Agriculture Reference
In-Depth Information
Table 6.6
Degrees of freedom, sum of squares and
mean squares from the analysis of variance of plant height
of a half diallel including parent selfs. In the analysis the
total variance is partitioned into differences between the
two replicate blocks (Reps), general combining ability,
specific combining ability and an error term (based on
interactions between replicates and other factors).
Similarly for general combining ability, the expected
mean square is:
σ
2
g
i
+
(
+
)(
/(
−
))
p
2
1
1
p
Therefore
g
i
12 074
−
1545
=
(
10
+
2
)(
1
/(
1
−
10
))
g
i
=
10 529
1.33
Source
df
Sum of
squares
Mean
squares
so
g
i
=
General combining
9
108 665
12 074
10 529
/
1.33
=
7897
ability
Specific combining
Now, from the equation above we can compare GCA
and SCA effects, as noted earlier we have:
2
g
i
/
[
45
113 497
2522
ability
Replicate blocks
1
959
959
2
g
i
+
s
ij
]=
×
/
2
7896.893
Replicate Error
54
83 428
1545
[
(
×
)
+
]
2
7896.893
439.288
Total
109
306 548
2812
=
0.973
As this value is very close to one, it indicates that
s
ij
is relatively small compared to
g
i
. Therefore addi-
tive genetic effects predominate. This means there is
a good chance that plant height at the F
1
stage in a
B. napus
breeding programme can be predicted with
good accuracy depending on the general combining
ability of chosen parental lines.
In many instances there is good agreement between
the general combining ability of a genotype and the phe-
notypic performance of the line. If this is the case then
all that is necessary is to determine the expression of the
parents and from these the expected expression of the
offspring can be estimated (compare with
h
n
). There-
fore in this example consider the regression of average
parental performance against the offspring (Figure 6.1).
It can be clearly seen that there is relatively good agree-
ment between parents and offspring. The regression
equation is offspring mean
combining ability by 2522
1.63. This 'F' value
is compared to F-values found in statistical tables at dif-
fering probability levels and with 45 and 54 degrees of
freedom. When this is done, with some degree of dif-
ficulty, it is found that the probability of this F value
occurring if SCA were not significant is 95.7, there-
fore specific combining ability is just significant at the
5% level.
Consider now the variance ratio for general combin-
ing ability. The appropriate F-value is 12 074
/
1545
=
=
7.8. When this value is compared to the appropriate
F-values in statistical tables with 9 and 54 degrees of
freedom we find that it exceeds the appropriate expec-
tation based on 99.9% confidence (i.e. approximately
3.54) and so we say that general combining ability
is highly significant. This, in combination with the
marginal significant of specific combining ability, sug-
gests an additive-dominance model with high additive
effects.
Now the expected mean square for specific combin-
ing ability of a half diallel and fixed effects is:
σ
/
1545
80.0.
Therefore the narrow sense heritability of these data is
approximately 0.73, which is relatively high in that 73%
of the total variation is additive genetic variance.
=
0.7265
×
parent
+
2
))
i
s
i
+
(
/(
−
2
p
p
1
Hayman and Jinks' analysis
Therefore
2521
))
i
s
i
−
1545
=
2
(
10
/(
10
−
1
Hayman and Jinks developed an analysis for diallels
that has been widely used by many plant researchers to
evaluate the mode of inheritance. This analysis is based
on a model that, for any one locus,
i
, with two alle-
les, the difference between the two homozygotes is 2
a
.
i
s
i
=
976
2.2
so
i
s
i
=
976
/
2.2
=
439
