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In-Depth Information
p
+
γ
t
2
q
(
M
t
|
M
c
)
q
(
M
c
|
p
+
γ
c
2
.
M
t
)
=
(15)
3
Simulation Study
×
To validate this approach, loci information from
Arabidopsis thaliana
Bay-0
Shah-
dara was used. Figure 2 illustrates the genetic map of the
Arabidopsis thaliana
Bay-0
×
Shahdara,which has five chromosomes and a total of 38 markers. For this simulation
study, 158 lines were used.
I
II
III
IV
V
0
T 1G11
F21M 12
M SA T 2-5
M SA T 2-38
NGA172
ATHCHIB2
M SA T 4-39
M SA T 4-8
M SA T 11-0
NGA8
M SA T 4-35
M SA T 4-15
25
M SA T 3-19
M S A T 5-14
NGA139
M SA T -36
M SA T 2-41
M SA T 2-7
NG A 248
M SA T 3-32
M SA T 3-21
M S A T 5-22
T 27K 12
50
M SA T 4-18
M SA T 4-9
M SA T 2-10
M SA T 2-22
M S A T 5-9
NG A 128
F5I14
M SA T 1-13
M SA T 3-18
M S A T 5-12
75
M SA T 4-37
M S A T 5-19
M SA T 1-5
G eneti c M ap
BAY-0 x SHADARA
100
cM
Fig. 2.
Genetic map of the
Arabidopsis Thaliana
Bay-0 by Shahdara
Using the loci matrix from the
Arabidopsis thaliana
dataset two loci
X
A
and
X
B
were randomly selected from the possible loci and the following model was used to
generate the data:
y
i
=
δX
Ai
+
δX
Bi
+
δX
Ai
X
Bi
+
i
,
(16)
where
δ
is the effect size,
i
∼
N
(0
,
1)
. Each dataset contained a sample size of 158
observations. Effect sizes of
0
,
1
/
2
,
1
,
3
/
2
,
2
,
5
/
2
,
3
,
7
/
2
,
4
,
9
/
2
and
5
were generated.
Each of these effect sizes was repeated 10 times.
Using the data set and the method proposed the following probabilties were cal-
culated:
P
(
X
A
|
X
A
,X
B
,D
)
.Thesewere
calculated for 110 simulated data sets. Using the following prior distributions
β
j
∼
N
(0
,
200)
and
σ
2
D
)
,
P
(
X
B
|
D
)
,
P
(
X
AB
|
D
)
and
P
(
X
AB
|
χ
2
(1)
for the model parameters and
P
(
M
i
)
is uniform over the
all models subject to the restriction of
r
=10
. For each simulated data set 5 chains of
16,000 samples were taken from the posterior distribution of the models, with the first
∼