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[Estimating Fish Populations]

Method
Students make math calculations with different colors of beans to learn a technique biologists use to estimate the total size of a population of fish.

Subjects: Math

Duration: One to two class periods

Group Size: Any

Grade Level: 6 - 12

Objectives:
Students will be able to:

Materials Needed:
Alaska Content and Performance Standards
Mathematics:
A-3: Perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, calculator, and computer.
B-1: Use computational methods and appropriate technology as problem-solving tools. B-3: Formulate mathematical problems that arise from everyday situations.
B-4: Develop and apply strategies to solve a variety of problems.
C-3: Develop, test, and defend mathematical hypotheses

Background:
Biologists and wildlife managers can make better management decisions if they know the total population size of a group of fish.

Determining the number of fish spawning in a small clear-water tributary is relatively easy. Biologists can set up weirs or counting towers and simply count the fish as they pass by. Determining the total number of salmon traveling through the vast, muddy waters of the Yukon River drainage is a much more difficult task. In these situations, biologists sometimes use a method to calculate population called mark/recapture.

Biologists use nets, fish wheels , or some other method to capture salmon. They insert a numbered plastic tag in the fish's back near the dorsal fin, then release it back into the river. At a point farther upriver, biologists use the same method to recapture fish. Here, they keep track of the total number of marked and unmarked fish caught. With this information, they can do the following calculation:

Estimated Population = MC divided by R

M = Fish caught and tagged in the marking event
C = Total fish recaptured
R = Total recaptured fish that were also tagged

For example, in the marking event, you catch and tag 100 salmon. In the recapture event, you catch a total of 90 salmon. Of these, 10 have the plastic tags. Using this information you do the following calculation:

100 Fish Caught and Tagged x 90 Total recaptured fish
10 Recaptured fish that had tags

100 x 90 = 9,000
10

Or, there are approximately 900 fish in the total population.

Procedure
Count out 1000 white beans and place them in a large jar before the activity. (Less than 1,000 will be too small for accurate calculations) Have the students count out 100 red beans to represent the fish tagged in the capture event. Add these to the jar and shake it well.

Pour the mixed beans out onto a tray and have the students count out 100 beans without looking them. This will represent the total fish caught in the recapture event. Then, have the students count out the number of tagged fish caught in this sample (the red beans). Plug these numbers into the equation to determine the total population of fish. Have the students count the actual number of beans to see how close their calculations came. Discuss the possible causes for any discrepancies.

Form the students into teams. Have each group retry this experiment with an unknown number of beans in each jar. Have teams experiment with larger and smaller sample sizes to see who can make the most accurate prediction of the sample size. Discuss the results.

Extensions:

Text and graphics by USFWS staff
Last modified 4, March,2009

Cyber Salmon
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