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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]\(\frac{50}{100}\)[/tex]

B. [tex]\(\frac{84}{100}\)[/tex]

C. [tex]\(\frac{50}{200}\)[/tex]

D. [tex]\(\frac{134}{200}\)[/tex]

E. [tex]\(\frac{100}{200}\)[/tex]



Answer :

Let's calculate the frequency of the dominant allele step by step.

1. Identify the different types of frogs and their contributions to the total alleles:
- Homozygous dominant frogs (AA): 50 individuals
- Heterozygous dominant frogs (Aa): 34 individuals
- Recessive homozygous frogs (aa): 16 individuals

2. Calculate the total number of frogs:
[tex]\[ \text{Total number of frogs} = 50 + 34 + 16 = 100 \][/tex]

3. Calculate the total number of alleles in the population:
Each frog has 2 alleles, so:
[tex]\[ \text{Total alleles} = 100 \times 2 = 200 \][/tex]

4. Calculate the number of dominant alleles contributed by each genotype:
- Homozygous dominant (AA) frogs have 2 dominant alleles each:
[tex]\[ \text{Dominant alleles from homozygous dominant} = 50 \times 2 = 100 \][/tex]
- Heterozygous dominant (Aa) frogs have 1 dominant allele each:
[tex]\[ \text{Dominant alleles from heterozygous dominant} = 34 \times 1 = 34 \][/tex]

5. Calculate the total number of dominant alleles:
[tex]\[ \text{Total dominant alleles} = 100 + 34 = 134 \][/tex]

6. Calculate the frequency of the dominant allele:
[tex]\[ \text{Frequency of the dominant allele} = \frac{\text{Total dominant alleles}}{\text{Total alleles}} = \frac{134}{200} \][/tex]

The option that corresponds to this calculation is:
[tex]\[ \boxed{D} \][/tex]
Therefore, the correct expression for the frequency of the dominant allele is:
[tex]\[ \frac{134}{200} \][/tex]