Estimating the number of fish in a lake using a method involving tagged fish typically uses the Lincoln-Petersen estimator, a commonly used formula in ecology for estimating wildlife populations. Here’s how it works step-by-step:
Methodology
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Initial Capture and Tagging:
- Capture a sample of fish from the lake.
- Tag these fish and release them back into the lake.
- Let the fish have time to mix back into the population.
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Recapture:
- Capture another sample of fish later.
- Record how many of these fish are tagged.
Formula
The Lincoln-Petersen estimator can be represented with the following formula:
\[ \hat{N} = \frac{(M \times C)}{R} \]
Where:
- \(\hat{N}\) = estimated total population of fish in the lake
- \(M\) = number of fish that were initially captured and tagged
- \(C\) = total number of fish captured in the second sample
- \(R\) = number of tagged fish recaptured in the second sample
Step-by-Step Example
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Initial Capture and Tagging:
- Suppose 100 fish are captured, tagged, and released (M = 100).
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Recapture:
- Later, let's say 50 fish are caught in the second sample (C = 50).
- Out of those 50 fish, 10 are found to be tagged (R = 10).
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Estimate the Total Fish Population: Using the formula:
\[ \hat{N} = \frac{(M \times C)}{R} = \frac{(100 \times 50)}{10} = \frac{5000}{10} = 500 \]
Conclusion
The estimated number of fish in the lake is approximately 500.
This method assumes that the tagged fish have mixed evenly within the population and that there are no significant losses in the population during the study period (due to factors like mortality, emigration, or changes in behavior).