A Hardy–Weinberg Test That Fails in the Wrong Direction
In a college genetics lab, 200 students genotype themselves at a biallelic single-nucleotide locus using a PCR-RFLP assay: the A allele retains a restriction site and yields two fragments, the G allele does not cut. Scored gel phenotypes are AA 110, AG 60, GG 30. The instructor asks the class to test Hardy–Weinberg equilibrium and supplies chi-square critical values (df = 2: 5.99 at the 0.05 level). Two complications surface. First, the class pools students from two campuses that differ substantially in ancestry. Second, in about 8 of the 200 gels the smaller fragment is faint, and two students whose gel showed only the uncut band were confirmed as AG by sequencing. A student concludes that because the locus is not in Hardy–Weinberg equilibrium, it must be under natural selection.
1. Carry out the Hardy–Weinberg test, state the direction of any departure, and explain what the chi-square result does and does not tell you.
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Allele frequencies. There are 400 alleles: 2(110) + 60 = 280 copies of A, so p(A) = 0.70 and q(G) = 0.30.
Expected counts under random mating, no selection, no migration, no mutation, and a large population:
- AA = 200(0.70)^2 = 98
- AG = 200(2 × 0.70 × 0.30) = 84
- GG = 200(0.30)^2 = 18
Chi-square. (110 − 98)^2/98 = 1.47; (60 − 84)^2/84 = 6.86; (30 − 18)^2/18 = 8.00. Total = 16.3 with df = 2, well above 5.99, so the null is rejected at the 0.05 level.
Direction. The departure is a heterozygote deficit: 60 observed against 84 expected, with both homozygote classes in excess. The fixation index is about (0.30 − 0.42)/0.42 = −0.29, a moderate deficit.
What it does not tell you. The test rejects a neutral null model; it does not identify a cause. Selection is one of several processes that produce a heterozygote deficit, and it is usually the last one to invoke, because simpler explanations (genotyping error, pooling of subpopulations, inbreeding, assortative mating, null alleles) produce the same signature. Note also that the class is a convenience sample of students, not a random sample of a defined population, which is a real limitation on any population-genetic inference from it.
2. Give two explanations for the heterozygote deficit that fit these data, and describe the specific test or calculation that would distinguish them. Use the numbers to check how far each explanation can go.
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Explanation 1 - genotyping error (allele dropout or a faint small fragment). A heterozygote whose cut fragment is too faint to see is scored as GG. This fits the observation that about 8 gels had a weak small band and that two GG-scored students were proven AG by sequencing. But the arithmetic limits it: the class needs 24 more heterozygotes to reach 84, and even rescoring all 8 ambiguous gels gives at most 68 AG, still 16 short. Genotyping error is a real contributor but cannot be the whole story. Discriminating test: re-genotype the ambiguous samples by Sanger sequencing or a different primer pair, and recompute chi-square on the corrected counts.
Explanation 2 - the Wahlund effect from pooling two campuses. When two subpopulations with different allele frequencies are pooled, the pooled sample shows fewer heterozygotes than the pooled allele frequencies predict, even if each campus is in perfect Hardy–Weinberg equilibrium. Discriminating test: estimate p separately for each campus and test Hardy–Weinberg within each. If both subpopulations are in equilibrium and the pooled sample is not, the deficit is a structure artefact, not selection.
The logic to carry forward: match the explanation to a prediction that differs between explanations, and use the data you already have to rule out explanations that cannot be large enough.
3. Evaluate the student's conclusion that the locus must be under natural selection, and describe the kind of evidence that would actually be required to support a selection claim.
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The conclusion overreaches in three ways.
First, Hardy–Weinberg equilibrium is a null model of no evolutionary processes at all. Rejecting it tells you that something is happening - drift, migration, nonrandom mating, mutation, selection, or a technical artefact - not which one. A heterozygote deficit is actually the least specific signature, since error, pooling, inbreeding and null alleles all generate it.
Second, the deviation here is more plausibly technical or demographic. Roughly 4% of genotypes were ambiguous on the gel, the class pools two ancestrally distinct campuses, and students are not a randomly mating population. Any of these produces the observed pattern without any fitness difference.
Third, selection is a claim about fitness. Genotype frequencies alone cannot establish it.
What would be required: a properly defined population sampled at random; allele and genotype frequencies measured across generations or across a life-cycle stage contrast (for example, larvae versus survivors); direct evidence that genotypes differ in survival or reproduction; and ideally a functional or ecological mechanism explaining why one allele is favored. Until then, the defensible statement is that this convenience sample departs from Hardy–Weinberg expectations for reasons that are most likely technical or due to population structure.