Questions: Wahlund Effect and Population Substructure

Question 1

A population geneticist samples 1,000 individuals from a large geographic region and finds a significant heterozygote deficiency relative to Hardy-Weinberg expectations. The most common explanation a student offers is inbreeding within the population. What alternative explanation should the geneticist consider first?

• A. Selection against heterozygotes, since this is the most common cause of heterozygote deficiency
• B. The Wahlund effect — the sample may have been drawn from multiple subpopulations with different allele frequencies, and pooling them produces apparent heterozygote deficiency even if each subpopulation is individually in HWE
• C. Genetic drift in a small founder population that colonized the region recently
• D. Assortative mating based on genotype, which is common in most species

Answer: (B)

When a heterozygote deficiency is observed in a large sample drawn from a broad geographic area, the Wahlund effect is one of the first explanations to consider — often before inbreeding. If the sample unknowingly pools individuals from multiple subpopulations with different allele frequencies, the pooled sample will always show a heterozygote deficit relative to what you'd predict from the overall allele frequency, even if random mating occurs within each subpopulation. This is a mathematical consequence of population structure, not a biological process occurring within individuals. Distinguishing Wahlund effect from inbreeding requires examining whether the sample is geographically or genetically structured.

Question 2

Two isolated subpopulations are combined into a single sample for a population genetics study. In subpopulation X, the frequency of allele A is 0.9. In subpopulation Y, the frequency of allele A is 0.1. Both populations are in Hardy-Weinberg equilibrium. What will happen when their genotype data are pooled?

• A. The pooled sample will also be in HWE, since both source populations are in HWE
• B. The pooled sample will show excess heterozygotes, since crossing divergent populations produces hybrid vigor
• C. The pooled sample will show a heterozygote deficiency — fewer heterozygotes than predicted by HWE given the pooled allele frequency of 0.5
• D. The pooled sample will show no deviation from HWE because the allele frequency differences cancel out

Answer: (C)

HWE within each subpopulation does not guarantee HWE in the pooled sample. In subpopulation X (p=0.9), expected heterozygosity = 2(0.9)(0.1) = 0.18. In subpopulation Y (p=0.1), expected heterozygosity = 2(0.1)(0.9) = 0.18. The actual heterozygosity in the pooled sample averages to 0.18. But the pooled allele frequency is 0.5, and HWE would predict 2(0.5)(0.5) = 0.50 heterozygotes. Observed = 0.18, predicted = 0.50 — a dramatic heterozygote deficiency. The more divergent the allele frequencies between subpopulations, the larger the Wahlund deficit.

Question 3

If a population sample shows a heterozygote deficiency compared to Hardy-Weinberg prediction, this is sufficient evidence that mating within the sampled population is non-random.

• T. True
• F. False

Answer: False

This is the classic Wahlund effect misconception. Heterozygote deficiency can arise from non-random mating (inbreeding, assortative mating), selection against heterozygotes, or the Wahlund effect — pooling of subpopulations with different allele frequencies. The Wahlund effect requires no departure from random mating within any subpopulation; it is a statistical artifact of treating a structured sample as a single unit. A forensic geneticist, conservation biologist, or medical association study researcher who ignores the Wahlund effect and assumes any heterozygote deficiency indicates inbreeding will draw incorrect conclusions.

Question 4

Two subpopulations can each individually satisfy Hardy-Weinberg equilibrium while the pooled sample from both subpopulations shows a heterozygote deficiency.

• T. True
• F. False

Answer: True

This is the core mathematical claim of the Wahlund effect. HWE within a population requires only that allele frequencies predict genotype frequencies through random mating within that population — it says nothing about what happens when you mix two populations with different allele frequencies. The heterozygote deficiency in the pooled sample is a consequence of Jensen's inequality: when you average across groups with different allele frequencies, the mean of the squared (homozygote) terms exceeds the square of the mean allele frequency, leaving less 'room' for heterozygotes. Each subpopulation can be in perfect HWE while the pooled sample shows a substantial deficit.

Question 5

Explain why pooling two populations with different allele frequencies always produces fewer heterozygotes in the pooled sample than Hardy-Weinberg predicts, even when each population individually is in perfect Hardy-Weinberg equilibrium.

Model answer: HWE predicts heterozygote frequency as 2pq, where p and q are the overall allele frequencies in the pooled sample. But the actual heterozygote frequency in the pooled sample is the average of heterozygote frequencies within each subpopulation — each calculated using that subpopulation's local allele frequencies. Because heterozygosity (2pq) is a concave function of allele frequency, the average of local heterozygosities is always less than the heterozygosity you'd predict from the average allele frequency. Mathematically, variance in allele frequencies among subpopulations directly reduces observed heterozygosity. The more divergent the subpopulations' allele frequencies, the larger the deficit.

This result follows from Jensen's inequality applied to the concave 2pq function. It means that any time you see a heterozygote deficiency in a geographically broad sample, population substructure (Wahlund effect) must be considered alongside inbreeding and selection. F_ST — the standard measure of population differentiation — is essentially a formalization of this variance in allele frequencies, quantifying how much heterozygosity is lost to subdivision.