Question
In a species of frogs, frogs that have at least one dominant allele “G” (dark green) have a dark green phenotype. The recessive allele “g” is for light green. In a population that is in Hardy Weinberg equilibrium, 88% of the frogs are dark green. Please use this information to solve the next 3 questions. Show all work. It is likely you will need a calculator. Solve all values in the space below first before answering the questions. G- dark green p^2 +2pq= .88 QUESTION 1: What is the allele frequency of the “G” allele? QUESTION 2: What percentage of the frog population is heterozygous? QUESTION 3: If this frog population had 20,000 frogs, how many of the frogs would be homozygous dominant?
Answers
Answered by
GPT-4o mini
To solve the questions based on the given information in a population of frogs that follows the Hardy-Weinberg equilibrium, we will use the Hardy-Weinberg equations. The two relevant equations are:
1. \( p^2 + 2pq + q^2 = 1 \) (where \( p^2 \) represents the frequency of homozygous dominant individuals, \( 2pq \) represents the frequency of heterozygous individuals, and \( q^2 \) represents the frequency of homozygous recessive individuals).
2. \( p + q = 1 \) (where \( p \) is the frequency of the dominant allele and \( q \) is the frequency of the recessive allele).
Given that 88% of frogs are dark green, we can represent this as:
\[
p^2 + 2pq = 0.88
\]
Since the remaining frogs would be light green (homozygous recessive), we have:
\[
q^2 = 1 - 0.88 = 0.12
\]
To find \( q \):
\[
q = \sqrt{0.12} \approx 0.3464
\]
Now, we can find \( p \):
\[
p = 1 - q = 1 - 0.3464 \approx 0.6536
\]
Now let's summarize our findings for answering the specific questions.
### QUESTION 1: What is the allele frequency of the “G” allele?
The allele frequency of the dominant allele \( G \) (denoted as \( p \)) is approximately:
\[
p \approx 0.6536 \text{ or } 65.36\%
\]
### QUESTION 2: What percentage of the frog population is heterozygous?
To find the percentage of the population that is heterozygous (\( 2pq \)), we calculate:
\[
2pq = 2 \times p \times q = 2 \times 0.6536 \times 0.3464 \approx 0.4538
\]
Thus, the percentage of the population that is heterozygous is approximately:
\[
2pq \approx 0.4538 \text{ or } 45.38\%
\]
### QUESTION 3: If this frog population had 20,000 frogs, how many of the frogs would be homozygous dominant?
To find the number of homozygous dominant frogs (\( p^2 \)), we first need to calculate \( p^2 \):
\[
p^2 = (0.6536)^2 \approx 0.4279
\]
Then we find the number of homozygous dominant frogs by multiplying \( p^2 \) by the total population of 20,000 frogs:
\[
\text{Number of homozygous dominant frogs} = p^2 \times \text{Total population} = 0.4279 \times 20000 \approx 8558
\]
### Summary of Answers
1. **Allele frequency of “G”:** Approximately 65.36%
2. **Percentage of heterozygous frogs:** Approximately 45.38%
3. **Number of homozygous dominant frogs in a population of 20,000:** Approximately 8558 frogs.
1. \( p^2 + 2pq + q^2 = 1 \) (where \( p^2 \) represents the frequency of homozygous dominant individuals, \( 2pq \) represents the frequency of heterozygous individuals, and \( q^2 \) represents the frequency of homozygous recessive individuals).
2. \( p + q = 1 \) (where \( p \) is the frequency of the dominant allele and \( q \) is the frequency of the recessive allele).
Given that 88% of frogs are dark green, we can represent this as:
\[
p^2 + 2pq = 0.88
\]
Since the remaining frogs would be light green (homozygous recessive), we have:
\[
q^2 = 1 - 0.88 = 0.12
\]
To find \( q \):
\[
q = \sqrt{0.12} \approx 0.3464
\]
Now, we can find \( p \):
\[
p = 1 - q = 1 - 0.3464 \approx 0.6536
\]
Now let's summarize our findings for answering the specific questions.
### QUESTION 1: What is the allele frequency of the “G” allele?
The allele frequency of the dominant allele \( G \) (denoted as \( p \)) is approximately:
\[
p \approx 0.6536 \text{ or } 65.36\%
\]
### QUESTION 2: What percentage of the frog population is heterozygous?
To find the percentage of the population that is heterozygous (\( 2pq \)), we calculate:
\[
2pq = 2 \times p \times q = 2 \times 0.6536 \times 0.3464 \approx 0.4538
\]
Thus, the percentage of the population that is heterozygous is approximately:
\[
2pq \approx 0.4538 \text{ or } 45.38\%
\]
### QUESTION 3: If this frog population had 20,000 frogs, how many of the frogs would be homozygous dominant?
To find the number of homozygous dominant frogs (\( p^2 \)), we first need to calculate \( p^2 \):
\[
p^2 = (0.6536)^2 \approx 0.4279
\]
Then we find the number of homozygous dominant frogs by multiplying \( p^2 \) by the total population of 20,000 frogs:
\[
\text{Number of homozygous dominant frogs} = p^2 \times \text{Total population} = 0.4279 \times 20000 \approx 8558
\]
### Summary of Answers
1. **Allele frequency of “G”:** Approximately 65.36%
2. **Percentage of heterozygous frogs:** Approximately 45.38%
3. **Number of homozygous dominant frogs in a population of 20,000:** Approximately 8558 frogs.