STUDENTS: Type the answers to the exercises and questions neatly and hand them in or e-mail them to your instructor before the next session.

Exercises

1. Write the equations for the Gutierrez metabolic pool model with Ivlev-Watt functional responses for two interacting species, a herbivore and a carnivore, when the plant population is assumed to be constant.
2. Prove that the Ivlev-Watt-Gutierrez metabolic pool model for 2 species satisfy all the conditions for a plausible predator-prey model.
3. Mathematically define the zero-growth isoclines for the Ivlev-Watt-Gutierrez metabolic pool model with 2 species. Draw the isoclines and plot an approximate trajectory starting at a particular location in phase space.
4. Write the equations for a metabolic pool model with Holling "disk" functional responses for two interacting species, a herbivore and a carnivore, when the plant population is assumed to be constant.
5. Prove that the metabolic pool with "disk" equation for 2 species does not conform to all the conditions for a plausible predator-prey model.
6. Mathematically define the zero-growth isoclines for the metabolic pool model with "disk" equation and 2 species. Draw the isoclines and plot an approximate trajectory starting at a particular location in phase space.

Reading

1. Gutierrez, A. P. 1996. Applied population ecology: a supply-demand approach. John Wiley, New York (pages 64-103).
2. Watt, K. E. F. 1959. A mathematical model for the effect of densities of attacked and attacking species on the number attacked. Canadian Entomologist 91: 129-144.
3. Royama, T. 1971. A comparative study of models for predation and parasitism. Researches on Population Ecology, Supplement No. 1 (pages 55-57).

Questions

1. How did Ivlev derive the functional response of a consumer?
2. How does Watt's derivation of the consumer functional response differ from that of Ivlev?
3. What is the general food chain equation that forms the basic structure for the metabolic pool model?