In a population of 100 rabbits 40 are short eared. Short ears are recessive to long ears. There are only two alleles for this gene. Long eared are 60 which are in 1:1 ratio of homozygous and heterozygous. Find out the dominant allelic frequency?.

Options

A. 0.55
B. 0.45
C. 0.09
D. 0.37

Answer

To find the dominant allelic frequency in the given population of rabbits, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Total population of rabbits = 100
- Number of short-eared rabbits (recessive trait) = 40
- Number of long-eared rabbits (dominant trait) = 60
- Short ears are recessive to long ears.

2. **Determine the Frequency of the Recessive Trait:**
- The frequency of short-eared rabbits (recessive trait) can be calculated as:
\[ \text{Frequency of short-eared rabbits (q²)} = \frac{\text{Number of short-eared rabbits}}{\text{Total population}} = \frac{40}{100} = 0.4 \]

3. **Calculate the Frequency of the Recessive Allele (q):**
- To find the frequency of the recessive allele (q), we take the square root of q²:
\[ q = \sqrt{q²} = \sqrt{0.4} \approx 0.6325 \]

4. **Use the Hardy-Weinberg Principle to Find the Frequency of the Dominant Allele (p):**
- According to the Hardy-Weinberg principle, the sum of the frequencies of the dominant allele (p) and the recessive allele (q) is equal to 1:
\[ p + q = 1 \]
- Rearranging this gives us:
\[ p = 1 - q \]
- Substituting the value of q:
\[ p = 1 - 0.6325 \approx 0.3675 \]

5. **Conclusion:**
- The frequency of the dominant allele (p) is approximately 0.37.

### Final Answer:
The dominant allelic frequency is **0.37**.

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