Question

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?

Short answer

Answer: After one generation of feeding on Bt corn, the frequency of the resistance allele "B" in the corn borer population is approximately 0.1736 or 17.36%.

Step-by-step solution

Identify the initial allele frequencies

The problem states that the initial frequency of the resistance allele 'B' is 0.02. Since the 'B' allele is dominant, we are given that 10% of corn borer larvae survive if they have at least one copy of this allele. The remaining 90% of the larvae that do not have the resistance allele die off. Let 'b' represent the non-resistant allele. Given that there are only two alleles in the population, the frequency of the non-resistant allele 'b' is 1 - 0.02 = 0.98.

Determine initial genotype frequencies using Hardy-Weinberg principle

According to the Hardy-Weinberg principle, the genotype frequencies can be found using the equation: \(p^2 + 2pq + q^2 = 1\), where p represents the frequency of one allele and q represents the frequency of the other allele. In our case, p = B and q = b. \(BB\) frequency = \((0.02)^2 = 0.0004\) \(Bb\) frequency = \(2(0.02)(0.98) = 0.0392\) \(bb\) frequency = \((0.98)^2 = 0.9604\)

Evaluate the next generation's allele frequency after the selective pressure

In the next generation, only 10% of the non-resistant larvae (\(bb\)) survive after feeding on the Bt corn. So the new frequency of \(bb\) genotype is reduced to 10% of its initial value, which is 0.1 × 0.9604 = 0.09604. Now we can update the genotype frequencies to account for the selection pressure: New \(BB\) frequency = 0.0004 New \(Bb\) frequency = 0.0392 New \(bb\) frequency = 0.09604 The total frequencies should still sum up to 1, so we can normalize the frequencies: Normalized \(BB\) frequency = \(\frac{0.0004}{0.0004 + 0.0392 + 0.09604} = 0.0035\) Normalized \(Bb\) frequency = \(\frac{0.0392}{0.0004 + 0.0392 + 0.09604} = 0.3402\) Normalized \(bb\) frequency = \(\frac{0.09604}{0.0004 + 0.0392 + 0.09604} = 0.6563\)

Calculate the frequency of allele 'B' after selection

To find the frequency of resistance allele 'B' after one generation, we can use the genotype frequencies as follows: New 'B' frequency = (2 * Normalized \(BB\) frequency + Normalized \(Bb\) frequency) / 2 = \((2*0.0035+0.3402)/2 = 0.1736\) So, after one generation of corn borers feeding on Bt corn, the frequency of resistance allele 'B' in the population will be around 0.1736 or 17.36%.

Key concepts

Hardy-Weinberg Equilibrium

Every population with organisms that have two alleles can be analyzed using the Hardy-Weinberg Equilibrium principle. This principle is a mathematical model used to study genetic variation in populations that are not influenced by external forces.
It serves as a null hypothesis indicating a perfect situation where allele frequencies are stable over time, meaning there is no evolution happening.
The Hardy-Weinberg Equation is given by:

• \(p^2 + 2pq + q^2 = 1\)

Here, \(p\) and \(q\) represent the frequencies of the two alleles, say 'A' and 'a'.
The terms \(p^2\), \(2pq\), and \(q^2\) represent the respective frequencies of the genotypes \(AA\), \(Aa\), and \(aa\).
Conditions like random mating, no mutation, no migration, infinite population size, and no selection must be met for a population to be in Hardy-Weinberg Equilibrium.
This concept allows scientists to understand the genetic structure of populations and predict how it may change under different environmental pressures.

Genetic Resistance

Genetic resistance is a crucial concept, especially in agriculture, where organisms develop resistance to certain chemicals or treatments over time.
In the context of genetically modified crops like Bt corn, genetic resistance refers to the ability of pests to survive despite the presence of an insecticide produced by the plant.
It occurs when individuals in the pest population have a resistance allele, allowing them to survive the insecticide while others perish. Over time, these individuals reproduce, passing the resistance allele to the next generation and increasing its frequency.
In our example, only corn borer larvae with the dominant resistance allele 'B' survive, leading to a scenario where natural selection favors these individuals.
This process demonstrates how genetic resistance can evolve rapidly, shifting the dynamics of pest control in agricultural environments. It's vital to monitor allele frequencies to manage resistance effectively.

Allele Frequency

Allele frequency is a fundamental concept in population genetics.
It refers to how common an allele is within a population, expressed as a proportion or percentage.
Calculating allele frequencies allows researchers to infer genetic diversity and understand evolutionary pressures.
In our problem, we began with a resistance allele 'B' frequency of 0.02, indicating that 2% of the alleles in the population were resistant to the Bt insecticide.
After one generation and selective pressure from the insecticide, the frequency of the 'B' allele increased significantly, reaching approximately 0.1736 or 17.36%.
This dramatic shift highlights how quickly allele frequencies can change under strong selective pressures.
Understanding allele frequencies helps in making predictions about the future genetic composition of populations, providing insights into evolutionary processes.

Transgenic Crops

Transgenic crops are plants that have had genes inserted from another species to install new traits, such as pest resistance or herbicide tolerance.
Bt corn is a well-known example, designed to produce an insecticide specifically targeting corn borers.
Creating transgenic crops involves biotechnology techniques like gene splicing. These crops offer significant advantages:

• Reduction in chemical pesticide use
• Increased crop yields
• Better pest management

However, the introduction of transgenic crops also raises concerns.
A critical issue is the potential for pests, like corn borers, to develop resistance to the introduced traits, as seen in the resistance allele 'B'.
Strategies such as planting non-Bt refuges are often used to manage resistance development and prolong the effectiveness of transgenic crops.
Understanding both the benefits and risks associated with transgenic crops is essential for sustainable agricultural practices.