How a DNA Match Is Expressed and What the Number Means

A DNA result arrives as two statements. One is a comparison conclusion: the reference profile is included, is excluded, or the comparison is inconclusive. The other is a figure, and the figure is what most of the argument turns on. The two statements come from different steps of the analysis, rest on different assumptions, and can fail independently of one another.

What the typing measures

Short tandem repeats are stretches of DNA in which a brief unit of bases repeats, and the number of repeats at a given location varies between people. An analyst extracts DNA from the sample, estimates how much is present, copies the target regions by polymerase chain reaction, and separates the copies by size in a capillary instrument. The instrument records fluorescence as the fragments pass a detector.

The record it produces is an electropherogram: a trace of peaks, each assigned a locus and a repeat number. Two peaks at a locus indicate different inherited variants. One peak indicates the same variant from both parents, or a variant whose partner failed to copy. Peak height, expressed in relative fluorescence units, carries the information used to judge whether a peak is real, whether material has been lost, and how many people contributed.

The national index rests on a designated core set of loci, and a contributing laboratory operates under published quality assurance standards, accreditation and external audits required by 34 U.S.C. § 12592. More loci means more power to discriminate between people. Whether a result appears at every locus depends on how much DNA survived, and degraded material commonly yields the smaller fragments while the larger ones fall away.

Inclusion, exclusion and the space between

An exclusion is the strongest conclusion the method offers. If the evidence profile carries a variant the reference does not have, and the analyst can rule out an artifact or an additional contributor, the reference did not contribute that material. An exclusion needs no statistic to mean something.

Inclusion is different. The phrase "cannot be excluded" says only that every variant in the reference is accounted for at the loci interpreted. It does not say the reference is the source, and standing alone it does not say how unusual the agreement is. A profile built on few loci can include very large numbers of people, and the phrase reads the same whether the agreement is remarkable or ordinary. The statistic exists to fill that gap.

Inconclusive is a third outcome, reported when the data will not support a comparison or a meaningful figure. Laboratories differ in how readily they use it, and the criteria sit in the standard operating procedure rather than in the report. An inconclusive result on a clean sample is a different event from one on a degraded trace.

Where the frequency comes from

A frequency estimate is built from allele frequency tables compiled from population samples. For each locus the analyst converts the frequencies of the observed variants into a genotype frequency, then multiplies across the loci. Multiplication assumes that the two variants at a locus are independent of each other, and that the loci are independent of one another. Both assumptions are approximations, and both hold better in a large mixed population than in a small, isolated one.

Population structure is handled by a correction that inflates the estimate to allow for shared ancestry within subgroups. The effect is conservative by design: it makes the profile look more common than raw multiplication would suggest. A laboratory also chooses which population tables to report, which is why a report often carries separate figures for several broad groups rather than one national figure.

Because those tables come from samples and not from a census, the result is an estimate carrying its own uncertainty. The National Academies report on strengthening forensic science treated nuclear DNA typing as the discipline with the firmest quantitative footing, while pressing every discipline to state the limits of what it reports. The figure is defensible, and it is still an estimate.

Two forms the statistic takes

The random match probability answers a frequency question: how often the profile would be expected among unrelated people. It suits a single-source profile, where there is one genotype to describe. It says nothing about relatives, who share variants at a rate set by inheritance rather than by population frequency, which is why a report sometimes carries a separate figure for siblings or other close relations.

A likelihood ratio answers a comparative question. It states how much more probable the observed data are if one proposition holds than if a stated alternative holds. That is the form used for mixed samples and for results produced by probabilistic genotyping software, because such data cannot be reduced to a single genotype. Its value depends on the two propositions chosen, so the propositions belong in the report beside the ratio.

Neither figure speaks to how the material reached the item, when it was left, or what kind of cells it came from. Those are separate questions, and the distance between a statistic about a profile and a claim about conduct is the subject of secondary transfer and the limits of touch DNA. Where more than one person contributed, the figure also rests on assumptions examined in the interpretation of mixed profiles.

Lineage markers and counting estimates

Two marker systems break the pattern. Y-chromosome typing targets the male portion of a sample and is used where a small male contribution sits beneath a large female one. Mitochondrial typing works on material in which nuclear DNA has degraded past use, such as hair shafts without roots and old skeletal remains, because each cell carries many copies of the mitochondrial genome.

Both are lineage markers. A Y haplotype passes intact down the male line, so a father, his sons, his brothers and his paternal cousins are expected to share it. A mitochondrial sequence descends the maternal line the same way. The markers within each system travel together, so the product rule cannot be applied across them; multiplying would assume an independence that inheritance does not supply.

The frequency is therefore estimated by counting. The analyst searches a haplotype database, records how often the observed type appears, and reports an upper confidence bound that accounts for the size of that database. Such figures are far less discriminating than those from nuclear typing, and no counting estimate distinguishes members of one lineage from each other. A report that omits the limitation invites a reader to hear more than the method delivered. Whether the laboratory held accreditation, and what an external audit examined, is taken up in crime laboratory accreditation and audits.