A student conducts a mark-recapture experiment to estimate the population size of sunfish in a small pond near her home. In the first catch, she marked 45 individuals. Two weeks later, she captures 62 individuals, of which 8 are already marked. What is the estimated size of the population based on these data?

Question

Zhang

Biology

30 December, 11:18

A student conducts a mark-recapture experiment to estimate the population size of sunfish in a small pond near her home. In the first catch, she marked 45 individuals. Two weeks later, she captures 62 individuals, of which 8 are already marked. What is the estimated size of the population based on these data?

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Answers (1)

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Easton Cherry · Answer 1

348.75 individuals, however you may need to round

Explanation:

To solve this problem, you need to think of the proportions you are given. Since she marked 45 fish in the beginning, and assuming none died, you can assume that there are 45 marked fish in the whole population. Therefore, when she takes the sample of 62 and sees that there are 8 marked fish, a good strategy is to take that proportion and use it to solve for the population like so:

8 (marked fish in sample) / 62 (total in sample) = 45 (total marked fish) / x (total population. Next cross-multiply 45 * 62 and 8 * x and set them equal to each other, getting you to the equation 2790 = 8x. Finally, to find x, the population size, divide 2790 by 8 to get x = 348.75.