Instructions

• First, do your reading assignment
• Next, go through Session 5 on the Internet making rough notes and questions you want answered.
• 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 6 in Principles of Population Dynamics.
• Berryman, A. A. 1978. Population cycles of the Douglas-fir tussock moth (Lepidoptera: Lymantriidae): the time-delay hypothesis. Canadian Entomologist 110: 513-518.
• Berryman, A. A. 1986. On the dynamics of blackheaded budworm populations. Canadian Entomologist 118: 775-779. (optional reading)

Exercise

1. Simulate the dynamics of predator and prey automata using the PAS Predator-Prey Game PG3 (see here for an example). It is also possible to program a computer to perform the simulations (click here for information). Simulate the dynamics on various sized lattices and under different degrees of environmental stochasticity (random mortality).

1. Describe the spatial and temporal dynamics you observe.
2. How does the size of the lattice affect the stability of the system?
3. How does environmental stochasticity affect the stability of the system?
4. Try starting the simulation with lots of prey and few predators in one corner of the board. This situation mimics the accidental introduction of a pest, and the later release of its predators to control it, commonly called classical biological control. Describe the dynamics you observe.

B. Simulate the dynamics of a reactive predator-prey interaction using the R-functions for two interacting species with parameters A_P = A_N = 1, C_P = 0, C_N = 0.002, C_PN = 6, C_NP = 4, F = 0, N₀ = 180, P₀ = 20 (see here for details). Simulations can be executed on a spreadsheet or with the PAS two-species modeling and simulation program P2b.

1. Plot the time trajectories and phase portrait (see figures of simulation using Microsoft Excel spreadsheet).
2. Repeat the above simulation only this time include random environmental variation acting on the prey population (e.g., s_N = 0.1). Plot the time trajectories and phase portrait and describe the dynamics that you observe.
3. Calculate the zero growth isoclines for each species (click here for methods) using the same parameters and plot the isoclines in phase space (see figures for Excel plots). Note that PAS program P2b can also be used to plot isoclines. Draw in the vectors of population change in phase space and label the community equilibrium.
4. Analyze the sensitivity of the model by changing the values of the predator parameter C_PN to 1 and 0.8. Discuss the sensitivity of the model to this parameter. How does the position of the community equilibrium on the prey isocline affect the dynamics of the predator-prey interaction? Explain why the dynamics is highly sensitive to the position of the community equilibrium on the prey isocline. (Click here to see results of general sensitivity analysis).

Examples of the kinds of questions that may appear on the next examination are:

1. What is the 4^th principle of population dynamics?
2. What is a circular causal pathway?
3. What is a passive environmental factor?
4. Give some examples of passive environmental factors.
5. What is a reactive environmental factor?
6. Give some examples of reactive environmental factors.
7. What is the maternal effect?
8. What conditions need to be met before an environmental factor can be considered reactive?
9. How can the R-function for a consumer be extended to include reactive environmental factors?
10. Derive the R-function for a reactive prey population being consumed by a predator population.
11. What is meant by a ratio-dependent equation?
12. How does the 4^th principle affect population dynamics?
13. What is predator-prey phase space?
14. What is a zero-growth isocline?
15. How can you calculate the isoclines for a particular model?
16. What is a community equilibrium?
17. How are dynamics affected by the position of the community equilibrium on the prey isocline?
18. What is meant by the order of a dynamic system?
19. What is a first order difference equation?
20. What is a second order difference equation?
21. How do the parameters of the consumer-resource model affect the position on the community equilibrium?
22. What is "top-down" and "bottom-up" control?
23. What is the Lotka-Volterra equation and how does it differ from the logistic model?
24. Discuss the dynamics of the Douglas-fir tussock moth (or blackheaded budworm) with reference to the 4^th principle of population dynamics.

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