596
Behavior Genes
Twin 1
Twin 2
C
b
A
E
E
A
e
a
c
c
a
e
Fig. 7
An ACE path diagram. Path analysis can be
used to estimate the contribution of the path
coefFcients
a
,
c
,and
e
, to the covariance or
correlation between twin pairs.
β
, genetic correlation
between twin pairs, 1.0 for monozygotic twin pairs
and 0.5 for dizygotic twin pairs;
a
, path coefFcient for
additive genetic effects;
c
, path coefFcient for
common environmental effects;
e
, path coefFcient for
nonshared environmental effects;
A
, additive genetic
variance;
C
, common environment variance;
E
,
nonshared environment variance.
Finally, evocative correlation results from
others’ reactions to a person based at least
partially on that person’s genotype. For ex-
ample, a musically gifted child’s abilities
may be recognized by her teachers and par-
ents, who ensure that she has the tuition
and equipment to ful±l her promise.
Therefore, the phenotypic variance is the
consequence of additive genetic variance,
nonadditive genetic variance, common en-
vironmental variance, and nonshared envi-
ronmental variance, as well as the effect of
gene–environment interactions and corre-
lations. This can be expressed in Eq. (2):
V
P
=
V
A
+
V
D
+
V
C
+
V
E
+
V
G
×
E
+
2Cov
GE
(
2
)
where
V
G
×
E
is
the
variance
due
to
gene–environment
interaction
and
2Cov
GE
is
the
covariance
due
to
gene–environment correlation.
Although genetic and environmental
variance cannot be directly measured or
observed, it may be possible to estimate
them indirectly from the observed pheno-
typic variances and covariances.
The extent to which genes are account-
able for the phenotypic variance in the
population, or the proportion of variance
in the liability for a phenotype is referred
to as the heritability. Strict sense or nar-
row heritability refers only to the additive
genetic effects whereas broad heritability
(or degree of genetic determination) is
the proportion of the phenotypic variance
accounted for by total genetic variance
V
G
, including both additive and nonad-
ditive effects.
Broad heritability
=
V
G
V
P
(
3
)
Narrow heritability
=
V
A
V
P
(
4
)
Similarly, it may be of interest to estimate
the extent to which the variance of a pheno-
type is influenced by shared environment,
V
C
/
V
P
, and by environment that is not
shared,
V
E
/
V
P
. A useful methodology for
such tasks is provided by path analysis.
2.5
Path Analysis
Figure 7 illustrates a simple path model for
a trait where it is assumed that the variance
can be explained by additive genetic effects
(A), shared environmental effects (C), and
nonshared environment (E). The observed
correlation between a series of twins (twin
1 and twin 2) can be calculated for the trait
under investigation. The expected value
of the correlation between the twins in
terms of path coef±cients can be obtained
by tracing the connecting paths, providing
the equation:
r
(
Twin 1
)(
Twin 2
)
=
(
a
×
β
×
a
)
+
(
c
×
c
)
=
β
a
2
+
c
2
(
5
)
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