Agriculture Reference
In-Depth Information
has occurred at random (i.e. a zero correlation coeffi-
cient between the two stages). If the selection ratio is
greater than one then selection has been better than ran-
dom (i.e. a positive correlation between the stages). An
increased magnitude of selection ratio shows increased
efficiency of selection. For example if a selection ratio
of 2.0 is obtained then the genotypes selected in year 1
would be twice as likely to be re-selected in year 2 than
genotypes that were discarded in year 1.
It should be obvious that the selection ratio is related
to the heritability of the character being selected. It also
should be noted that the selection ratio will also be influ-
enced by the selection intensity. Obviously, irrespective
of the heritability, for a character, the selection ratio will
be zero, if the selection intensity is set so high that no
genotypes survive repeat selection. Similarly, the selec-
tion ratio will always be 1.0 where the selection intensity
is so low that no genotypes are discarded. The relation-
ship between selection ratio values and heritability is
linear and related to selection intensity (Figure 7.7).
Similarly, it is possible to estimate selection ratio
values for different selection intensities if the heritabil-
ity is known. Where heritability is zero, then there is
no response to selection and hence the selection ratio
is zero. The selection ratios with different selection
intensities and heritabilities are shown in Table 7.1.
Type I and II errors and selection ratios can be useful
in setting the selection intensity levels at each stage in a
breeding scheme. To estimate any of these it is necessary
to determine the frequency of genotypes which fall into
the
a
,
b
,
c
and
d
classes (Figure 7.6). In order to achieve
this, it is necessary to artificially select and reject geno-
types in one stage and to re-evaluate all selected and
rejected lines in a second stage.
It has been mentioned above that correlation analysis
can be useful in determining selection efficiency. This
can be done by the use of
inverse tetrachoric correlation
.
Tetrachoric correlations were first described by Digby in
1983. He showed that it was possible to determine the
correlation coefficient between two stages of evaluation
(i.e. two years of testing) from frequency tables like the
one shown in Table 7.1.
Inverse tetrachoric correlations are indeed the inverse
process where given the correlation coefficient between
two selection stages it is possible to estimate the values
of a, b, c and d (from Figure 7.6) and hence estimate
Type I and Type II errors and selection ratios at different
selection intensities.
The theory of tetrachoric correlations are beyond this
topic; however, values of the
b
(the frequency of geno-
types that would be selected at both stages of a two
stage selection) for varying selection intensities used at
the different stages and with correlation values between
the stages ranging from (0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
and 0.9) are shown in Table 7.2.
To illustrate the use of this table consider the follow-
ing example. It is known that the correlation coefficient
for seed yield, between two assessment years (year 1 and
year 2) is equal to 0.7. What would be the Type I error
and Type II error given that selection was carried out at
the 20% level in year 1 and at the 15% level in year 2.
From the table with
p
1
at 0.2 and
p
2
at 0.15 and with
a correlation coefficient of 0.7 we have a
b
value of 093
(or 93 genotypes out of 1000).
Table 7.1
Selection ratios values with different selec-
tion intensities and heritability values.
Selection intensity
Heritability
Year-1
Year-2
0.2
0.4
0.6
0.8
(%)
(%)
30
25
20
15
10
5
0
k
= 5%
5
5
6.98
13.95
20.93
27.91
5
10
3.04
6.07
9.11
12.14
k
= 10%
5
15
1.82
3.63
5.45
7.28
k
= 20%
5
20
1.22
2.45
3.68
4.91
10
10
4.02
8.03
12.05
16.07
10
15
2.27
4.55
6.83
9.11
0
0.1
0.2
0.3
0.4 0.5
Heritability
0.6
0.7
0.8
0.9
1
10
20
1.50
3.01
4.51
6.02
15
15
2.88
5.76
8.65
11.53
15
20
1.87
3.74
5.60
7.47
Figure 7.7
Selection ratio values with increasing
heritability and different selection intensities.
20
20
2.33
4.67
7.00
9.34
