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were just being developed and was limited to models with one random
effect.
In order to estimate genetic parameters associated with the model, Muir
and colleagues ( Muir 2005; Muir & Schinckel 2002 ) recast Griffing's model
in terms of a mixed model methodology, with two random effects, one for
direct effect of the allele on the phenotype and another for effects on associ-
ates. Griffing termed the social or competitive effects, as “associative
effects”, which are now commonly referred to as indirect genetic effects
(IGEs) ( Agrawal et al., 2001; Bijma 2010a, b; Bijma and Wade, 2008;
McGlothlin and Brodie, 2009; Wade et al., 2010 ). An important result of the
mixed model approach of Muir (2005) and later ( Bijma et al. 2007a ) is that
genetic variances and covariances associated with direct (
D ) indirect (
A ),
σ
σ
and their covariance (
σ DA ) could be estimated by use of REML ( Patterson
and Thompson, 1971 ). These genetic parameters, in combination with
weights for the between- and within-group deviations, unified the concepts
of multilevel (kin and non-kin), group, and within group selection ( Bijma
et al., 2007a, b; Griffing, 1977 ). Bijma et al. (2007a, b) used the term g to
define the strength of multi-level selection, ranging from 0 to 1 correspond-
ing respectively to within and between group selections.
As a result of the two-component model of Muir (2005) , the direct and
IGEs can be directly estimated for each individual using best linear unbiased
prediction (BLUP) ( Henderson, 1975, 1984; Henderson and Quaas, 1976 ).
As a result, any combination of weights could be placed on those effects
resulting in optimal selection ( Bijma et al. 2007b ). Muir and colleagues
( Muir, 2005; Muir and Schinckel, 2002 ) used this approach, in comparison
with individual selection, to select for increased 6-week weight in Japanese
quail housed in multiple random groups of size 16. We used a base index in
which the IGEs were summed over all (n
1) interacting genotypes in a
group of size n, plus the direct effect known as the total breeding value
[TBV, ( Bijma et al., 2007a, b )]. We demonstrated that selection for TBV
was effective in increasing 6 week weight while reducing mortality. In con-
trast, individual selection did not increase 6 wk wt while having the negative
effect of increasing the rate of mortality.
An interesting consequence of defining the index as the trait of selection,
in terms of the TBV, is that the total heritable variance can exceed the
observed phenotypic variance ( Bijma et al., 2007a ) indicating that the
response to selection can be greater than the selection differential, and
explains the results we observed with poultry where the realized heritability
in the initial generations were
2
1. Basically the response to selection
includes the heritable social environment, not just the direct effects
Muir and Schinckel (2012) examined multi-level selection for quail
housed in kin groups for 43 days weight and survival in Japanese quail. We
showed that multi-level selection occurs whenever BLUP selection is applied
if quail are housed in groups because BLUP weights all information from
.
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