In the following lessons you will explore some of the principles of population ecology, the study of how animal and plant populations change over time and the factors that influence their numbers. In the first lessons you will study the logistic growth curve. This is a common mathematical model used to describe the growth of a population over time when the reproduction of individuals is influenced by density dependent factors.

In the last lessons you will explore the population ecology of the Gypsy Moth, a major insect pest in the Eastern United States. The ecology of this moth is very complex, and you will study some of the factors that influence the severity of the damage caused by Gypsy Moth outbreaks.

You will be expected to be familiar with the terms we have discussed in class such as carrying capacity, density independent and dependent factors, rate of growth, etc.

In addition, you will become familiar with using Microsoft Excel spread sheets as a tool for modeling population dynamics. Excel will be used throughout these lessons. If you do not have Excel on your computer at home, you will need to complete these lessons at school. The Excel spread sheets used in these lessons are modifications of similar ones created by Jim Breck of the University of Michigan.

Begin by selecting the lesson you want to study from the list below. Remember to use the answer form to email me your answers.

• Lesson 1: Logistic growth with fixed carrying capacity
• Lesson 2: Logistic growth with variable carrying capacity, your hypotheses
• Lesson 3: Logistic growth with variable carrying capacity, the experiment
• Lesson 4: The Gypsy Moth, background information

In the first lesson you will use the information you learned in class to study the influence of the rate of population increase (r), the carrying capacity (K), and the initial population size (N₀) on the shape of the logistic growth curve.

When you go to the Excel spread sheet, you will see a box in the upper left hand corner with four numbers highlighted in yellow. They are the initial population size, N₀, the rate of increase, r, the average carrying capacity, K_ave, and the standard deviation of the carrying capacity, K_std. These are the only four variables that you can change in this model. Since this first lesson will assume there is no variation in the carrying capacity, set K_std to .01 for all your work. This will set the variability in K very close to zero.

Now set N₀= 2, r= .1, and K= 200. Go to Graph 1 (tab at the bottom of the spread sheet)and view the resulting logistic growth curve. Note the general shape of the curve (the red line), especially the section where the population is growing and the time it takes the population to reach K.

Go back to Sheet 1 and change the carrying capacity to 400 and to 800 and view the new growth curves. Now do the same thing but with various combinations of r=.6 and K=400 and 800. Then repeat this procedure with N₀= 5 and 10. In all you should have viewed 18 different graphs. As you view these different growth curves, keep in mind the following questions.

• Does changing the carrying capacity, K, have any effect on the time it takes for the population to reach K? Explain.
• Does changing the rate of increase, r, have any effect on the time it takes for the population to reach r? Explain.
• Does changing the initial population size, N₀ have any effect on the time it takes for the population to reach K? Explain.

Excel Spread Sheet (right click & open in new window or save to disk)
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In the first lesson you studied the logistic growth curve when the carrying capacity, K, was held constant. You know that this is a very unrealistic assumption. In our region, the K of a population will vary tremendously from season to season. Even within a season factors such as temperature, moisture, and the number of predators in an area can fluctuate rapidly.

In lesson 3 you will study the logistic model and let K vary randomly around a set average value. This is still an over simplification of the "real world." But at least it recognizes that K is unlikely to remain constant. To do this you will set N₀= 2 and the average K=200 for all of your work. You then will change the variation in K by setting K_std from 0.1 to 100. Remember K_std is the standard deviation of the K values around its average. You will also vary the rate of growth, r, from 0.1 to 0.6.

In this model, if the carrying capacity drops to zero, that means the environment can no longer support the population and it will go extinct. Your task here is to use the information you obtained in the first lesson to make some well reasoned hypotheses concerning the relationships among K, r, and the chance that a population will go extinct because K has dropped to zero. Use the Answer Form link to send me a paragraph stating your hypotheses and your supporting explanations.

In particular, you need to predict what will happen to the chance that a population goes extinct as the variability in carrying capacity increases. Also, you need to predict if increasing the rate of growth,r, will increase or decrease the chance of extinction as the variation in K increases.

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In the previous lesson you made some hypotheses concerning the relationships among K, r, and the chance that a population will go extinct because K has dropped to zero in a logistic model that allows K to vary around some set average. In this lesson you will run this model and test your hypotheses

To do this you will use the same Excel spread sheet you used in lesson 1. In this case set N₀= 2 and the average K=200 for all of your work. Set r= 0.1 and K_std= 20. Go to Graph 1 to view the results. You will see three plots. The jagged blue line is the carrying capacity, K. It is fluctuating around the 200 mark because you set the average K to 200 and its standard deviation to 20. The yellow line is the expected logistic curve if K had remained constant at 200, and the red line is the actual logistic curve responding to the variation in K. If the population had gone extinct, the red line would have dropped to the zero point for the remaining generations plotted on this graph.

