Head lice are now reported resistant to the most popular insecticides used again

Question

Head lice are now reported resistant to the most popular insecticides used against them. Suppose the resistant allele is completely dominant for resistance (R vs the susceptible S allele). The R/R, R/S genotypes produce 125 eggs per female each and S/S survive to produce only 5 eggs on average. A generation of the lice is about 1 months. If an initial infestation starts with an initial frequency of R = 0.25. Assume that treatment starts immediately, then (a) What is the fitness of each genotype; (b) what is the expected frequency of the R allele after 1 month? (c) and after 2 months?

Explanation / Answer

(a)

Survival rate of S/S genotype = 5 / (125+5) = 5/130 = 0.0385

Survival rate of R/R and R/S genotype = 125 / 130 = 0.9615

To calculate fitness we use the highest survival rate so that fitness is normalized

W(RR) = 0.9615 / 0.9615 = 1

W(RS) = 0.9615 / 0.9615 = 1

W(SS) = 0.0385 / 0.9615 = 0.04

(b)

Freq(R) = 0.25

So, Freq(S) = 1 - 0.25 = 0.75

Expected frequency after 1 month = p + pq = 0.4375

(c) Expected frequency after two months = p + 2*pq = 0.625

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