# Limiting factors and models of population growth (1 of 2)

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## Objective

Students will be able to 1) categorize factors that limit population growth as density-dependent or density-independent; 2) define carrying capacity; and 3) accurately predict how density-dependent factors will limit the growth of populations.

#### Big Idea

Factors that affect population size can be density-dependent or density- independent. How might we use modeling to understand the impact of each type of factor on population growth?

## FRAME: What are the limits of population growth?

How does a population grow? Students have just developed an essential vocabulary of population ecology. In "Limiting factors and models of population growth" students will explore the cause and effect relationships among these terms. Students will also learn about how these populations grow over time and how environmental scientists model this growth. Why don't population sizes become infinitely large? How can population density work against population growth?

In the first lesson, students explore factors the limit population growth. They will look at the West Nile Virus, dense cities, and natural disasters. From these examples, students will develop a definition of carrying capacity. Finally, students will use online modeling software to identify cause and effect relationships among limiting factors and population growth.

In the second, students expand their understanding of population growth to include mathematical representations of exponential and logistic growth. Students will graph real historical data of American bison and work through a case study of the population dynamics of African lions. Students will also respond to a series of assessment questions to check for understanding.

Over the course of two lesson, successful students will have met the following objectives:

1. categorize factors that limit population growth as density-dependent or density-independent;
2. define carrying capacity
3. accurately predict how density-dependent factors will limit the growth of populations
4. distinguish between an exponential and logistic growth model
5. draw exponential and logistic growth curves
6. identify exponential and logistic growth in populations of American Bison and African Lions.

## FLIPPED: West Nile

What is the purpose of this section?

Students will preview the concepts that will be explored in this lesson. By the end of this assignment students should have described the spread of virus using population ecology terminology.

What will students do?

Using the service videonot.es, students take notes from a Crash Course Ecology episode. Here are the student tasks:

• Develop a content summary every two minutes
• Develop a final short paragraph summary of the main ideas
• Explain how population ecology help us to explain the spread of West Nile Virus.
• Develop one question about the content.  What was confusing?

Here is the episode:

## ENGAGE: Thought question

8 minutes

What will students do?

Students revisit the idea of population density.  As they watch the short clip below about dense urban environments, they respond to the following thought questions:

• What are some of the consequences of living in densely populated areas? What tasks are easy? What tasks are hard?
• Will these cities be able to support more and more people forever?

Students record responses, share them in groups, and then groups share out composite responses with the class. Finally, students will discuss cities through the lens of the FLIPPED assignment through teacher-facilitated discussion. What can happen when many members of a species live in the same place?

What will teachers do?

This task requires understanding of population density. Teachers may need to frame the task by reminding students of the population density definition from the prior lesson. Teachers may also want to reference the model of West Nile Virus spread from the FLIPPED assignment. If students live in a dense urban area like New York City, teachers should ask simple questions about daily tasks to prime students' thinking about what life is like in a densely populated area.

## EXPLORE: Population campaigns and natural disasters

12 minutes

What is the purpose of this section?

Students will examine resources that provide information about density-dependent and density-independent factors, but do not provide explicit definitions.  By the end of this section, students should be able to develop tentative definitions of density-dependent and density-independent factors using provided examples.

What will students do?

1) Examine this overview of population control campaigns from China, India, and Kenya. Each of these countries decided to limit population growth.  Why?  Scientists would explain that each country decided to limit population growth because of "density-dependent limiting factors"?  What do you think density-dependent limiting factors are?

2) Read this brief article about a 2015 oil spill in the Galapagos.  What are the negative consequences of the oil spill?  Why?  Scientists would explain that the oil spill threatens multiple species because it is a "density-independent limiting factor"?  What do you think density-independent limiting factors are?

What are the key teacher moves in this activity?

The key teacher move in this activity is to provide basic clarification of dependent and independent and to push students' thinking during small group or individual conversations. What does it mean to be dependent? What does it mean to be independent? Where do you find evidence for claims about resources?  Is that the only possible explanation?

## EXPLAIN: Definitions and carrying capacity

15 minutes

What is the purpose of this section?

