  The likelihood ratio (LR) is a commonly used measure for determining the
strength of forensic match evidence. When a forensic expert determines a high
LR for DNA found at a crime scene matching the DNA profile of a suspect they
typically report that 'this provides strong support for the prosecution
hypothesis that the DNA comes from the suspect'. However, even with a high LR,
the evidence might not support the prosecution hypothesis if the defence
hypothesis used to determine the LR is not the negation of the prosecution
hypothesis (such as when the alternative is 'DNA comes from a person unrelated
to the defendant' instead of 'DNA does not come from the suspect'). For DNA
mixture profiles, especially low template DNA (LTDNA), the value of a high LR
for a 'match' - typically computed from probabilistic genotyping software - can
be especially questionable. But this is not just because of the use of
non-exhaustive hypotheses in such cases. In contrast to single profile DNA
'matches', where the only residual uncertainty is whether a person other than
the suspect has the same matching DNA profile, it is possible for all the
genotypes of the suspect's DNA profile to appear at each locus of a DNA
mixture, even though none of the contributors has that DNA profile. In fact, in
the absence of other evidence, we show it is possible to have a very high LR
for the hypothesis 'suspect is included in the mixture' even though the
posterior probability that the suspect is included is very low. Yet, in such
cases a forensic expert will generally still report a high LR as 'strong
support for the suspect being a contributor'. Our observations suggest that, in
certain circumstances, the use of the LR may have led lawyers and jurors into
grossly overestimating the probative value of a LTDNA mixed profile 'match'
