Select the correct answer.

In a particular species of frogs, black spots are a dominant trait and their absence is a recessive trait. In a population of frogs, 50 are homozygous for the dominant trait, 34 are heterozygous dominant, and 16 show the recessive trait. Which expression is the correct way to calculate the frequency of the dominant allele?

A. [tex][tex]$\frac{50}{100}$[/tex][/tex]
B. [tex][tex]$\frac{84}{100}$[/tex][/tex]
C. [tex][tex]$\frac{50}{200}$[/tex][/tex]
D. [tex][tex]$\frac{134}{200}$[/tex][/tex]
E. [tex][tex]$\frac{100}{200}$[/tex][/tex]



Answer :

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]