Biology Lessons Part 2: Population Biology


 Lesson 2.7: How Do Populations Grow?

To Ponder
Introduction and Background
Supplementary Resources
AAAS Benchmarks
Exercise 1: A Lily Pad Puzzle
Exercise 2: Growth of the Lily Pad Population
Exercise 3: Exponential Growth of Populations
Exercise 4: Carrying Capacity of the Ecosystem
Exercise 5: How Do Populations Affect Each Other?
Exercise 6: The Delicate Balance of Ecosystems Simulation

Grade Level

Prospective and Practicing K-8 Teachers; may be adapted for use in K-12 classes


Exercises 1 and 2 will take approximately 2 hours.

To Ponder


What is a population?


2. How big can a population grow? Can it keep expanding forever?

How do growing populations affect surrounding communities?




These are some materials you may want for the sample experiments supplied with this lesson.

For each group of 3 to 4 students:

  • 64 index cards
  • 4 pairs of scissors
  • a ruler or yard stick
  • masking tape


    Once you have completed this lesson you should be able to:


Define population, exponential growth, carrying capacity, population crash, S curve, J curve, ecosystem.
  2.  Describe how populations grow and how the carrying capacity of an environment controls the growth of populations.
  3. Describe how invasive species can affect the balance of ecosystems.



Ecologists study the size and rate of growth of populations in order to predict how they will change with time. By learning how and why a population of birds, plants, or fish thrives or dies out in a particular area, ecologists can understand the delicate balance of the earth's ecosystems and how humans affect this balance. This lab has several activities and exercises which demonstrate how populations grow and how





Exercise 1: A Lily Pad Puzzle


Lily pads can grow fast. Imagine that you discover a variety of lily pads that can double in number every day. It takes 10 days for them grow to cover a pond halfway.


Question 2.

How many more days will it take for the lily pads to completely cover this pond? (Circle one.)

a) About 10 more days

b) About 5 days

c) Tomorrow

d) Never, since the lily pads won't ever fill up the pond completely



Why do you think this?


Exercise 2: Growth of the Lily Pad Population

   To Do

1. Work in groups of 3 to 4 students. Imagine that your lab table or desk is the surface of the pond in your backyard. Using a ruler, measure a square, 48" X 48" on your desk or lab table. Place masking tape down to mark the edges of your "pond."
   2. Get 64 index cards (3" X 5") from your teacher. Pretend that each card is a lily pad.
    3. Lay one card in the corner of the "pond" to represent the first lily pad.

Now pretend that a day has passed. Double the number of lily pads in your pond.

   5. Pretend another day has passed and double your lily pad population again.
   6. Keep on doubling the population until half of the entire surface of the pond has been filled.
Question  7. How many lily pads does it take to fill half of your pond?
   8. How many days passed before half of the pond was filled with lily pads?

How many more days will pass before the entire pond has been filled?


 To Do 10.

Repeat the demonstration, this time carefully counting up how many lily pads are present in each generation. Use Table I below to keep track of your data.

Table I: Lily Pad Population
Generation (Number of Days)   Number of New Lily Pads  Number of Lily Pads in the Population


Now make a graph of your results, using Figure 1 as a guide. Generations should be along the x-axis and total number of lily pads in the population should be on the y-axis.

Figure 1: Growth Curve for the Lily Pad Population


 Question 12.

Is this graph linear, or does it increase more or less rapidly than a linear graph?


Figure 1A: Exponential Growth Versus Linear Growth

Background 13. In Thailand, water plants such as lily pads are a daily problem citizens must cope with. Since cities are build around waterways, people often commute using boats and ferries instead of cars. The outboard engines are frequently getting clogged with lily pads, which grow quickly and are hard to eliminate.

Exercise 3: Exponential Growth of Populations

 Background  1. The rate at which the lily pad population started to grow after several days was quite alarming. If you are to keep any of your pond clear, you'll have to cut out more than half of the lily pads out of the pond every day! WHEW!
2. The graph you have constructed represents exponential growth. It is called a "J-curve". Exponential growth occurs when there no limits to the size to which a population can grow. Food, water, and living space are some of the resources individuals need to live healthfully and to reproduce to their maximum potential. When such resources are unlimited, populations may undergo exponential growth.
3. Some characteristics of exponential growth curves are slow initial growth and then a rapid, dramatic population "explosion" after several generations.

There are several factors affecting the shape of the growth curve.

