To determine the frequency of the dominant allele in this population, we follow these steps:
1. Understanding Allele Frequency:
- The frequency of an allele in a population can be determined by counting the total number of that allele and then dividing by the total number of all alleles for the trait.
2. Identifying Genotypes:
- Homozygous dominant individuals (let's denote them as [tex]\(AA\)[/tex]) have two dominant alleles.
- Heterozygous dominant individuals (denoted as [tex]\(Aa\)[/tex]) have one dominant allele and one recessive allele.
- Recessive individuals (denoted as [tex]\(aa\)[/tex]) have two recessive alleles.
3. Counting Dominant Alleles:
- Each of the 50 homozygous dominant frogs contributes 2 dominant alleles. Therefore, the number of dominant alleles from homozygous dominant individuals is [tex]\(50 \times 2 = 100\)[/tex].
- Each of the 34 heterozygous frogs contributes 1 dominant allele. Therefore, the number of dominant alleles from heterozygous individuals is [tex]\(34 \times 1 = 34\)[/tex].
Combining these, the total number of dominant alleles is:
[tex]\[
100 + 34 = 134
\][/tex]
4. Counting Total Alleles:
- Each frog, regardless of genotype, contributes 2 alleles (one from each parent). With 100 frogs in total (50 homozygous dominant + 34 heterozygous + 16 recessive), the total number of alleles is:
[tex]\[
100 \times 2 = 200
\][/tex]
5. Calculating 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. This is expressed as:
[tex]\[
\frac{\text{Number of dominant alleles}}{\text{Total number of alleles}} = \frac{134}{200}
\][/tex]
Therefore, the correct answer is:
D. [tex]\(\frac{134}{200}\)[/tex]
