Question

The following genotypes are found in a population: AA/35, Aa/25, and aa/10. What are the allele frequencies of A and a ?

• A. A = 0.32, and a = 0.68
• B. A = 0.36, and a = 0.63
• C. A = 0.68, and a = 0.32
• D. A = 0.63, and a = 0.36

Hint:

To quickly double-check your calculations, always ensure that $p + q = 1$. This simple step helps eliminate options where the sum of the two allele frequencies is not equal to 1.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Allele frequency represents the proportion of a specific allele among all the alleles of that gene present in a population.
For diploid organisms, each individual carries two alleles for any given autosomal locus.
Key Formula or Approach:
The total number of alleles in a population is equal to twice the total number of individuals ($2N$).
The frequency of allele $A$ ($p$) and allele $a$ ($q$) can be calculated using:
\[ p = \frac{2 \times N_{AA} + N_{Aa}}{2N} \]
\[ q = \frac{2 \times N_{aa} + N_{Aa}}{2N} \]

Step 2: Detailed Explanation:
Let us extract the genotype counts from the problem:
- Homozygous dominant ($N_{AA}$) = $35$
- Heterozygous ($N_{Aa}$) = $25$
- Homozygous recessive ($N_{aa}$) = $10$
Calculate the total number of individuals ($N$):
\[ N = 35 + 25 + 10 = 70 \text{ individuals} \]
The total number of alleles in this population is:
\[ 2N = 2 \times 70 = 140 \text{ alleles} \]
Now, calculate the total number of $A$ alleles:
\[ \text{Total } A \text{ alleles} = (2 \times 35) + 25 = 70 + 25 = 95 \text{ alleles} \]
Calculate the frequency of $A$ ($p$):
\[ p = \frac{95}{140} \approx 0.678 \approx 0.68 \]
Now, calculate the total number of $a$ alleles:
\[ \text{Total } a \text{ alleles} = (2 \times 10) + 25 = 20 + 25 = 45 \text{ alleles} \]
Calculate the frequency of $a$ ($q$):
\[ q = \frac{45}{140} \approx 0.321 \approx 0.32 \]
As a consistency check, we verify that the frequencies sum to $1$:
\[ p + q = 0.68 + 0.32 = 1.00 \]

Step 3: Final Answer:
The allele frequencies are $A = 0.68$ and $a = 0.32$, corresponding to option (C).