Agriculture Reference
In-Depth Information
to produce segregating progeny from which superior
cultivars would have high frequency.
In simplest terms, the cross between two parents
(i.e. parent i
Griffing's Analysis of a diallel is by analysis of vari-
ance, where the total variance of all entries is partitioned
into: general combining ability; specific combing abil-
ity and error variances. In cases where reciprocals
are included, then reciprocals (or maternal effects)
are also partitioned. Error variances are estimated
by replication of families. To avoid excessive repeti-
tion, only Method 1 (complete diallel) and Method 2
(half diallel) both including parents will be considered
further.
Degrees of freedom (df ), sum of squares (SS) and
mean squares (MSq) from the analysis of variance for
Method 1 for the assumption of model 1 (fixed effects)
are shown in Table 6.1. Also shown are the expectations
for the mean squares (EMS).
Similar
×
parent j ) in Griffing's Analysis would
be expressed as:
X ij = µ +
g i +
g j +
s ij
where
is the overall mean of all entries in the diallel
design, g i is the general combining ability of the i th
parent, g j is the general combining ability of the j th
parent and s ij is the specific combining ability between
the i th parent and the j th parent.
General combining ability (GCA) measures the aver-
age performance of parental lines in cross combination.
GCA is therefore related to the proportion of variation
that is genetically additive in nature.
Specific combining ability (SCA) is the remaining
part of the observed phenotype that is not explained
by the general combining ability of both parents that
constituted the progeny.
µ
expected
mean
squares
for
Method
1,
model 2 (random effects) are shown in Table 6.2.
Considering now Method 2 (the half diallel), the
degrees of freedom (df ), sum of squares (SS), mean
squares (MSq) and expected mean squares (EMS) for
Table 6.1 Degrees of freedom, sum of squares and mean squares from the
analysis of variance of a full diallel including parent selfs (Method 1) 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
2 p
1
1
p
2
)) ij s ij
SCA
p
(
p
1
)/
2
S s
M s
σ
+
2
/(
p
(
p
1
2
))) i < j r ij
(
)/
σ
+
(
/(
(
Reciprocal
p
p
1
2
S r
M r
2
2
p
p
1
p 2
2
Error
(
r
1
)
S e
M e
σ
Table 6.2 Degrees of freedom, sum of squares and mean squares from the analysis
of variance of a full diallel including parent selfs (Method 1) assuming random
effects. Also shown are the expectations for the mean squares.
Source
df
SS
MSq
EMS
2
s +
g
σ
+
(
/(
))σ
σ
GCA
p
1
S g
M g
2 p
1
1
p
2 p
2
p 2
p 2
s
(
)/
σ
+
((
+
))/
σ
SCA
p
p
1
2
S s
M s
2
p
1
2
r
(
)/
σ
+
σ
Reciprocal
p
p
1
2
S r
M r
2
p 2
2
Error
(
r
1
)
S e
M e
σ
For Method 1, where r is the number of replicates; p is the number of parents; S g is
1
2
p 2 X .. ; S s is 1
2
p 2 X .. ;
/
i (
X i . +
X . i )
/
/
ij x ij (
x ij +
x ji )
/
i (
X . i +
X i . )
+
/
2 p
2
2
1
2 p
1
2 and X i . is
S r is 1
/
2
i < j (
x ij
x ji )
j x ij =
x i 1 +
x i 2 +
x i 3 +···
, that is, sum over rows;
X . j is
i x ij =
x 1 j +
x 2 j +
x 3 j +···
, that is, sum over columns and X .. is
ij x ij is sum of all
observations.
 
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