Evolution__3rd_Edition

116 PART 2 / Evolutionary Genetics
. . . given certain assumptions
The selection coefficient s ≈ 0.5
We have to make a number of assumptions. One is that resistance is controlled by a
single allele (we shall return to this below). Another concerns the degree of dominance:
the allele conferring resistance might be dominant, recessive, or intermediate, relative
to the natural susceptibility allele. The case of dominant resistance is easiest to understand.
(If resistance is recessive we follow the same general method, but the exact result
differs.) Let us call the resistance allele R and the susceptibility allele r. All the
mosquitoes that die, in the mortality tests used in Figure 5.7, would then have been
homozygous (rr) for susceptibility. Assuming (for simplicity rather than exact accuracy)
Hardy–Weinberg ratios, we can estimate the frequency of the susceptibility gene as
the square root of the proportion of mosquitoes that die in the tests. The selection
coefficients are defined as follows, where fitness is measured as the chance of survival
in the presence of DDT:
Genotype RR Rr rr
Fitness 1 1 1 − s
If we define p as the frequency of R and q as the frequency of r, equation 5.5 again gives
the change in gene frequency: selection is working against a recessive gene. Figure 5.7
shows the decline in frequency of the susceptible mosquitoes, which are the recessive
homozygotes. We therefore need a formula for the change in q in one generation (∆q),
rather than ∆p (as on p. 106). The decrease in q is the mirror image of the increase in p,
and we just need to put a minus sign in front of equation 5.5:
spq
∆q =
sq
− 2
1 − 2
(5.7)
The generation time is about 1 month. (The generations of mosquitoes overlap,
rather than being discrete as the model assumes; but the exact procedure is similar in
either case, and we can ignore the detailed correction for overlapping generations.)
Table 5.7 shows how the genotype frequencies were read off Figure 5.7 in two stages,
giving two estimates of fitness. Again, the formula for one generation has to be applied
Table 5.7
Estimated selection coefficients against DDT-susceptible Anopheles culicifacies, from
Figure 5.7, where the relative fitness of the susceptible type is (1 − s). The estimate assumes the
resistance allele is dominant. Simplified from Curtis et al. (1978).
Frequency of
susceptible type
Before After Time (months) Selection coefficient
0.96 0.56 8.25 0.4
0.56 0.24 4.5 0.55
..