To find the correct expression to calculate the frequency of the dominant allele in this population of frogs, let’s follow these steps carefully:
1. Identify the number of frogs with each genotype:
- Homozygous dominant (AA): 50 frogs
- Heterozygous dominant (Aa): 34 frogs
- Homozygous recessive (aa): 16 frogs
2. Calculate the total number of frogs:
Given the numbers, the total population of frogs is:
[tex]\[
50 \, (\text{homozygous dominant}) + 34 \, (\text{heterozygous dominant}) + 16 \, (\text{homozygous recessive}) = 100 \, \text{frogs}
\][/tex]
3. Determine the number of dominant alleles:
Each homozygous dominant frog (AA) contributes 2 dominant alleles.
Each heterozygous dominant frog (Aa) contributes 1 dominant allele.
Homozygous recessive frogs (aa) do not contribute any dominant alleles.
Therefore, the number of dominant alleles is calculated as:
[tex]\[
(50 \, \text{homozygous dominant frogs} \times 2 \, \text{dominant alleles per frog}) + (34 \, \text{heterozygous dominant frogs} \times 1 \, \text{dominant allele per frog})
\][/tex]
[tex]\[
= 50 \times 2 + 34 \times 1 = 100 + 34 = 134
\][/tex]
4. Calculate the total number of alleles:
Since every frog has 2 alleles (one from each parent), the total number of alleles in the population is:
[tex]\[
100 \, \text{frogs} \times 2 \, \text{alleles per frog} = 200 \, \text{alleles}
\][/tex]
5. Calculate the frequency of the dominant allele:
The frequency of the dominant allele is the ratio of the number of dominant alleles to the total number of alleles. Thus, the frequency of the dominant allele is:
[tex]\[
\frac{\text{number of dominant alleles}}{\text{total number of alleles}} = \frac{134}{200}
\][/tex]
Therefore, the correct answer is:
[tex]\[ D. \frac{134}{200} \][/tex]
