Page 187 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Solving the MME equations gave these results:

Effects Solutions
Sex
Male 7.356
Female 5.529
Animal Total additive genetic merit including marker information
3 0.167
4 −0.167
5 0.419
6 0.432
7 0.645

The application of Eqn 10.21 is valuable as only one equation is fitted per animal,
but its application to a large data set may be limited because of the tabular method
of calculating the relationship matrix needed and its inverse.

10.9 Analysis of Data with QTL Bracketed by Two Markers

This section deals with the extension of the model of Fernando and Grossman (1989)
by Goddard (1992) to handle situations in which MQTL is bracketed between two
markers. The use of marker information when MQTL is bracketed between two
markers should enhance the accuracy of EBVs compared with information with a
single marker.

10.9.1 Basic model

Consider a chromosome with a series of marker loci with at most one QTL located
between each pair of markers:

M Q M
j j j+1

Each animal inherits two alleles at the Q locus: one from its sire and the other from
j
its dam. A marker haplotype consisting of the marker alleles at M and M would be
j j+1
associated with each of the MQTL alleles. Let the jth chromosome segment that ani-
mal i inherited from its sire be of the marker haplotype (kl) and the value of the
MQTL allele be v or simply v . Similarly, let the value of the MQTL allele from
ij(kl) ij(p)
its dam be v . Summed over all chromosome segments, the breeding value of ani-
ij(m)
mal i (a ) is:
i
i å
+
a = u + v ij p å v ij m)
()
i
(
j j
Similar to Eqn 10.3 the model for the phenotypic record of animal i is:
i å
+
y = x b + u + v ij p å v ij m) + e
i
(
i
()
j j
Use of Genetic Markers in Breeding Value Prediction 171