Page 220 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

12 Non-additive Animal Models

12.1 Introduction

The models considered in the previous chapters have dealt with only additive
genetic effects. Henderson (1985) provided a statistical framework for modelling
additive and non-additive genetic effects when there is no inbreeding. This chapter
covers some of these models. The ability to separate non-additive genetic effects
implies removal of some of the confounding that would otherwise bias the results
from the analysis. Moreover, the availability of estimates of non-additive genetic
effects for individuals could be used in mate selection, which would maximize the
use of both additive and non-additive genetic variance. In this chapter, the predic-
tion of dominance and epistatic effects using mixed model methodology is dis-
cussed. In practice, the application of non-additive models in genetic evaluation
has been limited due to lack of genetic parameters and due to the fact that these
effects tend to be highly confounded with others, such as common maternal
environment.

12.2 Dominance Relationship Matrix

Dominance genetic effects result from the action of pairs of alleles at a locus
on a trait. If two animals have the same set of parents or grandparents, it is
possible that they possess the pair of alleles in common. The dominance rela-
tionship between two such animals represents the probability that they have
the same pair of alleles in common. Thus for a group of animals, the domi-
nance genetic relationship matrix (D) among them can be set up. The domi-
nance relationship between an individual x with parents s and d and y with
parents f and m in a non-inbred population can be calculated (Cockerham,
1954) as:
d = 0.25(u u + u u ) (12.1)
xy sf dm sd fm
where u represents the additive genetic relationship between i and j. For instance, for
ij
two full-sibs with both parents unrelated to each other:

d = 0.25[(1)(1) + (0)(0)] = 0.25
with the assumption that there is no common environmental variance.

204 © R.A. Mrode 2014. Linear Models for the Prediction of Animal Breeding Values,
3rd Edition (R.A. Mrode)