In a population of 1000 individuals , 500 individuals have Aa genotype and 500 have AA genotype. What will be the proportion of a and A alleles in their gametes ?

Options

A. `1:1`
B. `1:2`
C. `1:3`
D. `3:1`

Answer

To determine the proportion of alleles \( a \) and \( A \) in the gametes of a population consisting of 1000 individuals, where 500 individuals have the genotype \( Aa \) and 500 individuals have the genotype \( AA \), we can follow these steps:

### Step 1: Identify the Genotypes and Their Contributions
- We have two genotypes in the population:
- \( 500 \) individuals with genotype \( Aa \)
- \( 500 \) individuals with genotype \( AA \)

### Step 2: Determine the Alleles in Each Genotype
- The \( Aa \) genotype contributes:
- \( 1 \) allele \( A \)
- \( 1 \) allele \( a \)

- The \( AA \) genotype contributes:
- \( 2 \) alleles \( A \)
- \( 0 \) alleles \( a \)

### Step 3: Calculate the Total Number of Alleles
- Total number of alleles in the population:
- Since each individual has \( 2 \) alleles, for \( 1000 \) individuals, the total number of alleles is \( 1000 \times 2 = 2000 \).

### Step 4: Calculate the Contribution of Each Allele
- From the \( Aa \) individuals (500):
- Total \( A \) alleles from \( Aa \) = \( 500 \times 1 = 500 \)
- Total \( a \) alleles from \( Aa \) = \( 500 \times 1 = 500 \)

- From the \( AA \) individuals (500):
- Total \( A \) alleles from \( AA \) = \( 500 \times 2 = 1000 \)
- Total \( a \) alleles from \( AA \) = \( 500 \times 0 = 0 \)

### Step 5: Calculate the Total Number of Each Allele
- Total \( A \) alleles in the population:
- \( 500 \) (from \( Aa \)) + \( 1000 \) (from \( AA \)) = \( 1500 \)

- Total \( a \) alleles in the population:
- \( 500 \) (from \( Aa \)) + \( 0 \) (from \( AA \)) = \( 500 \)

### Step 6: Calculate the Proportions of Each Allele
- Proportion of allele \( A \):
\[ \text{Proportion of } A = \frac{1500}{2000} = 0.75 \]

- Proportion of allele \( a \):
\[ \text{Proportion of } a = \frac{500}{2000} = 0.25 \]

### Step 7: Determine the Ratio of Alleles
- The ratio of allele \( a \) to allele \( A \):
\[ \text{Ratio of } a \text{ to } A = \frac{0.25}{0.75} = \frac{1}{3} \]

### Final Answer
The proportion of allele \( a \) to allele \( A \) in the gametes is \( 1:3 \).

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