A farmer plants Bt cotton that is genetically modified to produce its own insecticide. Of the cotton bollworms feeding on these Bt plants, only 8% 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 0.4. What will the frequency of the resistance allele be after one generation of cotton bollworms fed on Bt cotton

Hardy-Weinberg principle states that are used to calculate the genetic variation of a population at equilibrium.

The frequency of the resistance allele in the cotton bollworm is 0.6.

Hardy-Weinberg equation can be given as:

P² + 2PQ + Q² = 1

where,

P = dominant allele (R)

Q = recessive allele (r)

Frequency of R allele = 0.4

From the equation:

P + Q = 1

or,

Q = P - 1

Genetic frequency of the R allele  = P² = 0.4 x 0.4 = 0.16

Substituting the values:

Q = 1 - 0.4

Q = 0.6

Q² = 0.36

Thus, the frequency of the resistance allele will be 0.6.

To know more about the Hardy-Weinberg principle, refer to the following link:

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0.6

Explanation:

According to hardy-weinberg principle,

P2+2pq+q2=1

P+q=1

q=1-p

Given that Allele R frequency is 0.4

and p represent the dominant allele

P=0.4

P2=0.4^2 = 0.16 for genotypic frequency

Since p+q=1

q=1-p

where q stands for recessive allele r frequency and q2 stands for genotypic frequency for allele r

q= 1-0.4= 0.6

q2=0.6 ^2

q2=0.36