Fish Population Simulation
Estimating populations
One method of estimating the number of fish in a lake is to catch and tag a collection of
fish and then release them. At a later time we return and catch a sample of fish and
determine the proportion of tagged fish.We can then use that proportion to estimate the
total fish population in the lake. For example, suppose that we initially caught,tagged and
released a total of 50 fish. If we return later and catch a total of 60 fish, 18 of which were
tagged, we can then estimate of the number of fish in the lake.
Let’s simulate this situation using a bag with an unknown number of white beans. For
this exercise, please work in pairs at your table of 4. Remove 50 white beans and replace
with 50 black beans (the tagged fish). Then using a scoop, have one partner remove a
sample from the bag, count the respective numbers of black and white beans and return
the sample to the bag. The other partner will then follow and do the same. Each person at
the table should collect a sample, count the respective numbers and replace the sample.
Let L denote the number of fish in the lake. Determine your estimate for L by setting up
and solving a proportion. When you have calculated your estimate, please write your
estimate on a dot and place the dot in the appropriate bin in the histogram of results we
are constucting (comments can be made on the distribution of estimates - presumably a
bell curve).
For your estimate, what assumptions are you making?
Let L be the number of fish in the lake and assume we have tagged 50 fish.
Let b be the number of black beans and w the number of white beans in our sample. Then
b 50

w L
is our proportion. Since we have computed b and w, we can calculate L.
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