Instructions

• First, do your reading assignment.
• Next, go through Session 6 on the Internet making brief notes on the subject matter, including any problems or questions you have concerning your understanding of the material.
• Next, 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 7 in Principles of Population Dynamics.
• Paine, R. T. 1992. Food-web analysis through field measurement of per-capita interaction strength. Nature 355: 73-75.
• Berryman, A. A. 1993. Food web connectance and feedback dominance, or does everything really depend on everything else? Oikos 68: 183-185. (optional reading)

Exercises

1. Simulate the dynamics of a population obeying the time-delayed logistic equation

when A = 1, C = 0.001, Q = 1 and d = 1, 2, 3, 4 in a constant and noisy environment. Describe the effects of time delays on the dynamics of the single-delay logistic. You can do this on a spreadsheet or using PAS single-species program P1b. (see example in figures with s = 0 and d = 1, 2, 3, 4)

2. Simulate the dynamics of a population governed by two R-functions separated by an unstable threshold using a spreadsheet or the PAS single-species analysis program P1b.

when the parameters for the high-density R-function are A = Q_K = d_K = 1, C_K = 0.0001, for the low-density R-function are Q_J = d_J = 1, C_J = 0.001, the escape threshold is E = 3000, and the initial density of the population is 3000. Run many simulations with different levels of environmental noise (see figures with s = 0.4 and s = 0.6). Calculate the equilibrium points J and K.

3. Repeat exercise 2 with all parameters the same except d_K = 2 (see figures with s = 0.4 and s = 0.6). Describe the dynamics of population systems governed by two stabilizing processes separated by an unstable threshold when time-delays are present or absent in the stabilizing mechanisms and with different levels of environmental variability.

4. Review the ideas developed in papers by Berryman and Paine in your reading assignment.

Examples of the kind of questions that may appear on the examination are:

1. What is the 5^th principle of population dynamics?
2. Under what conditions does the 5^th principle operate?
3. What is meant "feedback dominance"?
4. What empirical and theoretical support is there for the concept of feedback dominance?
5. What is a "limiting factor" and how is it related to Liebig's law of the minimum?
6. What is the connection between the concepts of feedback dominance and limiting factors?
7. What is meant by "food web simplification" and how is the concept relevant to feedback dominance?
8. What is meant by the concept of "keystone predators" and how is it relevant to feedback dominance?
9. What is meant by the expression "hierarchy of limiting factors"?
10. Why do ecological systems have a high degree of temporal stability?
11. What determines the shape of the R-function?
12. What is the difference between a first order and second order system?
13. What is the relationship between the order and the dimension of a dynamic system?
14. How does the 5^th principle simplify the R-function for a system of order d?
15. Define the general stability criteria for the general nonlinear logistic equation with time lags.
16. How do time delays affect population dynamics?
17. Describe two ways by which feedback dominance can change in space and time?
18. Describe the conditions that give rise to R-functions with more than one stablizing equilibrium.
19. How does environmental variability affect the dynamics populations governed by R-functions with two stabilizing equilibria?
20. Why do populations with two stabilizing equilibria spread through space?
21. Discuss Paine's ideas of keystone predators and strong interactions in relationship to the 5^th principle.

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