A farmer plants transgenic Bt corn that is genetically modified to produce its own insecticide. Of the corn borer larvae feeding on these Bt crop plants, only 10 percent survive unless they have at least one copy of the dominant resistance allele B that confers resistance to the Bt insecticide. When the farmer first plants Bt corn, the frequency of the B resistance allele in the corn borer population is 0.02. What will be the frequency of the resistance allele after one generation of corn borers have fed on Bt corn?

Verified step by step guidance

1. Identify the initial allele frequencies: let the frequency of the resistance allele B be \(p = 0.02\), and the frequency of the susceptible allele b be \(q = 1 - p = 0.98\).
2. Calculate the genotype frequencies before selection using Hardy-Weinberg equilibrium: \(\text{freq}(BB) = p^2\), \(\text{freq}(Bb) = 2pq\), and \(\text{freq}(bb) = q^2\).
3. Apply the selection based on survival rates: individuals with at least one B allele (BB and Bb) survive at 100%, while bb individuals survive at 10%. Multiply each genotype frequency by its respective survival rate to get the post-selection genotype frequencies (unnormalized).
4. Normalize the post-selection genotype frequencies by dividing each by the total sum of the post-selection frequencies to ensure they sum to 1.
5. Calculate the new allele frequency \(p'\) of the resistance allele B after selection using the normalized genotype frequencies: \(p' = \text{freq}(BB) + \frac{1}{2} \times \text{freq}(Bb)\).

Key Concepts

Allele Frequency and Population Genetics

Allele frequency refers to how common a particular allele is in a population's gene pool. It is expressed as a proportion or percentage of all alleles for a specific gene. Changes in allele frequency over generations indicate evolutionary processes such as natural selection or genetic drift.

Natural Selection and Fitness

Natural selection is the process where individuals with advantageous traits have higher survival and reproduction rates. Fitness measures an organism's reproductive success. In this case, larvae with the resistance allele B have higher fitness on Bt corn, leading to increased frequency of B in the next generation.

Dominance and Genotype Fitness Effects

Dominance describes how alleles express in heterozygotes. Here, the resistance allele B is dominant, so individuals with one or two copies survive better. Understanding genotype-specific survival rates (e.g., BB, Bb, bb) is essential to calculate how allele frequencies change after selection.