Application of an insecticide to control mosquito populations in malaria infeste

ID: 10630 • Letter: A

Question

Application of an insecticide to control mosquito populations in malaria infested areas quickly resulted in a dominant mutation, R, resulting in insecticide resistance. However, the mutation also reduces the fertility of RR homozygotes. The fitness of different genotypes in areas where the insecticide is in use, are as follows:

rr (susceptible) 0.35
Rr (resistant) 1.0
RR (resistant) 0.85

What is the equilibrium frequency of the R allele in the population? Using the fitness values in the previous problem, and a starting frequency of 1% for the R allele, what is the expected frequency of the R allele after one generation in an environment where the insecticide is applied?

Explanation / Answer

According to HARDY WIENBERG LAW

P+Q=1

frequency of ----R allele=1%=0.01

frequency of ----rallele=1-0.01= 0.99

FITNESS VALUES

0.85

0.35

Frequency before selection

0.01 x0.01 =

0.0001

2 x 0.01 x0.99=

0.0198

0.99x0.99 =0.9801

Frequency after selection

0.0001 x0.85=0.85

0.0198 x1=0.0198

0.980 x0.35=0.343

According to Hardy weinberg law=

--------------before ---------p2+2pq+r2=1=0.0001 +0.0198 +0.980=1

After selection

p2+2pq+r2 =1= 0.85+0.0198+0.343

frequency of r allele=

=2pq /2 + r2 =1= 0 +0.0099 +0.343 =0.3529

frequency of R allele= 1-r= 1-0.3529=0.6471