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?

Answer 1

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.