Name:
Date:
Population Estimation and Growth Simulation
Biological Sampling
How do biologists determine the population of a species in a particular area? There are a
variety of ways that it can be done, however the most common method involves tagging. In this
method, biologist first capture and tag a sample of the animals. Then, after some time has passed
for the animals to return to their environment and to “redistribute” themselves, the scientist take
repeated random samples and calculate the percentage of the sample that is tagged. We would
expect that these sample percentages should vary “around” the true population percentage. Using
this assumption, one can calculate the approximate population size given that they know the
original number tagged and the mean percent tagged from the samples.
Purpose
To estimate the size of a population, chart the growth of the population, and observe the
effects of an environmental carrying capacity.
Introduction
In this lab you will use a simple equation to estimate the size of any population. After
estimating the size of the population, you will determine the growth of the population over
successive years until the population hits the carrying capacity of the environment. This is a
simulation using beans as fish.
Materials
1 lunch bag with beans
Marker
Calculator
Graph paper
Part 1 Fishing Exercise
Procedure
1. Carefully and gently mix up the fish in the bag.
2. Remove a sample (a large handful, approximately 40) of fish from the bag.
3. Count the total number of fish that you removed and record this in Table 1 under
“total in sample”.
4. Count the number of beans that have the mark and record the number of marked
beans in Table 1 under “# of tagged fish in sample”.
5. Mix the population thoroughly to get the tagged population “redistributed” among the
population
6. Without looking (to prevent your personal bias) remove a sample of fish from the
“pond”. Count the number of tagged and total number of fish in your sample,
recording these numbers. Also calculate the percent tagged in the sample, using two
decimal places for accuracy and consistency.
7. Mix the population thoroughly and repeat the sampling for a total of 20 samples. The
sample sizes do not have to remain the same, but you do want to get fairly large
handfuls of fish each time.
8. When you are finished, find the mean percent tagged from your set of samples.
Name:
Date:
Table 1
Original Number Tagged
Sample #
# of Tagged Fish in Sample
Total Sample Size
Percent Tagged in
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average Percentage Tagged
Part 2 Using Inferential Statistics to Calculate the Population Size
How do we predict our population size? We expect that the sample percent tagged should vary
fairly closely around the true population proportion of originally tagged fish. Using ratios for
Algebra, we can do the following:
The mean of the 20 sample percentages = number originally tagged
population size
1. Using Algebra to solve the equation above….
Population size = number originally tagged
the mean of the 20 sample percentages
2. Record the Predicted Population Size in Table 2.
Name:
Date:
Table 2
Predicted Population Size for
Your Pond
Actual Population
Percent Error
3. Now count your entire population of fish. Record this number in Table 2
4. Calculate your percent error by using this equation:
Percent Error= Actual Total Population – Predicted Population
Actual Total Population
This value is an absolute value (there cannot be a negative number). Record this
in Table 2 under “Percent Error”.
Part 3 Analysis/Discussion of Results Answer the questions below in complete sentences.
1.
2.
3.
4.
What could cause your results to be off from the actual population?
How would sample size and population size affect these results?
How would the number of samples affect these results?
If you were predicting a large population (as in a real pond) would the number you were
off really have been that bad relatively speaking?
5. What concerns should a biologist have about a species’ s habitat before they use this
method to approximate the size of a population? ( think back to your notes on population
dispersion, size, and density)
Part 4
Using your Predicted Population (PP) the given birth rate, death rate, and the change in
population equation to calculate the growth or decline of the population over 10 years.
Important information to know:
The birth rate (BR) of the fish per100 fish per year is 50.
The death rate (DR) of the fish per 100 fish per year is 30.
The change in bean population (CP) is equal to BR-DR.
The way that you can calculate the new fish population year after year is by using the following
equation:
The New Population # = (CP) X Predicted Population + Predicted Population
100
For example, if the current population is 200, and if you use the birth and death rate from above,
then the equation would look like this:
The New Population # = 20 X 200 + 200 = 4000 + 200 = 40 + 200 = 240
100
100
After 1 year the population went from 200 to 240.
Name:
Date:
Now here’s the catch: the environment has only enough resources to sustain 600 fish. If the
population of beans exceeds 600 fish, then you will switch the birth rate and death rate. In other
words the BR will equal 30 and the DR will equal 50.
Table 3: Population Growth Data
Year
0 (record your calculated total
pop.)
1.
Population in Beans
2
3
4
5
6
7
8
9
10
Part 5 Graph the results.
When graphing the information, make a straight line across the graph (parallel to the X axis) at
the 600 bean level. Be sure your graph has a title and is properly labeled.
Part 6 Analysis/Discussion – Answer the questions below in complete sentences.
1. Describe your graph in terms of exponential, logistic, and type of population change curve.
2. Was the determined percent error accurate?
3. List two factors that could have led to inaccuracies of this estimation technique?
4. How could you use this technique to estimate the population of grasshoppers in
your backyard? (Restate the procedure in your own words, beginning with the original
collection, marking, and recapturing. Include the formula that you would use.)
5. In your own words, define Carrying Capacity.
6. What will eventually happen to this population size in reference to the carrying capacity
of the environment?
7. Can we use a similar model for studying humans? Why or why not