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?

Mark-Recapture is an indirect method technique used to estimate population size in the base of capture-mark-recapture events. The estimated size of the population is N = 384.75 individuals.

There are different methods to study population density. There are direct methods and indirect methods. Among these last ones, we might find the Mark-Recapture technique.

The Mark-Recapture technique assumes that

The method consists of

1) capturing a sample of individuals belonging to the population under study, in this case, the sunfish population.

2) After capturing the individuals, the researcher marks them and releases them again.

3) The third step is to sample again, capture a new amount of individuals, and count how many of them are marked.  These marked individuals belong to the first sample.

4) Calculating the population size by using different indexes, like the Lincoln Index.

The Lincolns Index states that to obtain the population size, the research must follow the following procedure:

1) Take an initial sample with n1 number of individuals.

2) Mark all the sampled individuals and release them.

3) Take a second sample with n2 number of individuals.

4) Count the number of marked individuals, m.

To estimate the total number of individuals in this population, N, the following equation must be considered:

                                         N = (n1 x n2)/m

In the exposed example, we know that

So now we need to replace the terms to get the population size.

N = (n1 x n2)/m

N = (45 x 62) / 8

N = 2790 / 8

N = 384.75 individuals.

The estimated size of the population is N = 384.75 individuals.

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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.