Biology Reference
In-Depth Information
As with the first example, the numerator ( H p ) genotype ( A,B ) occurs in only one
of four ways (0.25). Considering the denominator ( H d ): if the mother passed on
allele A (probability 0.5) the 'random man' would have to pass on allele B ( P B ),
the combined probability of these two events is 0.5
P B ; alternatively, the mother
could pass on allele B (probability 0.5) and a random man pass on allele A ( P A ),
with a combined probability of 0.5 × P A . This results in the equation below:
×
1
2 ( P A + P B )
In Table 11.1 all the potential combinations of alleles from a mother, child and
tested man are shown along with the resulting numerator, denominator and PI
equation.
We can apply the formulae in Table 11.1 to the paternity case that is presented in
Table 11.2.
The combined PI is calculated by applying the product rule and multiplying the
PI from each locus; in this case the PI is 2 920 823. This can be represented by the
statement:
0 . 25
0 . 5 P A + 0 . 5 P B =
PI
=
Statement of positive paternity
The results of the DNA testing are 2 920 823 times more likely if the tested man
is the biological father of the child than if the biological father is another man,
unrelated to the tested man.
In addition to the standard paternity testing where the mother, child and alleged
father are available, testing can also be carried out when the mother is not available
[12, 18 - 20]. The formulae used are shown in Table 11.3.
We can apply these formulae to the paternity case shown in Table 11.2 (Table 11.4).
The strength of the PI will naturally vary depending on the given combinations
of genotypes in each case. As can be seen from the example above and Figure 11.2
the paternity indices are much lower when the mother is not available for testing.
Probability of paternity
The significance of LRs can be difficult for lay people to evaluate and the results
are often presented as a probability of paternity, making the results more accessible.
To calculate a probability of paternity requires Bayesian analysis and takes into con-
sideration non-genetic evidence: the LR is multiplied by the prior odds of paternity
that is determined by non-genetic evidence, such as the testimony of the woman. It
can be calculated using Equation 11.2.
non genetic evidence)
LR × Pr( H p | non genetic evidence) +
[1
LR
×
Pr( H p |
Probability of paternity =
(11.2)
Pr( H p |
non genetic evidence)]
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