Assume that the flower population described in the previous problem undergoes a different pattern of predation. Flower-color determination and the starting frequencies of C₁ and C₂ are as described above, but the new insects attack yellow and red flowers, not orange flowers. As a result of the predation pattern, the relative fitness values are C₁C₁ = 0.40, C₁C₂ = 1.0, and C₂C₂ = 0.80.
What are the equilibrium allele frequencies in the predation environment?

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the equilibrium allele frequencies (C₁ and C₂) under the given predation environment. The relative fitness values for the genotypes are provided: C₁C₁ = 0.40, C₁C₂ = 1.0, and C₂C₂ = 0.80.
2. Step 2: Recall the concept of equilibrium allele frequencies. At equilibrium, the allele frequencies remain constant over generations because the forces of selection balance out. This involves using the fitness values and solving for the allele frequencies that satisfy the Hardy-Weinberg principle under selection.
3. Step 3: Write the equation for the mean fitness (w̄) of the population. The mean fitness is calculated as: $w̄\; =\; p²w₁₁\; +\; 2pqw₁₂\; +\; q²w₂₂$, where p is the frequency of allele C₁, q is the frequency of allele C₂ (q = 1 - p), and w₁₁, w₁₂, and w₂₂ are the fitness values for C₁C₁, C₁C₂, and C₂C₂ respectively.
4. Step 4: Derive the change in allele frequency due to selection. Use the equation: $\Delta p\; =\; p(1\; -\; p)(w̄₁\; -\; w̄₂)/w̄$, where w̄₁ and w̄₂ are the average fitness contributions of alleles C₁ and C₂. At equilibrium, Δp = 0, which allows us to solve for the equilibrium frequencies.
5. Step 5: Solve for the equilibrium frequencies. Substitute the fitness values (w₁₁ = 0.40, w₁₂ = 1.0, w₂₂ = 0.80) into the equations derived in Steps 3 and 4. Use algebraic methods to find the values of p and q that satisfy the equilibrium condition. These values represent the equilibrium allele frequencies in the given predation environment.

Key Concepts

Allele Frequency

Allele frequency refers to how often a particular allele appears in a population relative to other alleles for the same gene. It is a key measure in population genetics, indicating the genetic diversity and evolutionary potential of a population. Understanding allele frequencies is crucial for predicting how traits may change over generations, especially under selective pressures like predation.

Relative Fitness

Relative fitness is a measure of the reproductive success of a genotype compared to others in the population. It is expressed as a value that indicates how well a particular genotype can survive and reproduce in a given environment. In this scenario, the relative fitness values for different flower color genotypes help determine which alleles will increase or decrease in frequency due to predation.

Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium is a principle that describes the genetic variation in a population that is not evolving. It provides a baseline to compare actual allele frequencies against expected frequencies under certain conditions, such as no selection, mutation, migration, or genetic drift. In the context of this question, understanding how predation affects allele frequencies can help determine if the population is in equilibrium or undergoing evolutionary change.