Hardy-Weinberg Equilibrium (HWE)
Definition
The expected genotype frequency in a large, randomly mating population with no selection, mutation, or migration. Under HWE, the frequency of a heterozygote Aa is 2pq and a homozygote AA is p-squared, where p and q are allele frequencies. The product rule assumes HWE holds at each locus; the theta correction relaxes this assumption for substructured populations.
- Applies to
- Large, randomly mating populations
- Heterozygote frequency
- 2pq
- Homozygote frequency
- p-squared (or q-squared)
- Forensic use
- Assumed by the product rule for match probability
- Correction for deviation
- Theta correction for population substructure
Common questions
What happens to DNA match probability calculations when HWE does not hold?+
When a population deviates from Hardy-Weinberg equilibrium, for instance due to substructure from non-random mating within subgroups, the simple product rule can understate or overstate the true match probability. Forensic statisticians apply the theta correction to adjust allele frequency estimates for that substructure.
Why is HWE assumed rather than tested for every forensic DNA calculation?+
Large reference population databases used in forensic statistics are generally tested and shown to be close to HWE for the core STR loci, so the assumption is well supported empirically rather than simply asserted. Analysts still apply conservative corrections like theta to account for any residual substructure.
Does HWE assume no mutation or selection is occurring?+
Yes, the classical Hardy-Weinberg model assumes no selection, mutation, or migration is changing allele frequencies between generations, alongside random mating and a large population size. Real populations violate these assumptions to some degree, which is why forensic statistics build in conservative safety margins rather than relying on the model exactly.
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...
- Product Rule
- The rule that, under independence, the joint probability of a multi-locus genotype equals the product of the individual locus genotype frequencies. Used...
- 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)....
- Allele Frequency
- The proportion of a specific allele variant at a given genetic locus in a defined population. Forensic match probability calculations multiply the...
- 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...
- 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...
- Minimum Allele Frequency (Minimum Frequency Ceiling)
- A conservative lower bound applied when an allele is absent or very rare in the database, to prevent an artificially inflated match...
- Population Substructure
- The condition in which allele frequencies differ systematically between subgroups within a nominally single population. Substructure means that individuals within a subgroup...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Reference Population Database
- A curated collection of allele frequencies or feature measurements from a defined population, used to estimate the probability that a randomly chosen...
Explained in these topics
- DNA Match Probability Calculation
- Population Databases for Forensic StatisticsThe expected genotype frequency distribution in a population that is randomly mating, large, and free from selection, mutation, and migration at a given locus....
- Allele Frequencies, Random Match Probability and the Likelihood RatioThe prediction that genotype frequencies in a large, randomly mating population equal the products of allele frequencies. Underpins the computation of genotype...