Ecosystems Curriculum

Section 5: Lesson Plan — Modeling Predatory-Prey Relationships

This lesson uses a computer simulation called StarLogo.³ StarLogo is a program created by researchers at the MIT Media Lab to show what happens at a population level when individuals act according to a given set of rules. The resulting outcome is not usually one that can be predicted from the individual interactions, so it can be quite surprising.

StarLogo models the predator-prey relationships differently than what most teachers are familiar with. Models of predation are typically based on classical models, such as the Lotka-Volterra model (as is the case with the Lynx-Hare Cycles model in Section 6). It specifies interactions between predator and prey populations through differential equations that describe the rate of change of different variables over time. These classical models aim to predict at a different level than the modeling approach in the StarLogo program. StarLogo describes the behavior of individuals rather than populations. Therefore the outcomes with the StarLogo program often parallel, but sometimes diverge, from the classical models. Wilensky and Reisman⁴ have explored this issue in depth and give examples of explorations that students have engaged in when exploring the relationship between their StarLogo models (or embodied approaches as they call them) and classical models. They offer at least one instance where a student discovered that the Lotka-Volterra model gave a mistaken prediction and that Gause had previously discovered the discrepancy in 1934! As Wilensky and Reisman point out, classical tools allow one to make aggregate level assumptions; however, models focused on the individual level require assumptions to be coded at the individual level, and then one waits to see what the aggregate level consequences are.

Note to Teacher: You will notice that when there are no consumers for grass (in Simulation #1) and for rabbits (in Simulation #2), the population increases to a certain point and then the program stops running. Discuss with students what happens when a population reaches the limits of what the environment can support. Can it continue to grow beyond that point? What do they think?

Materials

• Symbiosis Sheet (PDF 736 KB)
• StarLogo Simulation 1
• StarLogo Simulation 2
• Sheet for: What is Two-way Causality? (PDF 88 KB)
• Student Guide Sheet for StarLogo (PDF 120 KB)

Prep Step

• Read background information.
• Review the lesson plan.
• Follow this link for getting a copy of StarLogo on-line: http://education.mit.edu/starlogo/ or see above.
• Right-click on these links and select "Save Target As..." or "Save Link As..." to download Simulation #1 and Simulation #2 from our website.
• Photocopy the sheet, Symbiosis.
• Photocopy the sheet, What is Two-Way Causality?.
• Photocopy the sheet, Student Guide Sheet for StarLogo if you plan on having students work in small groups.

Analyze Thinking

Step 1: Review Domino Causality and Define Two-Way Causality

Remind students about domino causality from the first section. Ask them to think back to what they learned. In domino causality, the effects are uni-directional. So for instance, in the process of energy transfer, the green plants give energy to the insects but the insects do not give energy to the green plants. Then put a diagram on the board that looks like this:

Tell your students that this diagram shows a different type of causality. It is called two-way or mutual causality. Ask: "Can you think of any examples where organisms help each other?" Gather students' ideas and list them on the board. Some students may not be aware of any two-way relationships, while others may not be sure that they actually exist.

RECAST Thinking

Step 2: Introduce the Set of Stories about Symbiotic Relationships

Hand out the sheet called Symbiosis. Read and discuss each story about symbiotic relationships. After each story, ask:

• How do the organisms help each other?
• How is each organism a cause and an effect?

Note to the Teacher: The stories are in an order that most students will find is easiest to hardest. For example, it is easier to think of two animals helping each other than of two plants helping each other. Finally, most students don't think about organisms living inside us, so they might find this the most startling.

After you have read all of the stories about mutual symbiotic relationships, ask:

• What similarities and differences did you find between the stories?
• What did you find most interesting? …startling?
• Does any of this change the way you think about ecosystems? If so, how?

Step 3: Introduce the Set of Stories on Parasitic Symbiotic Relationships

Next read and discuss each story about parasitic symbiotic relationships. Your students are probably familiar with some parasitic relationships, such as ticks on their dogs, etc. After you have read all of the stories, ask:

• What similarities and differences did you find between the stories?
• What did you find most interesting? …startling?
• Does any of this change the way you think about ecosystems? If so, how?

Step 4: Analyze Current Thinking

If in the list generated in step 1, students came up with two-way causal relationships where prey provides food for predators and predators keep the size of the prey population small enough, then draw students’ attention to those examples. Otherwise say,

• "We have said that some animals cause there to be energy for other animals and so in that sense they help those animals, for instance the mice give energy to the owls. Are there any ways that the owls might also help the mice? Can you think of any other relationships in nature where the entire population of one species benefits from a relationship they have with another population?"

Collect students' ideas.

