Capture-Recapture

• Work with the idea of a sample• Become familiar with representative samples• Understand the capture-recapture method

Fish in the LakePage 103Materials Needed

A paper bagWhite beansRed beans

In this investigation you’ll simulate the capture-recapture method and examine how it works.

The bag represents the lake. The white beans are the untagged fish in the lake, and the red beans will replace white beans to represent tagged fish.

Your objective is to estimate the total number of fish in the lake.

Capture-RecaptureAn Application of Ratio Reach into the lake and remove a small sample of fish to

tag. Count and record the number of fish you removed. Replace these fish (white beans) with an equal number of tagged fish (red beans). Return the tagged fish to the lake.

Capture-RecaptureAn Application of Ratio Allow the fish to mingle (seal the bag and shake it). Reach into the lake and remove another small sample of

fish to tag. Count the size of the sample and the number of tagged fish removed. Replace these fish to the lake.

You have taken one sample by randomly capturing some of the fish. You could use this sample to estimate the number of fish in the lake, but by taking several samples, you will get a better idea of the ratio of tagged fish to total fish in the lake.

Replace the fish, mix them, and repeat the sampling process four times, filling in a row of your table each time.

Study your chart and choose a representative ratio for the ratio of tagged fish to the total number of fish. Explain how you chose this ratio.

If you mixed the fish well, should the fraction of tagged fish in a sample be nearly the same as the fraction of tagged fish in the lake? Why or why not?

Write and solve a proportion to find the number of fish in the lake.

Why is this method called capture-recapture? How accurate are predictions using this method?

Other examplesIn a capture-recapture process, 200 fish

were tagged. From the recapture results the game warden estimates that the lake contains 2500 fish. What percent of the fish were tagged?

What ratio can your write?What do the parts of the ratio represent?

2002500 100

p

Tagged fish

Total Fish

In a lake with 250 tagged fish, recapture results show that 11% of the fish are tagged. About how many fish are in the lake?

Write a ratio that describes the percent.Write a ratio that is equal to the 11%.Identify the parts of the ratio

11 250100 f

Tagged fish

Total Fish

A lake is estimated to have 5000 fish after recapture experiments that showed 3% of the fish were tagged. How many fish were originally tagged?

Write a ratio that represents 3%.Write a ratio that equals 3% using the fish.

Identify the parts of the ratio.

3100 5000

t Tagged fish

Total Fish