How Accurate is the Fish Population Estimate in the Lake?

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SUMMARY

The fish population estimate in the lake is calculated using the capture-recapture method, resulting in an estimated total of 1,428 fish. This estimate is derived from the formula N = 100(100/7), where 100 represents the initially tagged fish and 7 is the number of tagged fish recaptured. The assumptions necessary for this estimate include the random mixing of tagged and untagged fish and that the tagging does not affect the fish's likelihood of being recaptured.

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Ecologists, fisheries biologists, researchers in wildlife management, and students studying population dynamics will benefit from this discussion.

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Researchers of a department of engineering of fish are studying the fish of a lake. In the first phase of the work they collect 100 fish, place labels in all they and they return them to the lake. One week later them they come back to the lake, they collect more 100 fish and they observe that 7 of them possesses labels.

(a) Which the best estimate for the number of fish in the lake?

(b) That assumptions must be satisfied to justify the estimate of the previous item ?
 
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(a) N=100(100/7)=1428

(b) Extrapolation - since 7/100 of the caught fish were tagged, assume that 7/100 times (N) total number of fish = total number of that have been tagged (=100).
 

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