kdr resistance in a sprayed valley: heterozygote deficit and refuge design
Culicine mosquitoes in a valley are controlled with pyrethroid spraying. Resistance is conferred by a single point mutation (kdr) in the sodium-channel gene and is recessive: only RR individuals survive the diagnostic dose.
In 2019, before spraying, the frequency of R was 0.02. In 2023, after four seasons, researchers collected 1,000 mosquitoes from the valley floor: 100 were RR, 300 were RS (genotyped by PCR) and 600 were SS. In the same year, 12% of the valley - mostly nature reserve and unsprayed orchards - received no insecticide.
Adult dispersal is estimated at 1–2 km per generation, and the valley floor is 8 km wide. Generation time is about two weeks.
The regional health authority proposes continuing spraying across the whole valley floor. A consultant proposes leaving 20% of each sprayed area untreated as a refuge. Farmers object that any untreated patch will produce adults that later bite, and that they will lose yield.
1. Estimate the R allele frequency from the genotype counts, test the sample for Hardy–Weinberg equilibrium, and quantify the deviation. Explain why estimating q from the resistant phenotype alone would be misleading here.
Read the worked answer
Allele counting (no HWE assumption): total alleles = 2,000. R alleles = 2(100) + 300 = 500 → q = 0.25, p = 0.75.
HWE expectations: RR = 0.0625 × 1,000 = 62.5; RS = 2(0.75)(0.25) × 1,000 = 375; SS = 0.5625 × 1,000 = 562.5.
χ² = (100 − 62.5)²/62.5 + (300 − 375)²/375 + (600 − 562.5)²/562.5 = 22.5 + 15.0 + 2.5 = 40.0, df = 1. Critical value 3.84 at p = 0.05, so HWE is decisively rejected: there is a large excess of RR homozygotes and a deficit of heterozygotes.
Size of the deviation: F = (H_exp − H_obs)/H_exp = (375 − 300)/375 = 0.20 - a 20% heterozygote deficit.
The trap: estimating q from the frequency of resistant individuals (√0.10 = 0.32) is valid only if the population is in HWE - which is precisely what is being tested. Here it would overstate the resistance allele by about 28% and could trigger unnecessary escalation of spraying. Allele counting is the correct starting point; the HWE test then asks whether the genotypes are consistent with random mating.
2. Give two biologically plausible explanations for the heterozygote deficit and describe a field or laboratory test that separates them.
Read the worked answer
1. Population subdivision - the Wahlund effect. The sample mixes mosquitoes from sprayed areas, where RR survives and R is common, with mosquitoes from the 12% unsprayed refuge, where R is rare. Pooling two subpopulations with different allele frequencies always produces a heterozygote deficit relative to the pooled frequencies, with no selection against heterozygotes required. Test: genotype by collection site. If each site is close to HWE internally but q differs strongly between sites, subdivision is confirmed.
2. Restricted dispersal and assortative mating. Dispersal of 1–2 km per generation is much smaller than the 8 km valley, so matings are not random across the whole area: survivors in sprayed blocks mate mainly with each other, as do SS mosquitoes in the refuges. Test: mark–release–recapture, or genetic assignment of individuals to collection sites; alternatively compare genotype frequencies of larvae (products of local mating) with those of adults.
Formal alternatives to exclude: null alleles or PCR failure at the kdr site would make true heterozygotes score as homozygotes - repeat with a second primer pair. Heterozygote disadvantage is unlikely, because kdr heterozygotes normally die at the diagnostic dose, which would look like selection for SS rather than a deficit of RS.
The distinction matters: subdivision means the existing unsprayed 12% is already shaping the population, whereas a typing artefact means the resistance problem is worse than it appears.
3. Using the data, evaluate the consultant's 20% refuge proposal against the authority's whole-valley spraying plan. State what evidence would decide the question, and address the farmers' objection.
Read the worked answer
Refuge logic. Spraying kills SS and RS and spares RR, which drives R up from 0.02 (2019) to 0.25 (2023) - a very fast change over roughly 100 generations. A refuge produces SS mosquitoes; SS × RR matings give RS, which are susceptible at the diagnostic dose. Because resistance is recessive, the refuge removes resistance alleles efficiently instead of hiding them in heterozygotes.
But the data suggest the refuge is under-connected. F = 0.20 indicates limited mixing between sprayed and unsprayed areas, consistent with 1–2 km dispersal against an 8 km valley. A refuge placed at the edge, or concentrated in the nature reserve, will not deliver SS males into the middle of the sprayed blocks. The design should be strips within about 1 km of every sprayed area, not one large block. Note also that 12% untreated already exists; the first empirical step is to test whether R frequency and resistance are lower near the reserve than far from it - a natural before–after, control–impact comparison.
Evidence needed: R frequency by distance from untreated areas; per-farm spray records; the fraction of RS among survivors; larval density in refuges.
The farmers' objection is partly correct - refuges do produce adults - but misses that a refuge protects the insecticide as a shared resource. A farm that sprays everything gains one season and loses the product. Because 20% non-compliance across landholders can undo the plan, enforcement and compensation matter as much as the biology.