Agriculture Reference
In-Depth Information
Helios
420
Cyclone
Westar
320
Reston
Starr
220
Global
93.C.3
Jaguar
DNK.89.213
120
Hero
20
Figure 6.2
Scatter diagram of
V
r
and
W
r
values from arrays in a 10
110
160
210
260
310
360
410
×
10 half diallel
V
r
in
Brassica napus
.
Moving on to the
W
r
+
V
r
and
W
r
−
W
r
+
V
r
from each
Therefore
values
of
V
r
vary
significantly
array.
W
r
+
V
r
and
W
r
−
(
<
)
V
r
will contain all the infor-
mation that
W
r
and
V
r
contain. Now if dominance is
present then
W
r
+
between arrays
so we can say that domi-
nance is present. Values of
W
r
−
p
0.05
V
r
between different
arrays are not significantly different and therefore we can
say that there is no evidence of non-allelic interaction
and that only dominance is present.
These data are from homozygous parents and F
1
progenies. In many cases it is difficult to obtain large
quantities of F
1
seed and the actual diallel analysis needs
to be carried out on the F
2
(or higher) generations.
When this is done the same six assumptions listed at
the beginning of this section still apply. The regression
of
W
r
/
V
r
will vary from array to array. If
there is non-allelic interaction then
W
r
−
V
r
will vary
from array to array. If only dominance is present then
W
r
−
V
r
will not vary between arrays more than would
be expected by sampling variation. We can calculate the
values of
W
r
+
V
r
and
W
r
−
V
r
from the
V
r
and
W
r
values
obtained from each replicate and carry out a one-way
analysis of variance on the resulting data. When this is
done we have the two analyses of variance tables:
W
r
+
V
r
will still have an expected slope of unity if
the additive-dominance model is adequate to explain
the inheritance, and
W
r
−
V
r
V
r
should be constant across
arrays if no epistasis is present. Therefore, as far as the
example above is concerned, then it would make no dif-
ference if F
2
data were used. However, if a more detailed
analysis is to be carried out and the components
V
A
and
V
D
are to be estimated then some modification is
needed. The modification is not within the scope of
this topic.
Source
df
MSq
F
-value
Significance
<
<
Between
9
17 164
4.63
(0.01
p
0.05)
arrays
Within
10
3708
arrays
Estimating h
n
from Hayman and Jink's Analysis
If the crop under investigation in a diallel crossing
design complies with all the restraints of the Hayman
and Jinks design, then it is possible to obtain accurate
estimates of additive genetic variance (
V
A
) and dom-
inant genetic variance (
V
D
)
W
r
−
V
r
Source
df
MSq
F
-value
Significance
Between
9
5642
2.60
n.s.
straightaway and hence
determine the narrow-sense heritability (
h
n
). The aver-
age
W
r
value (
W
r
)
arrays
Within
10
2170
is an estimate of
2
V
A
. The
V
p
value is
a direct estimate of
V
A
, and the
V
xr
value is an estimate
of
4
V
A
. These relationships hold true irrespective of the
arrays
