Agriculture Reference
In-Depth Information
Table 6.3
Degrees of freedom, sum of squares and mean squares from the analysis of
variance of a half diallel including parent selfs (Method 2) assuming fixed effects. Also
shown are the expectations for the mean squares.
Source
df
SS
MSq
EMS
g
i
2
−
σ
+
(
+
)(
/(
−
))
GCA
p
1
S
g
M
g
p
2
1
1
p
2
))
j
s
ij
SCA
p
(
p
−
1
)/
2
S
s
M
s
σ
+
2
(
p
/(
p
−
1
2
(
−
)
{
(
+
)/
}
σ
Error
r
1
p
p
1
2
S
e
M
e
Table 6.4
Degrees of freedom, sum of squares and mean squares from the analysis of
variance of a half diallel including parent selfs (Method 2) assuming random effects. Also
shown are the expectations for the mean squares.
Source
df
SS
MSq
EMS
2
s
+
(
g
GCA
p
−
1
S
g
M
g
σ
+
σ
p
+
2
)σ
2
s
(
−
)/
σ
+
σ
SCA
p
p
1
2
S
s
M
s
2
Error
(
r
−
1
)
[
p
(
p
+
1
)/
2
]
S
e
M
e
σ
2
pX
..
}
Where
r
is number of replicates;
p
is number of parents;
S
g
is 1
/(
p
+
2
)
{
i
(
X
i
.
+
x
ii
)
−
4
/
;
S
s
i
<
j
x
ij
−
2
X
..
)
is
1
/(
p
+
2
)
i
(
X
i
.
+
x
ii
)
+
2
/((
p
+
1
)(
P
+
2
)
and
X
i
.
is
j
x
ij
=
x
i
1
+
x
i
2
+
x
i
3
+· · ·
,
that is, sum over rows;
X
..
is
ij
x
ij
=
is sum of all observations.
model 1 are shown in Table 6.3 and Method 2 and
model 2 in Table 6.4.
When SCA is relatively small in comparison to GCA
it should be possible to predict the performance of
specific cross combinations based only on the val-
ues obtained for GCA of parents. A relatively large
SCA/GCA variance implies the presence of dominance
and/or epistatic gene effects. It should also be noted that
if dominance
specific combining ability mean square and variance,
respectively.
The choice of Griffing method will depend on the
plant breeder or researcher's preference and on the char-
acters of the crop and trial under investigation. If,
for example, there is a suspicion that the particular
inheritance has a maternal or cytoplasmic effect then
Method 1 or Method 3 may be the desired choice. If,
however, there is no evidence of reciprocal differences
then Method 2 or Method 4 would be chosen. When
the variance components are of major importance then
it has been suggested that Method 1 will result in a more
accurate and constant variance estimation compared to
the other methods available. Conversely, it has been
reported that the inclusion of the parental genotypes
in the diallel design can cause an upward bias in the
estimation of the GCA and SCA variances.
Normally the F
1
generation is considered in Griffing's
Analysis. However, as no genetic assumptions are
involved then there are no reasons why F
2
or indeed
other segregating generations could not be analyzed.
Despite the attraction and simplicity of Griffing's
Analysis several researchers have criticized the technique.
additive effects are present, the GCA
component will also contain some of these effects in
addition to pure additive effects.
For inbred lines, the closer that the following
equations are equal to one (i.e. as SCA becomes small or
very small compared to GCA), then greater predictabil-
ity based on GCA will be possible. The ratio equations
for each model are:
×
Model 1 : 2
g
i
/
[
2
g
i
+
s
ij
]
g
g
s
σ
/
[
σ
+
σ
]
Model 2 : 2
2
where
g
i
g
are the general combining ability mean
square and variance, respectively and
s
ij
and
σ
,
2
s
σ
are
