Answer :
To find the frequency of the recessive allele, we need to analyze the given data about the chicken population and apply our understanding of genetic principles related to dominant and recessive traits. Here is the step-by-step breakdown of the solution:
1. Breakdown of the Population:
- There are 85 chickens homozygous for the dominant trait (let's denote it as [tex]\( RR \)[/tex]).
- 30 of these dominant chickens are actually heterozygous (i.e., having both the dominant and recessive alleles, denoted as [tex]\( Rr \)[/tex]).
- There are 25 chickens exhibiting the recessive trait (which means they are homozygous recessive, denoted as [tex]\( rr \)[/tex]).
2. Determine the Number of Each Genotype:
- Homozygous dominant ([tex]\( RR \)[/tex]): Since the part claims that 30 chickens are heterozygous ([tex]\( Rr \)[/tex]), the number of chickens truly homozygous dominant is [tex]\( 85 - 30 = 55 \)[/tex].
3. Compute the Total Number of Each Allele:
- Homozygous dominant ([tex]\( RR \)[/tex]) contributes two [tex]\( R \)[/tex] alleles per chicken.
The number of [tex]\( R \)[/tex] alleles from [tex]\( RR \)[/tex] chickens:
[tex]\( 55 \times 2 = 110 \)[/tex].
- Heterozygous dominant ([tex]\( Rr \)[/tex]) contributes one [tex]\( R \)[/tex] allele and one [tex]\( r \)[/tex] allele per chicken.
The number of [tex]\( R \)[/tex] alleles from [tex]\( Rr \)[/tex] chickens:
[tex]\( 30 \times 1 = 30 \)[/tex].
- The number of [tex]\( r \)[/tex] alleles from [tex]\( Rr \)[/tex] chickens:
[tex]\( 30 \times 1 = 30 \)[/tex].
- Homozygous recessive ([tex]\( rr \)[/tex]) contributes two [tex]\( r \)[/tex] alleles per chicken.
The number of [tex]\( r \)[/tex] alleles from [tex]\( rr \)[/tex] chickens:
[tex]\( 25 \times 2 = 50 \)[/tex].
4. Sum of the Alleles in Population:
- Total number of [tex]\( R \)[/tex] alleles:
[tex]\( 110 + 30 = 140 \)[/tex].
- Total number of [tex]\( r \)[/tex] alleles:
[tex]\( 30 + 50 = 80 \)[/tex].
5. Total Number of Alleles in the Population:
- Adding [tex]\( R \)[/tex] and [tex]\( r \)[/tex] alleles together:
[tex]\( 140 + 80 = 220 \)[/tex].
6. Frequency of the Recessive Allele ([tex]\( r \)[/tex]):
- The frequency is calculated as the number of [tex]\( r \)[/tex] alleles divided by the total number of alleles.
The frequency is [tex]\( \frac{80}{220} \)[/tex].
7. Simplify the Frequency:
- Simplify [tex]\( \frac{80}{220} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[ \frac{80}{220} = \frac{80 \div 20}{220 \div 20} = \frac{4}{11} \][/tex]
When presented with the given choices, while none are expressed in this exact simplified fraction, the closest corresponding fraction that simplifies to [tex]\(\frac{80}{220}\)[/tex] before reducing is:
B. [tex]\(\frac{80}{200}\)[/tex]
However, this is an error as [tex]\(\frac{80}{220}\)[/tex] simplifies to [tex]\(\approx 0.36\)[/tex], not directly representing [tex]\(\frac{80}{200}\)[/tex].
Therefore based on the simplistic options:
The closest simplified value can be matched with:
E. [tex]\(\frac{120}{200}\)[/tex]
Accuracy is important but the mathematical straightforward calculation is for [tex]\(\frac{80}{220}\)[/tex] that exactly determines the frequency to 0.36. Thus consistent option reflected correctly is similar to given simplified about closest measure provided here.
1. Breakdown of the Population:
- There are 85 chickens homozygous for the dominant trait (let's denote it as [tex]\( RR \)[/tex]).
- 30 of these dominant chickens are actually heterozygous (i.e., having both the dominant and recessive alleles, denoted as [tex]\( Rr \)[/tex]).
- There are 25 chickens exhibiting the recessive trait (which means they are homozygous recessive, denoted as [tex]\( rr \)[/tex]).
2. Determine the Number of Each Genotype:
- Homozygous dominant ([tex]\( RR \)[/tex]): Since the part claims that 30 chickens are heterozygous ([tex]\( Rr \)[/tex]), the number of chickens truly homozygous dominant is [tex]\( 85 - 30 = 55 \)[/tex].
3. Compute the Total Number of Each Allele:
- Homozygous dominant ([tex]\( RR \)[/tex]) contributes two [tex]\( R \)[/tex] alleles per chicken.
The number of [tex]\( R \)[/tex] alleles from [tex]\( RR \)[/tex] chickens:
[tex]\( 55 \times 2 = 110 \)[/tex].
- Heterozygous dominant ([tex]\( Rr \)[/tex]) contributes one [tex]\( R \)[/tex] allele and one [tex]\( r \)[/tex] allele per chicken.
The number of [tex]\( R \)[/tex] alleles from [tex]\( Rr \)[/tex] chickens:
[tex]\( 30 \times 1 = 30 \)[/tex].
- The number of [tex]\( r \)[/tex] alleles from [tex]\( Rr \)[/tex] chickens:
[tex]\( 30 \times 1 = 30 \)[/tex].
- Homozygous recessive ([tex]\( rr \)[/tex]) contributes two [tex]\( r \)[/tex] alleles per chicken.
The number of [tex]\( r \)[/tex] alleles from [tex]\( rr \)[/tex] chickens:
[tex]\( 25 \times 2 = 50 \)[/tex].
4. Sum of the Alleles in Population:
- Total number of [tex]\( R \)[/tex] alleles:
[tex]\( 110 + 30 = 140 \)[/tex].
- Total number of [tex]\( r \)[/tex] alleles:
[tex]\( 30 + 50 = 80 \)[/tex].
5. Total Number of Alleles in the Population:
- Adding [tex]\( R \)[/tex] and [tex]\( r \)[/tex] alleles together:
[tex]\( 140 + 80 = 220 \)[/tex].
6. Frequency of the Recessive Allele ([tex]\( r \)[/tex]):
- The frequency is calculated as the number of [tex]\( r \)[/tex] alleles divided by the total number of alleles.
The frequency is [tex]\( \frac{80}{220} \)[/tex].
7. Simplify the Frequency:
- Simplify [tex]\( \frac{80}{220} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[ \frac{80}{220} = \frac{80 \div 20}{220 \div 20} = \frac{4}{11} \][/tex]
When presented with the given choices, while none are expressed in this exact simplified fraction, the closest corresponding fraction that simplifies to [tex]\(\frac{80}{220}\)[/tex] before reducing is:
B. [tex]\(\frac{80}{200}\)[/tex]
However, this is an error as [tex]\(\frac{80}{220}\)[/tex] simplifies to [tex]\(\approx 0.36\)[/tex], not directly representing [tex]\(\frac{80}{200}\)[/tex].
Therefore based on the simplistic options:
The closest simplified value can be matched with:
E. [tex]\(\frac{120}{200}\)[/tex]
Accuracy is important but the mathematical straightforward calculation is for [tex]\(\frac{80}{220}\)[/tex] that exactly determines the frequency to 0.36. Thus consistent option reflected correctly is similar to given simplified about closest measure provided here.
