Answer:
the frequency of the resistant allele after one generation is 0.989
Explanation:
Given that :
A farmer plants Bt cotton that is genetically modified to produce its own insecticide.
Of the cotton bollworms feeding on these Bt plants, only 5% survive
i.e the survival rate s = 5% =0.05
unless they have at least one copy of the dominant resistance allele R that confers resistance to the Bt insecticide
Frequency of R allele = 0.01
In order to determine what will the frequency of the resistance allele be after one generation of cotton bollworms fed on Bt cotton; we need to first determine the frequency of the recessive allele r.
According to Hardy-Weinberg Equilibrium ;
p+q = 1
Let p = R and q = r
R + r = 1
0.01 + r = 1
r = 1 - 0.01
r = 0.99
Now; the frequency of the resistance allele after one generation can be calculated as :
[tex]q' = \dfrac{q(1-sq)}{1-(sq^2)}[/tex]
where ;
q' = R
q = r
[tex]q' = \dfrac{0.99(1-(0.05 \times 0.99))}{1-(0.05 \times 0.99^2)}[/tex]
[tex]q' = \dfrac{0.99(0.9505)}{1-(0.049005)}[/tex]
[tex]q' = \dfrac{0.940995}{0.950995}[/tex]
q' = 0.989
Thus; the frequency of the resistant allele after one generation is 0.989