Some students will deny the possibility of any benefits. Others may give indirect benefits such as they eat things that eat mice or they eat things that eat the things mice eat. Still others may realize that when reasoning about a population, the owls can help to keep the size of the mouse population at a level that the environment can sustain.

Step 5: Introduce and Explore StarLogo Simulation #1: Grass and Rabbits

The simulation in this step and in step 7 can be done as a class demonstration or in small groups in a computer lab. In this section’s resources, you will find: 1) General Instructions: StarLogo sheets with information on how to run the StarLogo simulation; 2) a Student Guide Sheet, which can be handed out to students to guide their small group exploration; and 3) a Teacher Guide Sheet, which can be used to walk you through the simulation as a class demonstration.

Either pass out the Student Guide Sheet or walk the class through the simulation using the Teacher Guide Sheet. Plan at least 30 minutes for this part of the lesson.

Step 6: Discuss the Role of Two-way Causality in the Grass and Rabbits Simulation

Collect students’ ideas by asking the following questions:

• Are there ways that the grass helps the rabbits? [As the rabbits eat the grass, they are able to reproduce. They need the energy they get from the grass to stay alive.]
• Are there any ways that the rabbits might also help the grass? [They might fertilize it. They help to spread the plant seeds.]
• Are the fates of the grass and the rabbits linked in any way?

Step 7: Introduce and Explore StarLogo Simulation #2: Rabbits and Foxes.

Either pass out the Student Guide Sheet or walk the class through the simulation using the Teacher Guide Sheet. Plan at least 30 minutes for this part of the lesson.

• Are there ways that the grass helps the rabbits? [As the rabbits eat the grass, they are able to reproduce. They need the energy they get from the grass to stay alive.]
• Are there any ways that the rabbits might also help the grass? [They might fertilize it. They help to spread the plant seeds.]
• Are the fates of the grass and the rabbits linked in any way?

Step 8: Discuss the Role of Two-way Causality in the Rabbits and Foxes simulation

Collect students’ ideas by asking the following questions:

• What are some things that will help keep the size of the rabbit population under control? [Predators such as foxes, wolves, and so forth.]
• What does the simulation tell you about whether predators can ever be helpful to the populations that they prey upon?

Discuss the difference between helping an individual versus helping a population. Explain that it doesn't really help the individual rabbit to be eaten, but it does help the population of rabbits. Usually it is the weakest or slowest rabbits that get caught, so the rabbits that survive to have baby rabbits are the ones who are strongest and fastest. That makes the rabbit population stronger and faster overall. If predators never ate any rabbits, the size of their population would keep growing and growoing and they wouldn't have enough food to eat, and they would starve to death.

Explore Causality

Step 9: Review Two-Way Causality Explanation

Hand out the sheet, "What is Two-Way Causality?." Read it as a group and discuss.

Review, Extend, and Apply

Step 10: Connect Two-Way Causality to the Interactions in the Simulations

Further the discussion of two-way causality in ecosystems by having students compare what the two simulations show.

Ask: "What do the two different simulations (depicting two different levels of relationships) show about two-way relationships in ecosystems?" Be sure that the following points come up:

• When something is eaten in the food web, there can be two-way effects. The process of energy flow is only one-way, like dominoes, but the nature of the interactions is two-way.
• Many populations affect each other.
• What seems bad on an individual level can be good on a population level.

Ask: "How are the two levels depicted in the two simulations similar?" Be sure that the following points come up:

• Both have a population that is getting eaten.
• Both show how the fates of populations are linked.
• Both show two-way effects.

Ask: "How are the two levels depicted in the two simulations different?" Be sure that the following points come up:

• Unlike animals, when grass or other plants are eaten, their seeds are often redistributed and can germinate. Being eaten actually benefits the individual plants. (This fits with how scientists think about the individual level. Students might not think that the grass would "like" being eaten but if what the grass "cares" about is making sure that it spreads its seeds, being eaten is a good thing.) When an individual rabbit is eaten, it can help the rabbit population stay in balance, but the individual rabbit does not benefit.
• When rabbits eat grass, the grass doesn't benefit in terms of population control. Grass doesn't crowd itself out. However, like a forest, the more trees there are, the less light, water, and nutrients there are for new trees to grow (and in the case of grass, being eaten can stimulate growth, too).
• When foxes eat rabbits, it is harder to see foxes as helpful to the cute little rabbits, than it is to see rabbits as helpful to the grass plants. It is also harder to see rabbits as "mean" for eating the grass.

Step 11: Review the Understanding Goals

Review the Understanding Goals for this section. As a class, consider why it is important to understand how populations interact and how their fates are linked. This is the focus of Section 6.