Agriculture Reference
In-Depth Information
of selection,
h
2
is the appropriate heritability (narrow-
sense heritability for inbreeding crops or broad-sense
heritability for out breeding crops),
Although the intensity of selection (
i
) has been exten-
sively tabulated for a range of different selection rates,
in cases where the initial population is large (i.e. greater
than 50 genotypes) and the proportion of genotypes
selected less 20%, then the following equation can
provide an estimate of
i
:
σ
is the phenotypic
standard deviation of the whole population and
i
is the
intensity of selection
, which is a statistical factor depen-
dent upon the proportion of the population selected.
The above equation is probably the most fundamental
equation in plant breeding and should be kept in mind.
The intensity of selection (
i
) is related to the percent-
age of the population that is selected (
k
), and takes the
values:
i
=
0.77
+
0.96
×
log
(
1
/
k
)
From the tabulated values of selection intensities
and the estimation equation it can be seen that there
is not a linear relationship between higher selection
rates (
k
) and greater response from selection. Retaining
10% of the selected population results in an intensity
of selection value of 1.755, while retaining only 1%
(i.e. a 10 fold reduction in selections) results in an
intensity of selection value of only 1.52 times larger
(i.e.
i
Percentage
i
selected (
k
)
1
2.665
2.665).
Consider a simple example which is represented
diagrammatically in Figure 7.1. Selection is to be car-
ried out on a base population with an average, or
mean, of 560 kg yield and with phenotypic standard
=
5
2.063
10
1.755
20
1.400
1000
X = 560
p
= 19.0
h
2
n
= 0.60
800
k = 10%
i = 1.755
R = 20.0
600
σ
p
400
Selected
fraction
200
S
0
500 510 520 530 540 550 560 570 580 590 600 610 620 630 640
1000
R
X = 580
p
<
19.0
h
2
n
= 0.60
800
600
400
200
Figure 7.1
Illustration of the response
from selection given population parameters
from the unselected population (top) to
predict the selected population (bottom).
0
500 510 520 530 540 550 560 570 580 590 600 610 620 630 640