  • reproductive rate (number of new organisms produced compared with number of deaths)
  • limits on resources: food, water, living space
 Question  5. What is the reproductive rate of the lily pads? (Hint: how many "offspring" does each lily pad produce per day?)

Is there a maximum number of lily pads that can grow in your pond?



Powerful Idea


Resources and space are typically limited in ecosystems. Exponential growth generally occurs only when the population is very small relative to available resources or very aggressive in taking resources away from other populations.




 Background 7.

Here is a graph of human population growth on the entire earth from 10,000 B.C. to the present.

Figure 2: World Population Growth, Source, PopExpo

Question  8.

How would you describe the growth of the human population today?

  9. What conditions do you think kept the human population lower and more under control before this century?
before now

Exercise 4: Carrying Capacity of the Ecosystem

 Background  1.

As you may have predicted, there is a maximum number of lily pads that can grow in your pond. This is called the carrying capacity. There are several factors which limit the carrying capacity of any environment. Some of them are:

  • climate
  • food and water availability
  • physical space
  • disease
  • predators



Figure 3 shows what happens to a population when it reaches the carrying capacity of the surrounding environment. This is called an "S curve" because it is roughly shaped like an "S".

Figure 3. "S curve" for a hypothetical population

 Question 3. Examine the first half of the "S" curve shown in Figure 3 (up to point A). What is the shape of this graph?
  4. What happens at point B (after about 13 generations)?
  5. What is the carrying capacity of the population recorded in Figure 3 (about how many organisms of this species can be supported in this ecosystem)?

What is the carrying capacity for the lily pad population in the pond environment referred to in Exercise II?


 Background 7.

If there is a sudden change which affects the amount of available resources (for instance, a drought or a frost) a population which is growing exponentially may experience a dramatic decrease in size. This is called a population crash. Some populations experience cycles of exponential growth followed by crashes. This pattern is called boom and crash and is illustrated in Figure 4.

Figure 4. "Boom and Crash" Pattern of Population Growth

Question 8. What happens at point "A"? What happens at point "B"?
 Background 9. Sometimes a population drops to zero when it crashes. An example is the Hohokam tribe in central Arizona, which lived there more than 2,000 years ago. Experts believe that the population was at one time over 1 million people, but somehow the entire Hohokam culture vanished.
 Questions 10. What was the carrying capacity of the earth for the human population prior to 1850 (see Figure 2)?

What is the carrying capacity of the earth for the human population today?

We don't know what the carrying capacity is because it hasn't been established yet.


Can a population grow exponentially forever?



Exercise 5: How Do Populations Affect Each Other?

 Background 1. In the early 1900's, wild rabbits were taken from England to Australia to be used for hunting. Since then, rabbits have multiplied exponentially and have severely affected the ecosystem where they live. The total damage done by wild rabbits in Australia is estimated at $600 million dollars. The loss of vegetation from rabbit grazing threatens the survival of native birds, mammals, and insects that rely on plants for food and shelter. Wild rabbits compete with livestock for available pasture and kill young trees and shrubs. The holes they dig contribute to soil erosion by removing vegetation and disturbing soil.
 Question 2.

Why doesn't this problem occur happen in the U.S. or in Europe, where the rabbit population remains at a relatively constant size?


 Background 3. In 1996, Australia was thought to have around 300 million rabbits. In order to reduce the rabbit population, an anti-rabbit virus called myxomatosis was released in 1950.
  4. In what ways are the rabbits in Australia similar to the lily pads mentioned in Exercise 1?

Exercise 6: The Delicate Balance of Ecosystems Simulation

 Background 1. Ecosystems are communities of organisms interacting with a particular environment. Invasive species can throw off the delicate balance of an ecosystem, destroying several species in the process. We are going to simulate the give-and-take of an imaginary ecosystem and observe what happens when the "delicate balance" of this ecosystem is corrupted.

A very simplified food chain is diagrammed below, which will serve as the basis for our simulation.


  3. Here are some general rules for this simulation:
    I.  Every generation, the number of producers doubles. Assume that the plant population has enough sunlight, carbon dioxide, and water to produce new organisms.
    II. Every generation, each native herbivore eats one plant to survive. Two native herbivores produce one new offspring each generation if they both consume one plant.
    III. Every generation, each predator must consume two native herbivores in order to survive into the next generation. The predators are capable of surviving for many generations.
    IV. Once an invasive herbivore enters the ecosystem, it is able to consume plants before the native herbivores can. The invaders each eat one plant every generation. Two invasive herbivores produce two new offspring each generation if they each have consumed one plant.

The invasive herbivores have no natural predators.

