Agriculture Reference
In-Depth Information
σ
g
is the genetic standard
mean of all inbred lines and
assuming that the additive-dominance model of inher-
itance is adequate to describe the character of interest.
Therefore the following approximations can be made:
deviation.
Following the calculation of the probability integral
from the predicted equations, the expected proportions
of transgressive segregants can be obtained from tables
of the normal probability integral.
In cases where it is easy to obtain a sample of inbred
(or near-homozygous) lines from a large number of
crosses (i.e. by using a doubled haploid techniques or
rapid cycle single seed descent) then this method will
produce excellent predictions as there are no dominance
effects to complicate estimation.
In many instances, however, it is not possible to pro-
duce inbred lines quickly and cheaply on a practical level
in a breeding programme, and so cross prediction will
involve estimating genetic means and variances from
early generations of crossing designs.
Although the triple test cross will provide breeders
with the best estimate of additive genetic means and
variances it requires a great deal of time and effort to
complete. A similar effort will be required to obtain
these estimates using the standard P
1
,P
2
,F
1
,F
2
,B
1
and
B
2
method. Both these mating designs therefore have
merit for genetic investigation but may have limited
use in a practical plant breeding situation where many
hundred of cross combinations need to be screened.
Evaluation of a random sample of F
3
families from
each cross under investigation offers a more practical
approach. Approximate genetic parameters can be esti-
mated from the mean of a random sample of F
3
families
and from variation between families derived from a
common cross.
For example, consider a single cross (P
1
×
=
mean of F
3
families
mean of all possible inbred lines
2
V
A
Both estimates will of course be accurate only if
dominance effects are relatively small in comparison to
additive effects. In cases where [
d
] is large, then the
average of all possible inbred lines can be estimated by
growing the parental lines in the prediction trial and
estimating
m
as (
P
1
+
2
σ
F
3
=
P
2
)/
2. Alternatively, when [
d
]
and
D
are large then they can be estimated by including
a bulk sample of the F
1
or F
2
in the prediction trial. This
latter option will of course also offer a better estimate
of
m
.
If the parental lines are included in the cross predic-
tion trial in which the F
3
families are evaluated, then
it is also possible to carry out a crude scaling test to
determine the dominance components and effect from:
(
P
1
−
P
2
)/
−
F
3
Using these predictions of the additive genetic mean
and the additive genetic variance we can predict the
probability that a single inbred line selected at random
will exceed a predefined target value (
T
)by:
T
2
−
mean F
3
√
(
2
F
3
)
Similarly, the probability that a single inbred line, taken
at random, would be less than a predefined target value
(
T
) would be:
σ
2
P
2
). Then
F
1
seed would be grown to produce F
2
single plants.
A random sample of these would be harvested and a
single plot grown from each of (say 20 to 25) single
plant plots. These plots would be evaluated to obtain
the average performance of the families and variation
between families would also be estimated.
The mean (average performance of families) of the
F
3
plots would be:
mean F
3
−
T
√
(
2
F
3
)
Following the calculation of the probability integral
from the predicted equations, the expected proportions
of transgressive segregants can, as above, be obtained
from tables of the normal probability integral.
σ
2
Setting target values
A number of different options are available in setting
target values on which the predictions are based. These
include:
m
+
1
/
4
d
2
σ
and the true variance of the F
3
family means (
F
3
)
would be:
•
To include a set of control cultivars in the same experi-
ments where the genetic parameters are estimated and
1
/
2
V
A
+
1
/
16
V
D
