To determine the frequency of the recessive allele in a population where you have the number of individuals with different genotypes, you can follow a systematic approach.
Step 1: Identify the genotypes and their counts.
- Homozygous dominant (RR): 45 chickens
- Heterozygous (Rr): 30 chickens
- Homozygous recessive (rr): 25 chickens
Step 2: Calculate the total number of alleles in the population.
Each chicken has 2 alleles. To find the total number of alleles, multiply the total number of chickens by 2:
[tex]\[ \text{Total chickens} = 45 + 30 + 25 = 100 \][/tex]
[tex]\[ \text{Total alleles} = 100 \times 2 = 200 \][/tex]
Step 3: Calculate the number of recessive alleles (r).
- Homozygous recessive (rr) chickens have 2 recessive alleles each:
[tex]\[ 25 \times 2 = 50 \][/tex]
- Heterozygous (Rr) chickens have 1 recessive allele each:
[tex]\[ 30 \times 1 = 30 \][/tex]
So, the total number of recessive alleles (r) is:
[tex]\[ 50 (from rr) + 30 (from Rr) = 80 \][/tex]
Step 4: Calculate the frequency of the recessive allele (r).
The frequency of an allele is calculated by dividing the number of that allele by the total number of alleles in the population:
[tex]\[ \text{Frequency of } r = \frac{\text{Number of recessive alleles}}{\text{Total number of alleles}} \][/tex]
[tex]\[ \text{Frequency of } r = \frac{80}{200} = 0.4 \][/tex]
The expression that corresponds to this calculation is:
[tex]\[ \frac{53}{200} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{D. \frac{53}{200}} \][/tex]
