To find the correct expression to calculate the frequency of the dominant allele in a population of frogs, we need to follow these steps:
1. Identify the Number of Each Genotype:
- There are 50 frogs that are homozygous dominant (AA).
- There are 34 frogs that are heterozygous dominant (Aa).
- There are 16 frogs that show the recessive trait (aa).
2. Calculate the Total Population:
- Total population = (number of homozygous dominant frogs) + (number of heterozygous dominant frogs) + (number of recessive frogs).
- Total population = 50 + 34 + 16 = 100 frogs.
3. Determine the Total Number of Dominant Alleles:
- Homozygous dominant frogs have 2 dominant alleles each. Therefore, the total number of dominant alleles from homozygous dominant frogs is [tex]\(50 \times 2 = 100\)[/tex].
- Heterozygous dominant frogs have 1 dominant allele each. Therefore, the total number of dominant alleles from heterozygous dominant frogs is [tex]\(34 \times 1 = 34\)[/tex].
- Recessive frogs (aa) do not contribute any dominant alleles.
- Therefore, the total number of dominant alleles in the population is [tex]\(100 + 34 = 134\)[/tex].
4. Calculate the Total Number of Alleles in the Population:
- As each frog has 2 alleles, and there are 100 frogs, the total number of alleles in the population is [tex]\(100 \times 2 = 200\)[/tex].
5. Determine the Frequency of the Dominant Allele:
- The frequency of the dominant allele is given by the ratio of the total number of dominant alleles to the total number of alleles in the population.
- Frequency of the dominant allele = [tex]\(\frac{\text{Total number of dominant alleles}}{\text{Total number of alleles}}\)[/tex].
Thus, the expression to calculate the frequency of the dominant allele is [tex]\(\frac{134}{200}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D. \frac{134}{200}} \][/tex]
