Fish Population Estimation using Capture-Recapture

The question asks us to estimate the total population size of fish in a lake based on capture-recapture data. This is a common ecological method used when a complete count of a population is impractical. The underlying principle is that the proportion of tagged fish in a second sample should be representative of the proportion of tagged fish in the entire population.

The method used here is the Lincoln-Peters index, which provides a simple way to estimate population size based on two samples.

Capture-Recapture Formula

The formula for the Lincoln-Peters index is:

\( N = \frac{M \times C}{R} \)

Where:

• \( N \) = Estimated total population size
• \( M \) = Number of individuals captured, tagged, and released in the first sample (Day 1)
• \( C \) = Total number of individuals captured in the second sample (Day 2)
• \( R \) = Number of tagged individuals recaptured in the second sample (Day 2)

Applying the Data

From the question, we have the following information:

• Number of fish tagged on Day 1 (\( M \)) = 45
• Total number of fish caught on Day 2 (\( C \)) = 50
• Number of tagged fish recaptured on Day 2 (\( R \)) = 15

Calculating the Population Size

Now, we substitute these values into the Lincoln-Peters index formula:

\( N = \frac{45 \times 50}{15} \)

First, multiply the numbers in the numerator:

\( 45 \times 50 = 2250 \)

So the formula becomes:

\( N = \frac{2250}{15} \)

Now, divide 2250 by 15:

\( N = 150 \)

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

Estimated Population Size

Based on the capture-recapture data, the estimated population size of fish in the lake is 150.