Question

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 unless they have at least one copy of the dominant resistance allele R that confers resistance to the Bt insecticide. When the farmer first plants Bt cotton, the frequency of the R allele in the cotton bollworm population is 0.01. What will the frequency of the resistance allele be after one generation of cotton bollworms fed on Bt cotton [answer]

Answer 1

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 :

$q' = \dfrac{q(1-sq)}{1-(sq^2)}$

where ;

q' = R

q = r

$q' = \dfrac{0.99(1-(0.05 \times 0.99))}{1-(0.05 \times 0.99^2)}$

$q' = \dfrac{0.99(0.9505)}{1-(0.049005)}$

$q' = \dfrac{0.940995}{0.950995}$

q' = 0.989

Thus; the frequency of the resistant allele after one generation is 0.989