Page 194 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

The basic assumption is that the use of SNPs as markers enables all QTL in the
genome to be traced through the tracing of chromosome segments defined by adja-
cent SNPs. It is assumed that the effects of the chromosome segments will be the same
across the population as a result of the LD between the SNPs and QTL. Thus it is
important that marker density is high enough to ensure that all QTL are in LD with
at least a marker.
The main advantages of genomic selection are similar to those outlined in
Chapter 10 with MAS. Briefly, it results in a reduction of the generation interval, as
young animals can be genotyped early in life and their GEBV computed for the pur-
poses of selection. In the dairy cattle situation, GEBV computed early in life can be
used to select young bulls, thereby reducing the cost of progeny testing, provided the
GEBV are accurate enough. In addition, higher accuracy of GEBV, about 20–30%
above that from a parent average, has been reported for young bulls. The computa-
tion of GEBV for an individual on the basis of the SNPs it has inherited means that
the differences in the genomic merit of full-sibs can be captured.
The implementation of genomic selection involves estimating the SNP effects in
a reference population that consists of individuals with phenotypic records and geno-
types. This is then followed by prediction of GEBV for selection candidates that do
not yet have phenotypes of their own.

11.2 General Linear Model

The general linear model underlying genomic evaluation is of the form:
m
y = Xb + ∑ M i g + e (11.1)
i
i
where m is the number of SNPs or markers across the genome, y is the data vector, b
the vector for mean or fixed effects, g the genetic effect of the ith SNP genotype and
i
e is the error. The matrices X and M are design matrices for the mean or fixed effects
i
and the ith SNPs, respectively. The matrix M is of dimension n (number of animals)
and m. The assumption is that all the additive genetic variance is explained by all the
marker’s effects such that the estimate of an animal’s total genetic merit or breeding
m
value (a) is: a = ∑M g . However, if it is assumed that a certain proportion of the addi-
i ii
tive genetic variance is not explained by markers, then the model can be extended to
include a residual polygenic effect (u), which is the proportion of the additive genetic
variance not captured by markers. The model can then be written as:
m
+
y = Xb + ∑ M i g + Wu e (11.2)
i
i
where W is the design matrix linking records to random animal or sire effects if an
animal or model has been fitted.

11.3 Coding and Scaling Genotypes

As explained in Eqn 11.1, M is the genotypic matrix that contains which marker
alleles each individual inherited. The genotypes of animals are commonly coded as

178 Chapter 11