Weevils, Pyrethroid, and a Misread Hardy–Weinberg Result
A population of 2,000 rice weevils lives in a grain storage building. Resistance to a pyrethroid insecticide is controlled by one gene with two alleles, R and r. Before any spraying, the keeper samples 400 weevils: 16 are RR, 128 are Rr, and 256 are rr. The building is sprayed every two weeks for one season. At the end of the season, a sample of 400 weevils contains 196 RR, 168 Rr, and 36 rr. Survival to adulthood in the sprayed building is 4% for rr, 60% for Rr, and 95% for RR. A neighboring unsprayed grain elevator has a weevil population with an R allele frequency of 0.05. The keeper concludes that because the sprayed population's genotype frequencies match Hardy–Weinberg expectations at the end of the season, the population is not evolving.
1. Calculate the R and r allele frequencies before and after spraying, test both samples against Hardy–Weinberg expectations, and evaluate the keeper's conclusion.
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Before: f(R) = 0.04 + ½(0.32) = 0.20, so f(r) = 0.80. Expected genotypes are RR = 0.04 (16), Rr = 0.32 (128), rr = 0.64 (256) - an exact match, so the population was in Hardy–Weinberg equilibrium before spraying.
After: f(R) = 0.49 + ½(0.42) = 0.70, so f(r) = 0.30. Expected genotypes are RR = 0.49 (196), Rr = 0.42 (168), rr = 0.09 (36) - again an exact match. The keeper's inference is wrong. Hardy–Weinberg equilibrium describes genotype frequencies within a generation given the allele frequencies; it does not mean allele frequencies stay constant over time. Here f(R) rose from 0.20 to 0.70, which is evolution. The population sits at equilibrium at each sampling point but has evolved between them.
2. Explain how the survival data produced this change, and predict what will happen to the R allele if spraying stops.
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The spray kills rr weevils (4% survival) while RR survives at 95% and Rr at 60%, so R is passed on disproportionately each generation. That is directional selection, and it explains the rise from 0.20 to 0.70.
If spraying stops, the outcome depends on fitness costs. If RR or Rr develops more slowly or lays fewer eggs without insecticide, rr will regain the advantage, R will decline, and the population may drift back toward 0.20. If there is no measurable cost, R will persist near 0.70 because nothing is removing it and it is already common. The prediction is conditional; the data needed are survival and reproduction of each genotype in an unsprayed building.
3. The neighboring elevator's population has f(R) = 0.05. Explain what would happen if weevils migrated between buildings, and why gene flow is not the same as natural selection.
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Migration of weevils between buildings is gene flow. Because the neighboring population has f(R) = 0.05, well below the sprayed population's 0.70, immigration would slightly lower f(R) in the sprayed building - the opposite direction from selection.
Gene flow is not natural selection because it does not sort variants by fitness within a population; it moves alleles between populations and tends to reduce differences between them. Selection changes frequencies because bearers of a variant survive and reproduce differently. Both can act at once, and the net change depends on the relative strengths of selection, gene flow, genetic drift, and mutation.