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In chickens, a flat single comb is a recessive trait, while the short, thick rose comb is dominant. In a particular population of chickens, 45 are homozygous for the dominant trait, 30 are heterozygous dominant, and 25 have the recessive trait. Which expression is the correct way to calculate the frequency of the recessive allele?
A. [tex]$\frac{80}{100}$[/tex] B. [tex]$\frac{80}{200}$[/tex] C. [tex]$\frac{55}{100}$[/tex] D. [tex]$\frac{55}{200}$[/tex] E. [tex]$\frac{120}{200}$[/tex]
2. Calculate the Total Number of Chickens: Adding together all the chickens: [tex]\[
\text{Total Chickens} = 45 (\text{Homozygous Dominant}) + 30 (\text{Heterozygous Dominant}) + 25 (\text{Recessive Trait}) = 100
\][/tex]
3. Calculate the Total Number of Alleles: Each chicken has two alleles, so: [tex]\[
\text{Total Alleles} = 2 \times \text{Total Chickens} = 2 \times 100 = 200
\][/tex]
4. Calculate the Number of Recessive Alleles: - Homozygous Dominant (RR) contributes 0 recessive alleles. - Heterozygous (Rr) contributes 1 recessive allele per chicken. - Homozygous Recessive (rr) contributes 2 recessive alleles per chicken.
5. Calculate the Frequency of the Recessive Allele (q): The frequency of an allele is the number of that type of allele divided by the total number of alleles. [tex]\[
\text{Frequency of Recessive Allele} = \frac{\text{Number of Recessive Alleles}}{\text{Total Number of Alleles}} = \frac{80}{200}
\][/tex]
6. Match the Frequency to the Given Choices: Let’s look at the provided options: - A. [tex]\(\frac{80}{100}\)[/tex] - B. [tex]\(\frac{80}{200}\)[/tex] - C. [tex]\(\frac{55}{100}\)[/tex] - D. [tex]\(\frac{55}{200}\)[/tex] - E. [tex]\(\frac{120}{200}\)[/tex]
The correct frequency of the recessive allele, as calculated, matches option B: [tex]\(\frac{80}{200}\)[/tex].
Therefore, the correct answer is: [tex]\[
\boxed{B}
\][/tex]
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