Page 86 - Linear Models for the Prediction of Animal Breeding Values

5 Best Linear Unbiased

Prediction of Breeding Value:

Multivariate Animal Models

5.1 Introduction

Selection of livestock is usually based on a combination of several traits of economic
importance that may be phenotypically and genetically related. Such traits may
be combined into an index on which animals are ranked. A multiple trait evaluation
is the optimum methodology to evaluate animals on these traits because it accounts
for the relationship between them. A multiple trait analysis involves the simultane-
ous evaluation of animals for two or more traits and makes use of the pheno-
typic and genetic correlations between the traits. The first application of best linear
unbiased prediction (BLUP) for multiple trait evaluation was by Henderson and
Quaas (1976).
One of the main advantages of multivariate best linear unbiased prediction
(MBLUP) is that it increases the accuracy of evaluations. The gain in accuracy is
dependent on the absolute difference between the genetic and residual correlations
between the traits. The larger the differences in these correlations, the greater the gain
in accuracy of evaluations (Schaeffer, 1984; Thompson and Meyer, 1986). When, for
instance, the heritability, genetic and environmental correlations for two traits are
equal, multivariate predictions are equivalent essentially to those from univariate
analysis for each trait. Moreover, traits with lower heritabilities benefit more when
analysed with traits with higher heritabilities in a multivariate analysis. Also, there is
an additional increase in accuracy with multivariate analysis resulting from better
connections in the data due to residual covariance between traits (Thompson and
Meyer, 1986).
In some cases, one trait is used to decide whether animals should remain in the
herd and be recorded for other traits. For instance, only calves with good weaning
weight may be allowed the chance to be measured for yearling weight. A single trait
analysis of yearling weight will be biased since it does not include information on
weaning weight on which the selection was based. This is often called culling bias.
However, a multi-trait analysis on weaning and yearling weight can eliminate this
bias. Thus MBLUP accounts for culling selection bias.
One of the disadvantages of a multiple trait analysis is the high computing cost.
The cost of multiple analysis of n traits is more than the cost of n single analyses.
Second, a multiple trait analysis requires reliable estimates of genetic and phenotypic
correlations among traits and these may not be readily available.
In this chapter, MBLUP involving traits affected by the same effects (equal design
matrices) and situations in which different traits are affected by different factors (non-
identical design matrices) are discussed. In the next chapter, approximations of MBLUP
when design matrices are equal with or without missing records are also examined.

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