A researcher captured 45 fish from a lake on day 1, tagged and released them back.
On day 2 the researcher caught 50 fish out from the same lake, of which 15 were already tagged.
Estimate the population size of fish in the lake with this information and pick the correct option.

Correct option is A

To estimate the population size of fish in the lake, we can use the mark-recapture method, also known as the Lincoln-Petersen index. The formula is as follows:

$$\text{Population size (N)} = \frac{M \times C}{R}$$

Where:

• M = Number of fish tagged on Day 1 = 45

• C = Number of fish caught on Day 2 = 50

• R = Number of tagged fish recaptured on Day 2 = 15

Now, plug in the values into the formula:

​$$N = \frac{(45 \times 50)}{15} = \frac{2250}{15} = 150$$​​

​So, the estimated population size of fish in the lake is 150.

Assumptions in the Mark-Recapture Method:

• Closed Population: The population is assumed to be closed, meaning there is no immigration, emigration, birth, or death during the study period.

• Random Mixing: After being released, the marked individuals mix randomly with the rest of the population.

• Marks are Not Lost: The marks used to identify individuals should remain visible and intact during the study.

• Equal Probability of Capture: Each individual in the population has the same probability of being captured in the second sample.

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