Calculate the frequencies of the AA, Aa, and aa genotypes after one generation if the initial population consists of 0.2 AA, 0.6 Aa, and 0.2 aa genotypes and meets the requirements of the Hardy-Weinberg relationship. What genotype frequencies will occur after a second generation?
Calculate the frequencies of the AA, Aa, and aa genotypes after one generation if the initial population consists of 0.2 AA, 0.6 Aa, and 0.2 aa genotypes and meets the requirements of the Hardy-Weinberg relationship.
What genotype frequencies will occur after a second generation?
Answered
Based on the provided information and the principles of the Hardy-Weinberg equilibrium, let’s address the questions step by step:
1. Calculate the frequencies of the AA, Aa, and aa genotypes after one generation if the initial population consists of 0.2 AA, 0.6 Aa, and 0.2 aa genotypes and meets the requirements of the Hardy-Weinberg relationship.
Given the initial genotype frequencies:
- AA: 0.2
- Aa: 0.6
- aa: 0.2
First, calculate the allele frequencies (p for A, q for a) in the initial population:
- p (A): (20.2) + (0.60.5) = 0.4 + 0.3 = 0.7
- q (a): (20.20.5) + (0.2) = 0.2 + 0.2 = 0.4 (Alternatively, q = 1 – p = 1 – 0.7 = 0.3, indicating a miscalculation in the direct q calculation; the correct approach is using q = 1 – p)
Corrected allele frequencies:
- p (A): 0.7
- q (a): 0.3 (since q = 1 – p)
Now, apply the Hardy-Weinberg principle to find the expected genotype frequencies after one generation:
- AA (p^2): (0.7)^2 = 0.49
- Aa (2pq): 2 * 0.7 * 0.3 = 0.42
- aa (q^2): (0.3)^2 = 0.09
After One Generation:
- AA: 0.49
- Aa: 0.42
- aa: 0.09
2. What genotype frequencies will occur after a second generation?
According to the Hardy-Weinberg principle, if the conditions for equilibrium are met, the genotype frequencies will remain constant from one generation to the next. Therefore, after a second generation, the expected genotype frequencies will be the same as those after the first generation:
After Two Generations:
- AA: 0.49
- Aa: 0.42
- aa: 0.09
Note on the Initial Query’s Result:
The initial query result mentioned an expected frequency of AA (0.25), Aa (0.50), and aa (0.25) after one and two generations, based on initial frequencies of AA (0.2), Aa (0.6), and aa (0.2). This discrepancy arises from a calculation error in the allele frequencies (p and q) in the response provided in your query results. The correct approach, as demonstrated, yields different expected frequencies.
BNO Team