Agriculture Reference
In-Depth Information
In terms of practicality, Type I errors are far more
important than Type II errors. Type I errors result from
wrongfully rejecting a genotype, based on phenotypic
performance in the early selection stage, which really
should have been selected. Therefore this results in dis-
carding potentially valuable genotypes. Type II errors
result from selecting genotypes in the first year which
really should have been discarded and therefore result
in a waste of resources which should have been better
used in other areas.
A second means to examine data from two stage selec-
tion frequencies uses
selection ratios
. Consider that all
the population is evaluated in year 1 and selection is car-
ried out such that a proportion of the population (
p
1
)
is selected while the remainder (
q
1
) is discarded. Then
all the population is re-evaluated in year 2 and again
selection is carried out such that a proportion (
p
2
)is
selected and the remainder (
q
2
) rejected. From this the
question arises as to what proportion of the population
selected in the second year would have been:
a
b
p
2
q
2
d
c
q
1
p
1
Reject
Select
Figure 7.6
Classification of phenotypes based on
independent culling of a single trait over two stages of
selection.
Consider the illustration in Figure 7.6 which shows
two stage selection of a single character. The distribu-
tions at the side and bottom of the figure show the
frequency distribution of each stage. For simplicity
assume that selection is being carried out over a two
year cycle. In the first year, a proportion of the total
genotypes (
p
1
) will be selected while the remainder (
q
1
)
are theoretically discarded, where
p
1
+
•
Selected in the first year
•
Discarded in the first year
1. Simi-
larly, in year two a proportion of genotypes would be
selected (
p
2
)
q
1
=
The ratio of these two proportions is termed the
selection ratio
and is given by:
and the remainder discarded (
q
2
), where
p
2
+
q
2
=
1. From this bi-variate distribution, each
genotype is classified as:
Year 1
Select
(
w
)
Reject
(
x
)
a.
rejected in the first year and selected in the second
year
b.
selected in the both years
c.
selected in the first year but rejected in the second
year
d.
rejected in both years
Year 1
Select
Reject
Select
Reject
b
c
a
d
(
y
)
(
w
−
y
)
(
z
)
(
x
−
z
)
Selection ratio = (
y
/
w
)/(
z
/
x
)
From this there are two areas of misclassification and
hence errors in selection. These have been termed:
Values of selection ratios can range from 0 (zero) to
infinity. If the selection ratio is equal to zero, then there
was no repeated selection over the two stages. A selec-
tion ratio between zero and one indicates that a higher
proportion of genotypes were selected in year 2 from
those discarded in year 1 than were selected from year 1
(i.e. negative correlation). A selection ratio less than 1
therefore suggests that selection has had a negative
effect (i.e. all the good genotypes have been discarded).
A selection ratio equal to one indicates that selection
Type I
error where genotypes have been rejected in
the first year and selected in the second. If the
proportion of genotypes selected in year 1 is
p
1
,
then the Type I error is calculated by
c
/(
+
)
.
Type II
error where genotypes are selected in the first
year but rejected in the second year. If the pro-
portion of genotypes selected in year 2 is
p
2
,
then the Type II error is given by
a
c
b
/(
+
)
a
b
.
