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Answer :
Sure! Let's solve the problem step by step using the given data.
### Step-by-Step Solution:
1. Determine the total number of birds:
- Red tail feathers: 16
- Blue tail feathers: 34
- Total birds: [tex]\(16 + 34 = 50\)[/tex]
2. Calculate the frequency of the blue allele:
We're given that blue tail feathers are the dominant trait. Therefore, the blue tail feather (dominant allele) contributes to a larger proportion.
[tex]\[
\text{Frequency of blue allele} = \frac{\text{Number of blue tail birds}}{\text{Total number of birds}} = \frac{34}{50} = 0.68
\][/tex]
3. Calculate the frequency of the red allele:
Since there are only two alleles (blue and red), their frequencies must sum to 1.
[tex]\[
\text{Frequency of red allele} = 1 - \text{Frequency of blue allele} = 1 - 0.68 = 0.32
\][/tex]
4. Calculate the frequency of heterozygotes (2pq):
The term "heterozygote" refers to individuals with one copy of each allele (blue and red).
[tex]\[
\text{Frequency of heterozygotes} = 2pq = 2 \times \text{Frequency of blue allele} \times \text{Frequency of red allele} = 2 \times 0.68 \times 0.32 = 0.4352
\][/tex]
5. Calculate the frequency of birds homozygous for the blue allele (p²):
Homozygous blue means that both alleles are blue.
[tex]\[
\text{Frequency of homozygous blue} = p^2 = (\text{Frequency of blue allele})^2 = 0.68^2 = 0.4624
\][/tex]
### Summary:
- Frequency of the red allele: 0.32
- Frequency of the blue allele: 0.68
- Frequency of heterozygotes (2pq): 0.4352
- Frequency of birds homozygous for the blue allele (p²): 0.4624
I hope this helps you understand how to calculate allele frequencies and the frequencies of different genotypes in a population! If you have any more questions, feel free to ask.
### Step-by-Step Solution:
1. Determine the total number of birds:
- Red tail feathers: 16
- Blue tail feathers: 34
- Total birds: [tex]\(16 + 34 = 50\)[/tex]
2. Calculate the frequency of the blue allele:
We're given that blue tail feathers are the dominant trait. Therefore, the blue tail feather (dominant allele) contributes to a larger proportion.
[tex]\[
\text{Frequency of blue allele} = \frac{\text{Number of blue tail birds}}{\text{Total number of birds}} = \frac{34}{50} = 0.68
\][/tex]
3. Calculate the frequency of the red allele:
Since there are only two alleles (blue and red), their frequencies must sum to 1.
[tex]\[
\text{Frequency of red allele} = 1 - \text{Frequency of blue allele} = 1 - 0.68 = 0.32
\][/tex]
4. Calculate the frequency of heterozygotes (2pq):
The term "heterozygote" refers to individuals with one copy of each allele (blue and red).
[tex]\[
\text{Frequency of heterozygotes} = 2pq = 2 \times \text{Frequency of blue allele} \times \text{Frequency of red allele} = 2 \times 0.68 \times 0.32 = 0.4352
\][/tex]
5. Calculate the frequency of birds homozygous for the blue allele (p²):
Homozygous blue means that both alleles are blue.
[tex]\[
\text{Frequency of homozygous blue} = p^2 = (\text{Frequency of blue allele})^2 = 0.68^2 = 0.4624
\][/tex]
### Summary:
- Frequency of the red allele: 0.32
- Frequency of the blue allele: 0.68
- Frequency of heterozygotes (2pq): 0.4352
- Frequency of birds homozygous for the blue allele (p²): 0.4624
I hope this helps you understand how to calculate allele frequencies and the frequencies of different genotypes in a population! If you have any more questions, feel free to ask.
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