Product Rule
Definition
The rule that, under independence, the joint probability of a multi-locus genotype equals the product of the individual locus genotype frequencies. Used to compute RMP for multi-locus STR profiles. Independence across loci is supported for unlinked markers but must be verified for the specific population database in use.
- Basis
- Independence of unlinked genetic loci
- Use
- Computing random match probability for multi-locus profiles
- Requirement
- Locus independence verified in the reference population
- Adjustment
- Often combined with theta correction for sub-structure
Common questions
Why must independence be checked before applying the product rule?+
If loci are linked or a population has sub-structure, multiplying individual frequencies together understates the true match probability, because the genotype combinations are not truly independent. Population genetic studies and linkage data for the marker set are checked before the rule is applied.
How does the product rule scale RMP with additional loci?+
Each additional independent locus multiplies in its own genotype frequency, so RMP drops sharply as more loci are typed. This is why modern STR kits with 20 or more loci produce match probabilities far smaller than older kits with fewer markers.
What correction is commonly paired with the product rule for courtroom use?+
A theta or FST correction is often applied alongside the product rule to account for population sub-structure, which inflates the computed RMP slightly and produces a more conservative, defence-favourable statistic.
Related terms
- Likelihood Ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Prosecutor's Fallacy
- The error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that...
- Random Match Probability (RMP)
- The probability that a randomly chosen unrelated person from the relevant population would match the evidence profile by chance. A very small...
- Theta (FST) Correction
- A correction factor applied to allele frequency estimates to account for population sub-structure (the tendency for allele frequencies to differ between sub-populations)....
- Hardy-Weinberg Equilibrium (HWE)
- The expected genotype frequency in a large, randomly mating population with no selection, mutation, or migration. Under HWE, the frequency of a...
- Defence Attorney's Fallacy
- The incorrect argument that a large global or national population means many unrelated individuals could share the profile, while ignoring the geographic...
- Defence Fallacy
- The converse error of inflating the importance of the RMP by arguing that, because many people in the population share the profile,...
- ENFSI DNA Working Group
- The European Network of Forensic Science Institutes DNA Working Group. Coordinates European forensic DNA standards, including the evaluative reporting guidelines adopted by...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- SWGDAM
- Scientific Working Group for DNA Analysis Methods; the US body that publishes interpretation guidelines and validation requirements for forensic DNA laboratories operating...
Explained in these topics
- DNA Match Probability CalculationThe statistical principle that the probability of independent events co-occurring is the product of their individual probabilities. Applied to STR profiles: th...
- Allele Frequencies, Random Match Probability and the Likelihood RatioThe multiplication of genotype frequencies across independent loci to compute the profile-level RMP. Justified by the chromosomal independence of CODIS and ESS...
- The Concept of Random Match Probability