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    Pictured Rocks

    National Lakeshore Michigan

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How Many Fish are in that Pond?



Students will:

1. Estimate abundance of fish in a pond using three mark-recapture statistical methods

2. Generalize that mark-recapture studies are beneficial to estimating wildlife populations

3. Recognize the relationship between small and large sampling populations to give consistent data

4. Determine the percent error for each statistical method.

Students sample, mark, and count the fish population in a pond.


The major purpose of this activity is for students to recognize the benefit of using mark-recapture techniques to estimate the size of a population. In the process of participating in this activity, students manipulate mathematical formulas and assess which method is the most accurate in estimating the size of a population.

Mark-recapture methods are commonly used to estimate the size of a population of many animal populations. The Petersen Method may be employed for a single marking and recapture period. The Schnabel and Schumacher methods are used for multiple marking and recapture periods.

Notations used in describing these methods are:

M =

Number of individuals originally marked

C =

The sample size taken at the time of recapture

R =

Number of marked individuals in the sample taken at the time of recapture

N =

Estimate of population abundance (number of animals present at the time of initial marking; assuming that mortality; emigration; immigration or recruitment are not occurring).

These methods assume that all members of the population retain their identity and are properly recognized and counted when captured. It is assumed that the two subgroups (marked individuals and those not marked) are proportion- ally represented in any sample with respect to their relative presence in the population.

The three methods are:

Petersen Method:

N = MC/R

Schnabel Method:

N = sum of MC values/sum of R values

Schmacher Method:

N = sum of M2C values/sum of MR values

The Petersen formula can be a biased estimator of population size. The Schnabel and Schmacher methods are said to be unbiased, especially when R>7.

1 pond
1 plastic container (such as a 16 oz. cottage cheese container) for every two students
2000 white beans and 2000 brown beans (fish) for class. One or two bags of each bean color-beans should be approximately the same size.
1 data sheet for every student
1 calculator



1. Have students place approximately 250 fish (beans) of one color into the pond.

2. Have one student in the group capture a small handful of the fish from the pond (about 80-90 fish). This sample is referred to as the number of fish captured designated as "C". Record number on data sheet.

3. Replace these captured fish with the same number of the other colored fish (if your fish are white then replace with brown fish and visa versa). Important! Return the captured fish into the main class containers of beans. Do not put these fish back into the pond because you want to keep the number of fish in the pond constant. These fish are the number of individuals originally marked designated as "M".

4. Add the marked fish into the pond. Make the fish swim by dispersing them through out the pond (i.e., mix with hand for 30-60 seconds).

5. Repeat step 2.

6. Have students count the number of captured fish and record on the data sheet. Record the number of marked fish which were recaptured designated as "R". Place the recaptured fish back into the pond.

7. Replace all of the unmarked fish in the sample with marked fish as in step 3.

8. Repeat steps 4 through 7 ten times. Twenty samples would be better statistically; however, the number of samples depends on the time available.

9. At the end of the ten samples, count the actual number of fish in the pond (both colors). Record on data sheet.

10. Using the data recorded on the data sheet, determine the three methods to estimate the population in the pond. Remember the Petersen Method can only be used for a single marking and recapturing period. You may want to have the students average the ten samples.

11. Using the population estimates for the three methods, calculate the percent error for each method using this formula: number of fish estimated / number of fish actually in the pond 100 = % error

12. Discuss the importance of consistent sampling techniques (capturing the same number of fish); sampling bias of methods and researcher (do not look at the beans when sampling, students tend to sample the marked fish); did the fish swim and disperse into the environment for the same amount of time; and how well did you mix the fish.

13. Compare the percent error and determine which sampling method was the most accurate.

14. Compare the data between student groups. Variations will occur with small sampling sizes versus large sampling sizes.

15. Discuss the importance of multiple samples compared to single samples, and how the number of recaptured fish in the sample determines the estimated size of the population.


Did You Know?

The Grand Sable Dunes are located just west of Grand Marais, Michigan, in Pictured Rocks National Lakeshore.

The Grand Sable Dunes are a federally designated Research Natural Area. The five square miles of dunes are an unusual glacial kame terrace with overlying dunes caused by fluctuating lake levels over the centuries. The dunes are located in Pictured Rocks National Lakeshore, near Grand Marais, Mich. More...