In a population, which is in Hardy-Weinberg equilibrium, the recessive allelic frequency is 0.8, in a population of 1300. Find out the number of dominant individuals in that population, if the gene in reference has only two alleles.

Options

A. 416
B. 468
C. 640
D. 52

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the Hardy-Weinberg Principle
The Hardy-Weinberg equilibrium states that in a population with two alleles for a trait, the frequencies of the alleles and genotypes will remain constant from generation to generation in the absence of evolutionary influences. The frequencies of the alleles can be represented as:
- p = frequency of the dominant allele
- q = frequency of the recessive allele

### Step 2: Identify the Given Information
From the question, we know:
- The frequency of the recessive allele (q) = 0.8
- The total population size (N) = 1300

### Step 3: Calculate the Frequency of the Dominant Allele
Using the relationship \( p + q = 1 \):
\[ p = 1 - q \]
\[ p = 1 - 0.8 = 0.2 \]

### Step 4: Calculate the Genotype Frequencies
In Hardy-Weinberg equilibrium, the frequencies of the genotypes can be calculated as follows:
- Frequency of homozygous dominant (AA) = \( p^2 \)
- Frequency of heterozygous (Aa) = \( 2pq \)
- Frequency of homozygous recessive (aa) = \( q^2 \)

First, calculate \( p^2 \):
\[ p^2 = (0.2)^2 = 0.04 \]

### Step 5: Calculate the Number of Dominant Individuals
The dominant individuals include both homozygous dominant (AA) and heterozygous (Aa). Thus, we need to find:
- Number of homozygous dominant (AA) individuals = \( p^2 \times N \)
- Number of heterozygous (Aa) individuals = \( 2pq \times N \)

First, calculate the number of homozygous dominant individuals:
\[ \text{Number of AA} = p^2 \times N = 0.04 \times 1300 = 52 \]

Next, calculate the heterozygous individuals:
\[ 2pq = 2 \times 0.2 \times 0.8 = 0.32 \]
\[ \text{Number of Aa} = 2pq \times N = 0.32 \times 1300 = 416 \]

### Step 6: Total Number of Dominant Individuals
Now, add the number of homozygous dominant and heterozygous individuals to find the total number of dominant individuals:
\[ \text{Total Dominant Individuals} = \text{Number of AA} + \text{Number of Aa} \]
\[ \text{Total Dominant Individuals} = 52 + 416 = 468 \]

### Final Answer
The number of dominant individuals in that population is **468**.

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