The frequency of two alleles in a gene pool is 0.19 ( A) and 0.81 ( a) . Assume that the population is in Hardy-Weinberg equilibrium and
(a) Calculate the percentage of heterozygous individuals in the population.
(b) Calculate the percentage of homozygous recessive in the population .

Options

A. `60% and 40%`
B. `66% and 31%`
C. `40% and 60%`
D. `31% and 66%`

Answer

To solve the problem, we will use the Hardy-Weinberg principle, which provides a mathematical model for studying genetic variation in a population at equilibrium. The principle states that allele and genotype frequencies will remain constant from generation to generation in the absence of other evolutionary influences.

Given:
- Frequency of allele A (p) = 0.19
- Frequency of allele a (q) = 0.81

We know that:
- p + q = 1

### (a) Calculate the percentage of heterozygous individuals in the population.

1. **Identify the formula for heterozygous individuals (2pq)**:
- The frequency of heterozygous individuals (genotype Aa) in the population can be calculated using the formula:
\[ 2pq \]

2. **Substitute the values of p and q**:
- Here, \( p = 0.19 \) and \( q = 0.81 \):
\[ 2pq = 2 \times (0.19) \times (0.81) \]

3. **Calculate the value**:
- First, calculate \( 0.19 \times 0.81 \):
\[ 0.19 \times 0.81 = 0.1539 \]
- Now multiply by 2:
\[ 2 \times 0.1539 = 0.3078 \]

4. **Convert to percentage**:
- To convert the frequency to a percentage:
\[ 0.3078 \times 100 = 30.78\% \]
- Rounding gives approximately 31%.

### (b) Calculate the percentage of homozygous recessive individuals in the population.

1. **Identify the formula for homozygous recessive individuals (q²)**:
- The frequency of homozygous recessive individuals (genotype aa) can be calculated using the formula:
\[ q^2 \]

2. **Substitute the value of q**:
- Here, \( q = 0.81 \):
\[ q^2 = (0.81)^2 \]

3. **Calculate the value**:
- Calculate \( 0.81^2 \):
\[ 0.81 \times 0.81 = 0.6561 \]

4. **Convert to percentage**:
- To convert the frequency to a percentage:
\[ 0.6561 \times 100 = 65.61\% \]
- Rounding gives approximately 66%.

### Final Answers:
- (a) Percentage of heterozygous individuals: **31%**
- (b) Percentage of homozygous recessive individuals: **66%**