Agriculture Reference
In-Depth Information
generation (i.e. F
1
,F
2
,F
3
, etc.) that is analyzed. From
these three estimates of
V
A
, we can produce a weighted
mean where:
can be derived from it and findout what is the probabil-
ity of one of these lines having a phenotype equal to, or
exceeding, any target level that we set, in other words,
that we would be aiming for with selection.
If we assume that the distribution of the final inbred
lines that are derivable have a normal distribution as is
generally the case in practice, then it can be described by
the mean and standard deviation. Since they are inbred
lines they will have a mean of
m
and a standard deviation
V
p
+
W
r
+
V
xr
]
The dominance genetic variance (
V
D
)
V
A
=
/
[
4
7
will vary from
generation to generation. Greatest
V
D
will be observed
in the F
1
generation as there is greatest frequency of
heterozygotes compared to other generations. In F
1
the
average
V
r
value (
V
r
)
of
√
V
A
, we can predict the properties of the distribu-
tion of all inbred lines possible and hence we can obtain
the frequency (
1
, and
V
D
can easily be estimated by substituting the already
calculated
V
A
value in to this equation. Therefore, when
analyzing data from F
1
family diallels:
D
is an estimate of
4
[
V
A
+
V
D
]
probability) of inbreds falling into
a particular category. In other words, we can simply
use the properties of the normal probability integral in
tables to say what the probability of obtaining an inbred
line with expression falling in a particular category. If
the probability is low it will obviously be difficult to
actually obtain such a line. If the probability is high it
will be easy to produce.
How do we put it into practice? If we have a set of
genotypes for use as Parents, which ones do we cross
to produce our desired new inbred lines? Do we take
A
=
4
V
r
−
=
V
A
From estimation of
V
A
and
V
D
we can now calcu-
late
h
n
:
1
2
V
A
+
1
2
V
A
/
1
4
V
D
+
σ
h
n
=
E
2
where,
E
is the replicate error term obtained from
the analysis of variance in the
B. napus
example shown
earlier in the Griffing's Analysis.
In F
2
families
V
D
=
σ
×
×
×
×
Z etc.? We will need
to decide between the crosses before we invest too much
time and effort, otherwise we may well be spreading our
efforts over crosses that will not produce the phenotypes
we want. If we take the crosses and estimate
m
and
V
A
for each, then we can estimate the probability of
obtaining our desired target values. From this we can
rank the crosses on their probabilities and only then
use the ones with the highest probabilities of producing
lines with the required expression of characters deemed
to be important.
In fact, the approach is even more general in that it
can be used to predict the properties of the F
1
hybrids
derived from the inbred lines. It can also be used to
predict the probability of combination of characters,
that is the probability of obtaining desirable levels of
expression in a series of characters.
What are the drawbacks to the approach? First, we
need to estimate
m
and
A
, and this involves a certain
amount of work in itself, but is fairly modest.
Second, it also assumes that the estimates we use are
appropriate to the final environment that the material is
to be grown. In other words, as in the case of heritabili-
ties, if we carry out the experiments in one environment
at one site in one year, we are assuming that this is rep-
resentative of other years and sites. We can, of course,
B and C
DorA
D and C
1
1
4
[
V
A
+
4
V
D
]
and so
V
D
−
F
2
=
16
V
r
−
1
4
V
A
, and in F
3
families,
V
D
−
F
3
=
4
[
+
A
/
1
16
V
D
]. It should be noted that the proportion of
V
D
in each family is decreased each generation by [
2
]
n
,
where
n
is the generation number (i.e. [
2
]
1
=1atF
1
;
[
2
]
2
1
4
at F
2
;[
2
]
3
=
=
/
1
16 at F
3
, etc.).
CROSS PREDICTION
There is one further way that it is possible to predict the
response to selection, in the long-term, although not
necessarily the rate of response. This approach is based
on the genetics underlying the traits, was proposed by
Jinks and Pooni, and is currently attracting considerable
attention in terms of experimental investigations and in
applying it to practical breeding. This will be covered in
more detail in the next chapter but needs mentioning
here to keep in view the options available to the breeder
in terms of making predictions.
If, to start with, we assume that we have an inbreeding
species and wish to produce a final variety that is true-
breeding.
What we want to know of any population or cross is
what is the distribution of inbred lines that we predict
