Instructions

• First, do your reading assignment.
• Next, go through Session 1 on the Internet making rough notes and questions you want answered.
• Then try to do the exercises and note any problems you want to discuss.
• Discuss problems or questions with you instructor in person or by e-mail.
• Make a final draft of your notes for this session in your notebook.
• Send a copy of your notebook covering this session to the instructor if you wish or save it until the end of the course.

Reading

• Berryman, A. A. 1997. Chapter 4 in Principles of Population Dynamics.
• Allee, W. C. 1931. Chapters 1 and 2 in Animal Aggregations. A study in General Sociology. Univ. Chicago Press.

Exercise

1. Use a spreadsheet such as Excel to simulate the dynamics of a population under the 2^nd principle using the appropriate R-function with parameters set at A = 1, W = 10, P = 11, F = 10, N₀ = 99, then with N₀ = 101. Calculate the escape threshold for P = 11, 21, 41. For information on how to execute these simulations, click here. Plot the trajectory on both arithmetic and logarithmic scales. Try several simulations starting with 101 individuals but including random environmental disturbances in the R-value (use the algorithm (RAND()+RAND()+…repeat 10 more times…) - 6 to generate a random standard normal deviate in Excel).
2. In 1 page or less review your reading of Allee (1931).

The type of questions that may appear on the next examination are:

1. What is a feedback function?
2. What is an R-function?
3. Why do we use the logarithms of population density to calculate the value of R?
4. What does the shape of the R-function tell you about the feedback operating on a population?
5. What is the 2^nd principle of population dynamics.
6. What is meant by intraspecific cooperation?
7. What is the law of increasing returns?
8. Distinguish between adapted and incidental cooperation.
9. What kinds of adapted traits result in intraspecific cooperation within a population?
10. What is an underpopulation or Allee effect?
11. Explain how difficulty in finding mates affects the shape of R-function.
12. Explain how the Allee effect can create an unstable threshold.
13. What is an extinction threshold?
14. What is the behavioral response of a predator?
15. Why is it called a cyrtoid behavioral response?
16. How did Holling derive his equation for the cyrtoid behavioral response?
17. How did Ivlev derive his equation for the cyrtoid behavioral response?
18. How does the cyrtoid behavioral response affect the per-capita death rate of the prey?
19. When the 2^nd principle is dominant what happens to the shape of the R-function?
20. Explain how the cyrtoid behavioral response of a consumer can create an unstable equilibrium.
21. What is an escape threshold?
22. What is a population threshold?
23. How can you recognize the dynamics of a population obeying the 2^nd principle?
24. How is the probability of a prey individual being killed by predators affected by the densities of predators and prey and by the demand of the predators for prey?
25. Derive a mathematical model for the R-function of a population under the influence of the 2^nd principle.
26. Explain the basic idea behind Thompson's parasitoid attack model.
27. What is the Poisson distribution?
28. What did you learn from your reading of Allee's book?

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