Students will norm understanding of key concepts--density-dependent limiting factors, density-independent limiting factors, and carrying capacity through discussion and modeling. By the end of this section, students should have a basic definition for each concept as well as a visual representation.

What will students do?

TASK 1: The whole class will share out proposed definitions from the EXPLORE activity.

TASK 2: Next, we will collectively view a clip explaining carrying capacity and develop a definition of carrying capacity as well as a description of a graph of carrying capacity.

A sample definition from Emily N.: "The graph of a population at is carrying capacity looks like it will go beyond the carrying capacity and then it will somewhat dwindle. This means the population also can’t grow anymore and stays at a constant rate on the carrying capacity. Basically the density dependent and density independent factors create the carrying capacity."

TASK 3:  Construct graphs of carrying capacity using the DRAW function in Google Docs. ACCESS “DRAWING” FROM THE “INSERT” MENU.  USE THE “LINE” AND “SCRIBBLE” FUNCTION TO CONSTRUCT YOUR DRAWING.  “SAVE AND CLOSE” TO AUTOMATICALLY INSERT YOUR DRAWING IN THIS DOCUMENT.

STUDENT WORK SAMPLES:

No limiting factors:

Description of graph (Why does this graph have this shape?):

The graph has this shape because there is no limiting factors. This shows that when there are no limiting factors than the population will have an instant boom because there is no factors to keep the population in check.

Density-dependent:

Description of graph (Why does this graph have this shape?):

This graph has this shape because it depends on the resources that it has. Like if there are a lot of resources it will be steep but if there are not resources it won't be steep.

Density-independent:

Description of graph (Why does this graph have this shape?):

The graph has this shape because the population is likely to go down because density-independent factors usually have to do with the climate and how this affects the environment.

Stabilized around carrying capacity:

Description of graph (Why does this graph have this shape?):

This graph has this shape because it shows a stable population of decrease and increase. It will never really grow but the population is stable regardless of the increase and decrease.

What will teachers do?
The primary teacher move here is to support students' construction of graphs. Many students will produce different visuals. Rather than providing corrective feedback, a more effective teacher move is to let students with different ideas communicate their understandings and negotiate with each other. The whole class will norm this work through teacher-facilitated direct instruction so students will not finish this activity having negotiated an incorrect answer. Students will deepen understanding of these concepts during the next lesson.

## ELABORATE: A model of carrying capacity and species interactions

15 minutes

What is the purpose of this activity?

Students will explore a model to understand how species interactions and other density-dependent and density-independent factors influence population growth and carrying capacities.

What will students do?

Students will manipulate variables in this model of population interactions to explore population ecology ideas developed in this lesson. To do this, they will complete the following tasks:

TASK 1: Students will identify the species that will be interacting from this short reading.

• What are the populations represented in the simulator?
• What is the goal of the simulation?

TASK 2: Students will manipulate variables in this model of population interactions to assess the influence of populations on each other. Student read the "learner" tab from the simulation activity for help with what to manipulate. During this exploration, students will answer the following questions:

• What would happen if there were lots more bunnies than wolves? Would the bunnies take over and live forever?
• What would happen if there were lots more wolves than there are bunnies? Would the wolves live forever?
• How do the rabbits and wolves live in balance in this game?
• What are the density-dependent factors? How do they change the carrying capacity of the different population?
• There are not density-independent factors in the game. If there were, what might they be and how would they influence the growth of these populations?

RESOURCES NOTES:

• Educators may want to extend this analysis through exploration of the competitive exclusion principle explored by Gause (concise definition). Resources for such work is included.
• Educators wanting a pen and paper "simulation" may want to try a modified version of this lab examining the reindeer of St. Matthew Island.

## EVALUATE and EXIT: practice problems and enrichment

5 minutes

As a check for understanding, students complete the questions from the PROTOTYPE ACTIVITY GUIDE and summarize the clip below using vocabulary terms from this lesson. The check for understanding questions must contain explanations of student responses; otherwise their value as a formative assessment is greatly reduced and teachers have fewer opportunities for specific feedback. An example from a student is included in the RESOURCES section.

Here is the clip: