To solve this problem, we need to determine the frequency of the dominant allele in the population.
First, let's identify the genotypes and their corresponding alleles:
1. Homozygous dominant (AA): These individuals have two dominant alleles (A).
2. Heterozygous dominant (Aa): These individuals have one dominant allele (A) and one recessive allele (a).
3. Homozygous recessive (aa): These individuals have two recessive alleles (a).
Given:
- There are 50 frogs that are homozygous dominant (AA).
- There are 34 frogs that are heterozygous dominant (Aa).
- There are 16 frogs that are homozygous recessive (aa).
Next, calculate the total population of frogs:
[tex]\[ 50 \, (\text{AA}) + 34 \, (\text{Aa}) + 16 \, (\text{aa}) = 100 \, (\text{total frogs}) \][/tex]
Now, we calculate the number of dominant alleles (A) in the population:
- Each homozygous dominant (AA) frog contributes 2 A alleles, so:
[tex]\[ 50 \times 2 = 100 \, (\text{A alleles from homozygous dominant}) \][/tex]
- Each heterozygous dominant (Aa) frog contributes 1 A allele, so:
[tex]\[ 34 \times 1 = 34 \, (\text{A alleles from heterozygous dominant}) \][/tex]
Adding these together gives the total number of dominant alleles:
[tex]\[ 100 + 34 = 134 \, (\text{total A alleles}) \][/tex]
To find the total number of alleles in the population, we multiply the total number of frogs by 2 (since each frog has two alleles):
[tex]\[ 100 \times 2 = 200 \, (\text{total alleles}) \][/tex]
Finally, the frequency of the dominant allele (A) is calculated by dividing the total number of A alleles by the total number of alleles:
[tex]\[ \frac{134}{200} \][/tex]
Therefore, the correct expression to calculate the frequency of the dominant allele is:
[tex]\[ \boxed{\frac{134}{200}} \][/tex]
Thus, the correct answer is:
[tex]\[ D. \frac{134}{200} \][/tex]