Hit the F9 key located in the top row of your keyboard. Notice that Excel recalculates a new graph using the same values. Do this for a total of 20 times and record how many times the population went extinct. Now go back to Sheet 1 and change the K_std= 40 and run Graph 1 20 times and record the number of extinctions. Repeat this for values of K_std= 50, 60, 70, 80, 90, and 100. Run each value of K_std 20 times and record the number of extinctions.

Now repeat this entire procedure for r= .3 and r= .6. You should have 24 data points. Add to this three more data points where K_std= 0 at r= 0.1, 0.3, and 0.4. You don't have to run the program for these last three points. They will all equal 0 since you know that the population can not go extinct if there is no variation in K. This gives you a total of 27 data points.

Use these data to evaluate your hypotheses from lesson 2. Use your email to send me your data and conclusions. We will pool all the class data for a more complete analysis of this experiment.

Excel Spread Sheet (right click & open in new window or save to disk)
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In this lesson you will be introduced to the Gypsy Moth, Lymantria dispar, and its ecology. This moth has caused tens of millions of dollars in damage to the eastern deciduous forests.  Efforts to stop or slow its spread across the United States have met with minimal success. The Gypsy Moth has a very complex relationship with the abiotic and biotic elements of its ecosystem. In this lesson you will be guided to a variety of web sites dealing with this insect pest and study the following general topics.

• The history of the moth’s introduction into New England and its spread across the eastern part of the nation
• The life cycle of the moth and how it actually damages the forests
• Natural predators and diseases of the Gypsy Moth
• Efforts to control the moth using biological agents

For a brief discussion of how this insect first entered the U.S. go to the Gypsy Moth in North America web site and click on the "Trouvelot" link. Email me answers to the following questions.

• Where was the Gypsy Moth first introduced into this country and where did it come from?
• Who was responsible for this introduction, and what was his motivation for bringing Lymantria to this country?
• Do you think that this type of deliberate introduction is the most common way unwanted foreign organisms are introduced into a new country today?  Explain.

Go back to the Gypsy Moth site and click on the "Spread" link to study changes in the moth's distribution since its introduction in 1868. Find the maps that show where Gypsy Moths populations were found in 1900, 1934, 1965, and 1994. Then find the map that predicts where the moth will be found by 2025 if control measures are not used.  If you want more detailed maps, you can go to this alternative link. Email me the following information.

• Has the rate of expansion of the moth's distribution remained constant since 1900?  Explain.
• For each of the five years (1900-2025) listed above, name the states where Gypsy Moth populations have been (or are predicted will be) found.
• Use these maps to prepare a graph that shows the relationship between time in years (independent variable) and the number of states reporting Gypsy Moth populations (dependent variable) between the years 1900-2025. Be sure your graph is appropriately labeled and formatted. Turn this graph into me at school.

Use the "Forest" link at the Gypsy Moth site and this Ohio State University site to learn about the life cycle of the moth and how it damages forests. Pay attention to the different stages of the life cycle and how the moth's activities interact with other elements of the forest ecosystem. Use the Answer Form to email me answers to the following questions.

• What are the four basic stages that the Gypsy Moth passes through during its life?
• Which of these stages is the one that survives over the winter?
• Which of these stages is the one that directly causes the damage to trees and how does it do this?
• Does this insect usually kill the tree directly or are there other factors at work that kill the trees? Explain.

Return to the Gypsy Moth site and click on the "Natural Enemies" link. Read about the various organisms that feed on the Gypsy Moth. Pay particular attention to which stage of the moth's life cycle is vulnerable to the various predators or disease agents. Email me the answers to the following questions.

• What predators or disease agents (if any) attack each stage of the Gypsy Moth?
• Which of these organisms do you think will kill the greatest numbers of the moth each year? Explain.
• What is the relationship between moisture in the environment and the activity of the fungus and other predators or diseases?

One last time go to the Gypsy Moth site and click on the "Management" link. Here you will find information and other links dealing with efforts to control the spread of the Gypsy Moth. Pay special attention to the distinction between "biological" and "chemical" control methods. Email me answers to the following questions.

• What is the difference between a "biological" and a "chemical" control method? Give an example of each.
• What are some of the organisms that scientists are trying to use in the biological control of the Gypsy Moth?
• Why are scientists looking in Europe and Asia for Gypsy Moth biological control agents?
• Suggest a reason why this strategy of using predators or disease agents from the moth's native range poses potential dangers to the U.S. forest ecosystems.

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Excel Spread Sheet (right click & open in new window or save to disk)

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