Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
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A note to teachers

Daphnia and Algae: a Study of Pond Dynamics

This page walks you through the student pages "What does the model look like?" and "What experiment can I do with the

The student questions are in red. The answers are provided on this page in blue


This lesson explores some of the relationships between algae and daphnia.

Algae and daphnia live in ponds and puddles. Algae have chlorophyll. That helps them make sugar. It also makes
the water green. Algae are small. You need a microscope to see them. 

Like plants algae need light and nutrients to grow. The nutrients are dissolved nitrogen in the form of nitrates, other
minerals and CO2. The nutrients come from bacteria that break down plant and animal wastes. If the water has a
lot of nutrients in it the algae can grow quickly, doubling in number every day. As they consume the nutrients their
growth slows. In a classroom aquarium you can supply the nutrients with dirty water from a fish tank. Every week
when you do a water change in the fish tank put some of it in the algae tank.

The algae get energy from sunlight. If the pond isn't under trees it gets plenty of sun in the summer. In the winter
there is less sun so the algae grow slower. You can grow algae in your classroom or home. Put a glass jar or tank
in a window that gets sun light. Fill the tank with dirty water from a fish tank. Some of the water will evaporate.
Add more fish water to keep the tank full. Over the next few weeks the algae will multiply. The water will become
dark green.

1 When the water is dark green will all of the algae receive the same amount of light? No, the algae on the top and next to the glass will absorb the light and cast a shadow on the algae below and behind them.

Temperature also effects alga growth. As the water temperature falls below 70 degrees the algae grow slower. As
the temperature approaches freezing the algae stop growing.

Algae Model

The model was written in a language called STELLA. This model explores some of the relationships between
algae and daphnia. 

To better understand the model we will look at its parts. 

Algae Growth

In our model each algae represents 1,000 algae. We start with 210 algae in the model. 

2 How many algae does this represent in our aquarium tank?210,000

When there are only a few algae all of the algae reproduce. The algae double in number everyday. As the
population increases more stop reproducing. Why? Because some algae are in the shade and don't get enough
light. The nutrients are also in limited supply. There aren't enough minerals and nitrates for a large population.

If you double click on the growth rate converter a graph will appear. This graph shows how the population effects
the growth rate. 
The population is the input. 
The growth rate is the output 

3. Is the growth rate function linear or nonlinear? linear

4 As the number of algae increases, what happens to the growth rate? 
A) it increases B) it decreases C) it doesn't change. 
B) it decreases

5 Is the slope of the graph positive or negative? It has a negative slope.

6 Next week some students decide to close the blinds. How would this change the growth rate? Explain your

The slope would still be negative and probably linear. The growth would be depressed. Perhaps it would start at .2
rather than .4. The slope would be less negative, closer to 0. 
The algae would get less light. It would be darker like it is in the middle of the aquarium with a lot of algae. Thus we
would start with a growth rate similar to the current rate at the middle range of daphnia.

Alga reproduction is the product of the number of algae and the algae growth rate. 
Algae X growth_rate

In our model the number of algae can be reduced when daphnia eat them. 
This relationship is represented by the consumption per head function. Double clicking on the consumption per
head converter will open this graph. 

7 Is this relationship linear or nonlinear? linear

8 As the number of algae increases from 0 to 1000 what happened to the number eaten by each daphnia?
It increases. The number eaten goes from 0 to 1. Remember that 1 algae really represents 1000 algae. In our model the maximum number of algae a daphnia can eat in one day is 1000.

The number of algae consumed is the product of the number of daphnia and the consumption per head. 
(daphnia+juvenile X .3) X consumption_per_head 9 Why are the number of juveniles multiplied by .3 and not 1? The juveniles are the babies. They start small and grow. When they are small they can't eat as much as an adult. .3 is an average value for the juveniles.



If all conditions are perfect daphnia live approximately 50 days. 
If there isn't enough food the daphnia don't live as long. 
This relationship is shown in the average life span graph. 

Consumption per head is the input. Average life span is the output. 

10 How many algae is a daphnia eating each day if it lives about 40 days? Remember each algae represents
1,000 algae. 
At 40.5 days they eat 700 algae. At 40 days they will eat a few less than 700.

The number of babies in a brood depends on the amount of food the mother can eat. This relationship is
represented in the food factor converter. 

Daphnia can have 8 babies in a brood. In the algorithm the brood size equals the food factor times 8. 

The number of babies born each day equals the brood size times the number of females.

