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Triticeae Genomics and Genetics 2012, Vol.3, No.2, 9
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19
and used for determining the position of uncommon
loci (present between the two common flanking loci)
that were added from the framework map on to the
consensus map. For placement of other uncommon
loci that were located above the first interval of
common markers and below the last interval of
common markers, a global ratio was similarly
computed (Arcade et al., 2004). Lastly, the remaining
uncommon loci of a framework map and all the QTLs
were positioned onto the consensus map by means of
homothetic function (monotonic transformation of
homogeneous function), using common markers
between framework maps and the consensus map. The
details of the procedure followed for projection are
described elsewhere (Chardon et al., 2004). Fifty
QTLs from 15 different studies were retained for map
projection: 27 QTLs were PHST QTLs (detected
using two parameters, SI and VI), 18 QTLs were
dormancy QTLs (detected using the parameter, GI)
and the remaining 5 QTLs were for associated trait
grain colour (GC).
3.3 QTL refinement (overview)
QTL refinement was achieved for 50 QTLs through
estimation of overview, which is a statistic, used for
estimating the probability that a given genomic region
comprises a QTL in an individual experiment
(Chardon et al., 2004). For this purpose, QTL
information (most likely position of the QTLs,
variance and total number of QTLs identified in all
earlier experiments) is utilized to estimate the average
value of overview statistic
P
(
x
) for every 0.5 cM
segment on the genetic map (Chardon et al., 2004). In
order to achieve this, we assume that the true position
of QTL is normally distributed around the most likely
position pi of the QTL, with a variance
N
(
p
i
, S
i
2
). The
value of
P
(
x
) was estimated using the following
formula: P(
x
,
x
+0.5)={
∑
_(i=1)^nbqtl
∫
_
x
^(
x
+0.5)
[
N
(
p
i
, S
i
2
)d(
x
)]}/nbE.
Where nbqtl is the number of QTL and nbE is the total
number of experiments. For identifying the high
density genomic regions that have a key contribution
to the variance of the trait of interest in the experiment
[a notable peak with high
P
(
x
) value], we also
calculated an average value
U
(
x
), which is the uniform
probability so that a
P
(
x
) value above the
U
(
x
) value
will suggest that the segment flanked by loci at
x
,
x
+
0.5 comprises a QTL in an experiment. The value of
U
(
x
) was estimated using the following formula:
U
(
x
)=[(bqtl/nbE)/Total length of map]×0.5.
A high value threshold
H
(
x
), which is fivefold the
value of
U
(
x
) was also calculated to identify the
genomic regions carrying a very high
P
(
x
) value as
done by Chardon et al (2004). A
P
(
x
) peak which
exceeds
H
(
x
) suggests a much higher level of
confidence for the presence of a QTL in the
corresponding 0.5 cM genomic region. For each
chromosome consensus map
P
(
x
),
U
(
x
) and
H
(
x
) were
plotted simultaneously.
3.4 Meta-QTL analysis
Meta-QTL analysis was conducted using BioMercator
software following Goffinet and Gerber (2000). This
software allows us to find out the number of
meta-QTL, which may be 1, 2, 3, 4 or n QTLs (n
meta-QTL means, the number of meta-QTL is equal to
number of projected QTLs). This is done by selecting
one of the five models available in the software, one
model for each possibility. A specific model is
selected on the basis of minimum value of Akaike
Information Criterion (AIC): the lower the AIC value,
the more likely the model. The aim of AIC is to
estimate the mean log-likelihood (MELL) for the real
positions
x
i
of the n QTLs (Sakamoto et al., 1986).
The AIC value is computed using the following
formula (Goffinet and Gerber, 2000): AIC=-2×
L
(
θ
[k]
,
X
[k]
,
X
)+2×
k.
Where
L
(
θ
[k]
,
X
[k]
,
X
) denoted the log-likelihood of the
observed vector
X
(QTL position),
k
denoted the
actual number of parameters (1, 2, 3, 4…n), the actual
value of parameters and
X
0
the actual value of the n
QTLs positions.
k
is an unbiased estimator of MELL,
therefore it is recommended to choose a model with
the minimum value of the Akaike Information
Criterion (AIC).
4 Conclusion
The present study for the first time demonstrated the
utility of meta-QTL analysis for PHST and dormancy
in wheat to identify genuine QTLs and the associated
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