Research Article

1766
Generally, mixed linear models of best linear unbiased prediction
(BLUP) in an animal model (AM) are used, and a pedigree of three
or more generations of ancestors is taken into account according
to the model equation:
Y = Xb + Zu + e (1)
where Y is the vector of measured performances, X and Z are
known matrices that relate performance to the systematic effects
of the breeding environment and the animals, b and u are the
estimated vectors of fixed systematic environmental effects and
the random effects of an animal (BV) with the additive numerator
relationship matrix (A), and e is the vector of random error.
Using this model equation, a system of normal equations is
constructed in which the unknown constants (b) and(u) are
estimated. These systems of equations are vast, and special
algorithms are required for their solution. 12
Most of the variability in any measured production trait is
caused by systematic environmental effects. The influence of
the herd–year–season, or herd–test-day, which identifies a
contemporary group of animals kept under the same conditions,
is usually the most important factor.
Evaluations are generally oriented to the MT-AM (multi-trait
animal model), RR-TDAM (random regression test-day animal
model), AM-maternal, and nonlinear methodologies for survival
(kit) analysis. 13–23
It is important to find a method of evaluation that minimises
residual error and simultaneously considers all of the effects that
may influence the performance variable being measured. From
a genetic perspective, it is important to ask: What proportion
of variability is explained by the statistical model used? Is this
proportion different in a model that does not account for genetic
effects? Is this model the best (optimal) of all the possibilities
tested? The proportion of variability explained by the statistical
model used (R 2 ) and other information criteria for testing the
suitability of the model, such as Akaike’s information criterion
(AIC), Bayes information criterion (BIC), Bayes factor (BF) and the
likelihood ratio test (LRT), are very important in answering these
questions. 24–28
Molecular-genetic information can be used to improve selection
programmes. 29 Animals are evaluated more accurately when their
entire genetic value is partitioned into causal factors and withinfamily
genetic components are exploited. The use of moleculargenetic
markers in breeding is the inclusion of additional criteria in
the selection indices. These markers increase selection differences
relativetoexistingtraditionalbreedingprogrammesbydecreasing
the correlation among sib individuals, increasing the accuracy of
animal selection, allowing the utilisation of genetic variability
that is usually included in non-utilisable residuum, and allowing
a shortening of the generation interval (because they may be
analysed in young animals). The use of selection markers is
conditional upon the timely laboratory analysis of the entire
subpopulation subjected to pre-selection (e.g., young bulls) and
rapid application before the determined gene linkages change.
This requires frequent updates of selection indices, as shown
below (Eqn (2)). The consistent application of genomic selection
markedly reduces the cost of a selection programme. 3,30
However, data analysis becomes more complicated, the number
of estimated parameters becomes higher, and a modified
information criterion (mBIC) is necessary for the selection of a
suitable model of evaluation. 31,32
In order to select individuals for breeding, marker-assisted
selection (MAS) may be applied if several genetic markers are to
www.soci.org J Pribyl et al.
be used. Alternatively, genomic selection utilises high numbers of
markers that densely cover the whole genome. 3,33 BV is usually
calculated in two steps. In the first step, the regression coefficients
(v) (substitution effects of the alleles of a considered locus) are
determined in a reference population with known performance
and highly reliable BVs. This reference population usually includes
only a part of the population under selection. From the first step,
quantitative trait loci (QTL) effects are estimated. Subsequently,
BV is determined for all of the young animals in the evaluated
(sub)population by means of a selection index, as described in
Eqn (2). 30
The reference population and the evaluated population are
separated by at least one generation. Therefore, the relationships
between markers and QTLs determined in the older generation
may not be fully applicable to the younger evaluated population,
as the QTLs are not fully covered by study markers. Furthermore,
the influences of selection, mutation, immigration of sires used
intensively in artificial insemination, changes in environment, and
the development of the commercial population under selection
can also affect the applicability of QTL data across generations.
Therefore, it is necessary to periodically redetermine u in Eqn (1),
allele frequencies (q) in Eqn (5), their inherence in the genotypes
of individual animals (T), and regression coefficients (v) in(3)so
that the gap between the reference and the evaluated population
will be as small as possible. 3,30,34
The GEBV of a given trait is calculated based on known loci and
remaining polygenes according to the selection index:
GEBVj = k1 DGVj + k2u ∗ j
where GEBVj is the genomic (total) BV for an individual (j)
determined based on the genomic information at the locus (i)
and remaining polygenic effect. DGVj is the direct genetic value,
calculated as the sum of BVs for a particular loci:
DGVj = �jTijvij
where Tij (with regard to Eqn (9)) is the ith element in the jth row
of the known incidence matrix correlating the genetic effects of
particular alleles to the observed individual, vij is the vector of
genetic marker effects, u ∗ j represents the BV calculated based on
the remaining polygenes, and k1 and k2 are the weights of the
information sources in the index. 35
If the GEBV is calculated for young animals without their own
production records, u ∗ j represents only information about their
parents. In cases where a high density of genetic markers is
available, the u ∗ j in Eqn (2) is frequently omitted.
GENETICALLY CONDITIONED VARIABILITY
OF PERFORMANCE
Reliably determined population-genetic parameters are a precondition
for genetic evaluation. We are usually interested in
phenotype variability (σ 2 P), which can be separated into genetic
additive (σ 2 A), genetic dominant (σ 2 D), genetic epistatic (σ 2 I), and
unpredictable residual (σ 2 E) components, plus covariance caused
by genotype/environment interaction (2σGE). 36 It is generally assumed
that the genotype/environment interaction is negligible.
Therefore:
σ 2 P = σ 2 G + σ 2 E = σ 2 A + σ 2 D + σ 2 I + σ 2 E
The additive effects that are accumulated over successive
generations of selection are used in breeding. Nevertheless, other
www.interscience.wiley.com/jsfa c○ 2010 Society of Chemical Industry J Sci Food Agric 2010; 90: 1765–1773
(2)
(3)
(4)