In a diploid population of Drosophila 9% of the population is black in colour. Black is recessive to grey. What is the frequency of heterozygous flies in that population, if it is in Hardy-Weinberg equilibrium?

Options

A. 0.42
B. 0.09
C. 0.49
D. 0.7

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 key steps are as follows:

### Step 1: Understand the given information
We know that in a diploid population of Drosophila, 9% of the population is black in color. Since black is recessive to grey, we can denote the alleles as follows:
- Let "b" represent the recessive allele for black color.
- Let "B" represent the dominant allele for grey color.

### Step 2: Determine the frequency of the recessive phenotype
The frequency of the black phenotype (homozygous recessive, bb) is given as 9%. In terms of frequency, this can be expressed as:
- \( q^2 = 0.09 \)

### Step 3: Calculate the frequency of the recessive allele (q)
To find the frequency of the recessive allele (q), we take the square root of the frequency of the recessive phenotype:
- \( q = \sqrt{q^2} = \sqrt{0.09} = 0.3 \)

### Step 4: Calculate the frequency of the dominant allele (p)
Using the relationship \( p + q = 1 \), we can find the frequency of the dominant allele (p):
- \( p = 1 - q = 1 - 0.3 = 0.7 \)

### Step 5: Calculate the frequency of heterozygous individuals (2pq)
The frequency of heterozygous individuals (Bb) can be calculated using the formula:
- \( 2pq \)
Substituting the values of p and q:
- \( 2pq = 2 \times 0.7 \times 0.3 = 0.42 \)

### Conclusion
The frequency of heterozygous flies in the population is 0.42 or 42%.

### Final Answer
The frequency of heterozygous flies in that population is **0.42**.

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