Biology Reference
In-Depth Information
To calculate the profile frequencies that allow for subpopulations, the following
equations are commonly used [21]:
For heterozygotes
:
2
(θ
+
(
1
−
θ)
p
A
)(θ
+
(
1
−
θ)
p
B
)
(
=
(8.1)
1
+
θ)(
1
+
2
θ)
For homozygotes
:
=
(
2
θ
+
(
1
−
θ)
p
A
)(
3
θ
+
(
1
−
θ)
p
A
)
(
1
+
θ)(
1
+
2
θ)
(8.2)
We can use this to recalculate the profile frequency presented in Table 8.1: the
calculations for the vWA and FGA locus are shown below with a theta value of 0.01.
vWA
FGA
2(0
.
01
+
(1
−
0
.
01)0
.
0850)
(0
.
01
+
(1
−
0
.
01)0
.
2500)
(1
+
0
.
01)(1
+
(2
×
0
.
01))
((2
×
0
.
01)
+
(1
−
0
.
01)0
.
1775)
((3
×
0
.
01)
+
(1
−
0
.
01)0
.
1775)
(1
+
0
.
01)(1
+
(2
×
0
.
01))
2[0
.
0942][0
.
2575]
(1
.
01)(1
.
02)
2[0
.
0942][0
.
2575]
(1
.
01)(1
.
02)
0
.
0485
1
.
0302
=
0
.
0471
0
.
0403
1
.
0302
=
0
.
0391
The impact of a theta value of 0.01 on this particular profile is a modest threefold
increase in the profile frequency, whereas a theta value of 0.03 leads to a frequency
that is over 20 times more common but still exceedingly rare (Table 8.3). It should
be noted that the impact of applying theta to a profile frequency calculation differs
between profiles (Figure 8.2). It should be noted that in a forensic context the theta
term is often used interchangeably with the term F
ST
.
The current practice in most legal systems is to use a theta value of between
0.01 and 0.03, apart from in exceptional circumstances where very high levels of
Table 8.3
The effect of different correction methods on the profile frequency calculated in
Table 8.1. With this profile, applying a minimum allele frequency of 0.0125 would have no impact
because the rarest allele frequency is 0.025
Calculation method
Profile frequency
Fold reduction relative to
uncorrected frequency
7.58
×
10
−
14
Uncorrected
-
Size bias
1.42
×
10
−
13
2 (1.88)
2.44
×
10
−
13
Subpopulation:
θ
=
0.01
3 (3.29)
1.62
×
10
−
12
Subpopulation:
θ
=
0.03
21
1.00
×
10
−
9
Profile ceiling - 1 in 1 billion
13 195
