, e ) = 0). Also m, which is used sub-
sequently in this chapter to represent the mean performance of animals in the same
management group, for instance animals reared under the same management system,
of the same age and sex, is assumed known. From Eqn 1.2, the problem of predicting
breeding value reduces to that of adjusting phenotypic observations for identifiable
non-random environmental effects and appropriately weighting the records of ani-
mals and their available relatives.
From the earlier explanation, if a is the breeding value of animal i, then:
i
1
a = g = a + a + m
1
i ai 2 s 2 d i
where a and a are the breeding values of the sire and dam, respectively, and m is the
s d i
deviation of the breeding value of animal i from the average breeding value for both
parents, that is, Mendelian sampling. The sampling nature of inheritance implies that
each parent passes only a sample one-half of their genes to their progeny. There is,
therefore, genetic variation between offspring of the same parents since all offspring
do not receive exactly the same genes. Mendelian sampling could be regarded as the
deviation of the average effects of additive genes an individual receives from both
parents from the average effects of genes from the parents common to all offspring.
The accurate prediction of breeding value constitutes an important component of
any breeding programme since genetic improvement through selection depends on
correctly identifying individuals with the highest true breeding value. The method
used to predict breeding value depends on the type and amount of information avail-
able on candidates for selection. The next section discusses the prediction of breeding
value using different sources of information. It should be noted that many applica-
tions of genetic evaluation deal with the prediction of transmitting ability, usually
referred to as predicted transmitting ability (PTA) or estimated transmitting ability
(ETA), which is one-half of the predicted breeding value.

1.3 Breeding Value Prediction from the Animal’s
Own Performance

1.3.1 Single record
When one phenotypic record is the only available information on each animal, the
estimated breeding value (EBV) (a ) for animal i can be calculated as:
i
ˆ
a = b(y − m) (1.3)
i i
2 Chapter 1