A trip to a different stream which had 30 fish marked at an earlier time produced 20 captured fish but none were recaptured with fish tags. Can you estimate the number of fish in this stream? Explain your answer.
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To estimate the number of fish in the stream, we can use a technique called the Lincoln-Petersen Index. This index is commonly used in ecology to estimate population sizes.
The Lincoln-Petersen Index formula is N = (M x C) / R, where:
- N is the total population size
- M is the number of fish marked initially
- C is the number of fish captured in the second sampling
- R is the number of recaptured fish with tags in the second sampling
In this case, we are given:
- M = 30 fish marked initially
- C = 20 fish captured in the second sampling
- R = 0 recaptured fish with tags
Using the formula, we can calculate the estimated population size:
N = (M x C) / R
N = (30 x 20) / 0 = undefined
Since the denominator (R) is 0, the estimated population size is undefined. It means that we cannot accurately estimate the number of fish in the stream based on the information provided. This is because we need at least one recaptured fish with tags to make a reliable estimate using the Lincoln-Petersen Index.