Three-person mixture with a minor contributor below threshold
Tape from a handgun grip yields a mixture. Peak-height proportions are approximately 60%, 30%, and 5–8%. The maximum allele count is 5 at three loci and 6 at one locus. The minor contributor's peaks are 40–90 RFU against an analytical threshold of 125 RFU, and alleles are absent at several loci where the minor would be expected to contribute. A person of interest shares all four of the minor's detectable alleles. The 60% major profile matches the complainant's boyfriend, a known contributor. The defense has named the person of interest's brother as an alternative. The laboratory has a validated probabilistic genotyping system for up to four contributors and also routinely reports combined probability of inclusion statistics.
1. How many contributors should be assumed, and what do the allele counts imply about drop-out?
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Three contributors is the best-supported assumption.
The theoretical maximum allele count is 2n, so three contributors can produce up to 6 alleles at a locus and four can produce up to 8. The observed maximum is 6 at one locus, which is fully explained by three contributors. Four contributors would require two drop-outs at every locus, including the locus showing 6 alleles, which is a much less parsimonious explanation given the observed peak heights.
The loci showing only 5 alleles indicate drop-out of at least one allele even under the three-person assumption. Drop-out is expected here: the minor's peaks are 40–90 RFU, at or below the analytical threshold, so the minor is a low-template contributor whose profile is necessarily partial.
The minor's true genotype cannot be reconstructed by simple allele counting. It must be modeled, which is precisely what the probabilistic system is for.
2. Which statistic should be reported, and what conditioning and assumptions does it require?
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Report a likelihood ratio from the validated probabilistic genotyping system, not a combined probability of inclusion.
CPI assumes a two-person mixture of unrelated contributors and treats every allele above threshold as a potential contributor allele. In a three-person mixture with drop-out, it mischaracterizes the number of contributors, ignores peak heights, and generally inflates the weight of the minor's contribution.
The LR should ask the specific question at issue: is the person of interest a contributor to this mixture? The proposition set should condition on the known boyfriend and on an unknown second contributor, with the person of interest as the third. Conditioning on known contributors is required; ignoring them would let their alleles be attributed to the person of interest.
The model must incorporate drop-out and drop-in parameters validated for this mixture type and template level, and the reported LR should include the effective number of contributors and the peak-height model used. A single LR should be accompanied by an assessment of the model's fit to the data.
3. How should the brother be addressed, and what limitations must appear in the report?
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The brother should be addressed explicitly rather than dismissed. A sibling shares a substantial proportion of alleles by descent, so a likelihood ratio calculated against an unrelated alternative overstates the weight if the true alternative is a brother. The laboratory should either run the LR with a sibling as the alternative, using validated identical-by-descent parameters, or state the reduction in the LR that a sibling relationship would produce. Reporting only the unrelated-alternative LR without that caveat is misleading.
The report must state:
- The number of contributors assumed and that it is an inference, not a measurement.
- That the minor's profile is partial because of drop-out, so the LR is conditional on the drop-out model.
- That the major's identity as the boyfriend was assumed, and the LR depends on that assumption.
- That a low-level contributor's DNA may be transferred indirectly and that the LR addresses source, not activity.
- That the result does not identify a person, only weighs the propositions tested.