Question

For a population census of 100 fish having 40:60 (male:female) ratio, genetically effective population will be

• A. 100
• B. 96
• C. 200
• D. 48

Hint:

Any skew in sex ratio reduces the effective population size below the census number (\(N_e < N\)).
The closer the sex ratio is to 1:1, the closer \(N_e\) is to the actual census size \(N\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In conservation genetics and population dynamics, the genetically effective population size (\(N_e\)) represents the number of breeding individuals in an idealized population that would show the same rate of inbreeding or genetic drift as the real population under study.
When the sex ratio is unequal, the effective population size is lower than the actual census size (\(N\)).

Step 2: Key Formula or Approach:
The formula for calculating the genetically effective population size with an unequal sex ratio is:
\[ N_e = \frac{4 \times N_m \times N_f}{N_m + N_f} \]
where:
- \(N_m\) is the number of breeding males.
- \(N_f\) is the number of breeding females.

Step 3: Detailed Explanation:
Given:
- Total census population (\(N\)) = \(100\)
- Male to female ratio = \(40:60\)
Therefore:
- \(N_m = 40\)
- \(N_f = 60\)
Now, substituting these values into the formula:
\[ N_e = \frac{4 \times 40 \times 60}{40 + 60} \]
\[ N_e = \frac{9600}{100} \]
\[ N_e = 96 \]

Step 4: Final Answer:
The genetically effective population size is 96, which corresponds to option (B).