Agriculture Reference
In-Depth Information
δ
i
's
There is therefore a linear relationship between
Table 5.12
Degrees of freedom and mean squares from the
analyses of variance of seed yield between and within progeny
that are polymorphic at the
AA
:
aa
,
BB
:
bb
and
CC
:
cc
loci.
−
and (1
2
R
),
δ
i
=
(
−
)
a
1
2
R
Source
df
AA
-
aa
BB
-
bb
CC
-
cc
locus
locus
locus
where the regression slope is an estimate of
a
.
The value of
a
and the accuracy of fit of regression is
dependant on
R
, the recombination frequency between
the three single band position and the QTL. We know
the map distance between A-B, and B-C. Therefore all
that is now required is to substitute in recombination
frequencies to find the recombination frequency which
has the least departure from regression in a regression
analysis of variance. It is usual to start with the assump-
tion that the QTL is located at the A-band position and
complete a regression analysis. Then assume that the
QTL is 2 cM from A, towards B, and carry out another
analysis. Repeat this operation until it is assumed that
the QTL is located at the C-locus. Thereafter determine
which of the regression analyses has the best regression
fit (with least departure from regression term) and the
QTL will be located at that map location. From this
the recombination frequencies between the various sin-
gle band position and the QTL can be calculated to
determine the usefulness of the linkage with the QTL
and hence the usefulness in practice.
To avoid duplication, the speculative map distances
from each single band position and the QTL in our
example is shown from around the map location with
minimum departure from regression are shown:
24 618
∗∗∗
11 211
∗∗∗
Between genotypes
1
2351 ns
36 147
∗∗∗
913
∗
Within genotypes
30
463 ns
Replicate error
93
459
459
459
The within genotypes effect is tested against the repli-
cate error, while the between genotype effect is tested
against the within genotype mean square.
Clearly, there is a significant relationship between
seed yield and alleles at the B-bands. Similarly, some
relationship exists between the C-band and yield,
although the variability with genotypes
CC
and
cc
are
highly significant, hence weakening the QTL relation-
ship. There is no relationship between seed yield and
bands at the A band.
From the above analysis of variance, our best guess to
the position of the QTL would be between the B and
C bands, and nearer to the B than the C. Determina-
tion of the position of the QTL on the chromosome
can be done using a number of statistical techniques.
The simplest technique involves regression, and will be
illustrated here.
Now the difference in yield between genotypes at
each band (
δ
i
) is an indication of the linkage between
the QTL and the single band position. In this example
we have:
A-locus
B-locus
C-locus
Residual
sum of
squares
δ
A-a
=
2.145;
δ
B-b
=
6.935;
δ
C-c
=
4.475
Given a simple additive-dominance model of inher-
itance, we find that lines with
BB
, plus the QTL +
will have expectation of
m
δ
i
2.145
6.935
4.475
+
a
and this genotype will
occur in the population with frequency
R
i
's
0.300
0.013
0.193
1932
1
2
R
, where
R
is the recombination frequency between the B-band
and the QTL. The
BB
lines without the QTL (QTL-)
will be
m
0.310
0.003
0.183
802
0.3198
0.01478
0.17148
0
0.330
0.017
0.163
339
−
a
, and will occur in the population with
1
2
(
−
)
frequency
, where
R
is the recombination fre-
quency between the B-band and the QTL. Similarly,
for
bb
we have,
bb
1
R
1
/
QTL
+=
m
+
a
, frequency
=
2
R
,
From
this
resulting
map
including
the
QTL
1
/
−=
−
=
2
(
−
)
would be:
bb
QTL
m
a
, frequency
1
R
. The
(δ
B
−
b
)
difference between the
BB
and
bb
genotypes
is
A - - - 30.5 m
µ
---B--1.5m
µ
- - QTL - - 17.1 m
µ
---C
(
−
)
therefore equal to
a
1
2
R
.
