Let's walk through the process of determining the frequency of the recessive allele based on the given chicken population data.
1. Determine the total number of chickens:
We have:
- Homozygous dominant (RR) chickens: 45
- Heterozygous dominant (Rr) chickens: 30
- Recessive (rr) chickens: 25
The total number of chickens is:
[tex]\[
45 + 30 + 25 = 100
\][/tex]
2. Calculate the total number of alleles in the population:
Each chicken has 2 alleles (since they are diploid organisms). Therefore, the total number of alleles is:
[tex]\[
2 \times 100 = 200
\][/tex]
3. Count the number of recessive alleles (r):
- Each recessive (rr) chicken contributes 2 recessive alleles:
[tex]\[
25 \times 2 = 50
\][/tex]
- Each heterozygous dominant (Rr) chicken contributes 1 recessive allele:
[tex]\[
30 \times 1 = 30
\][/tex]
Adding these together, the total number of recessive alleles is:
[tex]\[
50 + 30 = 80
\][/tex]
4. Calculate the frequency of the recessive allele (q):
The frequency of the recessive allele can be found by dividing the total number of recessive alleles by the total number of alleles in the population:
[tex]\[
\frac{80}{200} = 0.4
\][/tex]
Given this information, the correct expression for calculating the frequency of the recessive allele from the provided options is:
[tex]\[
\text{Option D:} \quad \frac{80}{200}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{80}{200}}
\][/tex]