 To Do 4. Have someone from your group cut out the playing pieces in your lab book. You need only one set of pieces (from one student's lab). Lay all of the cut out pieces out on your lab table.


  5. Next, divide up the tasks. Each member of the group is in charge of one population in the community: producers, native herbivores, predators, or invasive herbivores. Each member collects all of the playing pieces of their population and keeps them nearby.

Begin the simulation of the community in balance. The populations used in this first simulation are:

  • producers
  • native herbivores
  • predators
  7. The member in charge of producers starts by laying out 8 producers. Refer to the rules. What happens to this population of producers after one generation has passed?
  8. The member in charge of native herbivores lays out 8 pieces. How many producers will this population consume in one generation?

How many new offspring will the native herbivore population produce?


  10. The member in charge of predators lays out the 2 pieces. How many native herbivores will be eaten?

This completes one cycle of the simulation. Repeat steps 5-8 to go through another generation, this time writing down in Table 3 the number of producers, native herbivores, and predators you began with, and how many are remaining after one cycle of play. Compare these numbers to other groups nearby.

Table 3: Population Size at the Beginning and End of One Generation
  start finish
native herbivores    


Now repeat the simulation including the invasive herbivores. Pretend they have been brought into the area by humans. The populations used in this simulation are:

  • producers
  • native herbivores
  • predators
  • invasive herbivores
  13. Begin this simulation with 8 producers, the same as before. The number of producers doubles.
  14. Begin with two invasive herbivores. This time, the invasive herbivores eat the producers before the native herbivores. Refer to the rules. How many producers will the invasive herbivores eat? __________How many offspring will the invasive herbivores produce? _________
  15. The simulation begins with 8 native herbivores. The native herbivores eat after the invasive herbivores do.
  16. Next the predators eat prey. How many native herbivores remain after the predators have eaten? _________How many invasive herbivores remain? __________
  17. Go through another round of play. Start with the producers. Double the population size.

Next the invasive herbivores eat the producers. How many are eaten? ______How many new offspring are produced? ______How large is the total population of the invasive herbivores now? ______

  19. The native herbivores eat. How many producers are consumed? ______Then the predators hunt. Try to complete another round. What has happened?
Question 20. What happened to the population of producers?
  21. What do you predict will happen to the predator population? Why?

Why was the invasive herbivore population allowed to grow out of control?


  23. What is your prediction for the human population on earth? Do you think it will level off when it reaches its carrying capacity, or do you think it will crash? Choose one of these two scenarios and describe how and why you think changes will occur.

We are currently in the midst of what is described as the sixth major extinction on earth. That is, in the earth's history (4.5 billion years) there have been five other periods when species went extinct at the rate they are today. Do you think there is any relation between the exponential growth of the human population and the high extinction rate? Explain.





Postlethwait, J. H. & Hopson, J. L. The Nature of Life, Third Edition. San Francisco: McGraw-Hill, Inc. 1995.

Stefoff, Rebecca. Overpopulation (Earth at Risk). New York: Chelsea House Pub. 1992.

Gotelli, Nicholas J. A Primer of Ecology. Sunderland, MA: Sinauer Associates, Inc. 1995.

Brown, Lester R. , Hal Kane, Al Kane (Contributor). Full House : Reassessing the Earth's Population Carrying Capacity (The Worldwatch Environmental Alert). New York: W.W. Norton & Company. 1994.

Related AAAS Benchmarks


Section A: Diversity of Life

Grades 9-12 Benchmark 1 of 2

The variation of organisms within a species increases the likelihood that at least some members of the species will survive under changed environmental conditions, and a great diversity of species increases the chance that at least some living things will survive in the face of large changes in the environment.

Section D: Interdependence of Life

Grades 3-5 Benchmark 4 of 5

Changes in an organism's habitat are sometimes beneficial to it and sometimes harmful.

Grades 6-8 Benchmark 1 of 2

In all environments--freshwater, marine, forest, desert, grassland, mountain, and others--organisms with similar needs may compete with one another for resources, including food, space, water, air, and shelter. In any particular environment, the growth and survival of organisms depend on the physical conditions.

Grades 9-12 Benchmark 1 of 3

Ecosystems can be reasonably stable over hundreds or thousands of years. As any population of organisms grows, it is held in check by one or more environmental factors: depletion of food or nesting sites, increased loss to increased numbers of predators, or parasites. If a disaster such as flood or fire occurs, the damaged ecosystem is likely to recover in stages that eventually result in a system similar to the original one.