The babies spend 8 days growing. The model holds the babies in the juvenile conveyer. The conveyer is like the
oven at the pizza shop. The raw pizza goes in one side. 15 minutes later the cooked pizza comes out the other
side. After 8 days in the conveyer the mature daphnia are moved to the females' stock.

Daphnia can live 50 days. If they don't get enough food they don't live as long. The average life span graph determines how long the daphnia can live. 

The model calculates how many daphnia die by dividing the number of females by their average life span. 

This model simulates putting some daphnia in a tank of algae. 

11 Explain what you think would happen if you did this experiment. 
How would the number of daphnia and algae change. 
How many daphnia and algae would there be after 1 month, 2 months… 6 months.
Answers will vary.


Your teacher will show you the model and or give you a graph of its predictions. Use the graph to work through the

12 Find a section of the graph when the number of algae is increasing or high. Describe the number of daphnia
when the algae are increasing.
The number of daphnia is small, less than 20.

13 Find a section of the graph where the number of algae is decreasing. How is the number of daphnia changing in
this section?
The number of daphnia is increasing until the number of algae is less than the number of daphnia, then they both decrease.

14 What happens to the number of daphnia when the number of algae is below 250,000? The number of daphnia is decreasing or staying small.

Feedback loops are important in nature. Feedback loops help to keep systems in balance. In this model the number
of algae and daphnia change. They change in step with each other.

Look on the model. 15 Identify the loops where the number of algae changes the number of daphnia, which then changes
the number of algae. 


If you click on the graph numbers appear under algae, females, and replacing days. As you slide the cursor over the
graph you can watch the values change. 

16 What are the maximum and minimum values for the algae and daphnia?
algae maximums 930,330 978,920 983,810 974,730 984,210 973,360
algae minimums 1.66 0.73 1.30 0.68 1.40 0.69
daphnia maximums 499.14 371.01 276.85 363.20 270.90 368.25
daphnia minimums 0 0 0 0 0 0
juvenile maximums 6,171.34 6,366.18 6,147.42 6,370.45 6,124.01 6,375.99
juvenile minimums 22.66 11.25 21.63 10.72 23.46 12.91

17 If the daphnia drop this low, how can they increase again? There are a few juvenile daphnia left in the conveyer. Each day a few of them mature. They don't show up because they die due to lack of algae. When the algae level starts to rise, some of the new daphnia females survive and have broods, and the numbers start to rise again. 

Double click on the table 1 icon. This opens up a table of the runs data. Moving the scroll bar up and down allows
you to examine the entire run's data. This table also gives the number of juveniles.

18 What are the minimum and maximum values for the juveniles? See table above. Describe how the female and juvenile numbers
change relative to each other.
In general they rise and fall together. The juveniles hit their maximum a day or so later than the females. The juveniles hit their minimum after the females start to increase again.

This model simulates a pond with plenty of nutrients. The algae can grow at their maximum rate, doubling every day.
This would simulate a pond in a forest or wetlands. You can change the model to simulate a pond in town next to a
parking lot. In your city pond, there will be fewer nutrients. Fewer nutrients will reduce the algae's maximum growth
rate. The maximum number of algae will also be reduced.

You want to compare the two ponds. STELLA will help you do that. Open a new graph by clicking on the pink
graph pad in the tool bar. Clicking on a blank place on the screen will open the graph pad. Double click on the graph
to open its editing mode. Click the Comparative box. Double click the females to select it. 

Run the model again to record the female values.

Open the growth rate converter by double clicking on it. Change the maximum number of Algae from 1000 to
900.00 and hit enter. That changes all of the values in the Algae column. Next change the maximum growth rate from
1.000 to 0.900. Change the first 4 values for growth rate to 0.900. 

Run the model again. 

19 Describe the change in the daphnia values in the two ponds.

Except for the fifth peak, the second run (.9 max) has lower values, the third and sixth being significantly lower. There is some variability in both runs. The second run (less fertile water) has more variation. 

You can make more changes to the growth rate and see what effect it has.

This is the graph produced with the growth rate values at 800 and .8.

Developed by
The Shodor Education Foundation, Inc.

Copyright © 1999-2001 by The Shodor Education Foundation, Inc.

This project is supported, in part,
by the

National Science Foundation

Opinions expressed are those of the authors
and not necessarily those of the National Science Foundation.

Last Update: Saturday, 16-Feb-2002 13:29:11 EST
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