Homework for Session 4

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 logistic survival model when there are two interacting species, a herbivore and a carnivore, and the base trophic level, the plant population, is assumed to be constant.
  2. Prove that the logistic survival model for two species satisfies all the conditions for a plausible predator-prey model.
  3. Mathematically define the zero-growth isoclines for the logistic survival model with 2 species. Draw the isoclines and plot an approximate trajectory starting at a particular location in phase space.

Reading

Berryman, A. A. 1999. Alternative perspectives on consumer-resource dynamics: a reply to Ginzburg. Journal of Animal Ecology 68: 1263-1266.

Berryman, A. A. and A. P. Gutierreez. 1999. Dynamics of insect predator-prey interactions. In C. B. Huffaker and A. P. Gutierrez (Eds.). Ecological Entomology (pp. 389-423). John Wiley and Sons, New York.

Varley, G. C., G. R. Gradwell and M. P. Hassell. 1973. Insect Population Ecology: an analytical approach. Blackwell, London (pages 1-9).

Questions

  1. Describe the general survivorship model and its corresponding R-function.
  2. How does the general survivorship equation relate to Morris' "key factor" and Varley et al.'s "k-value"?
  3. What is meant by competition for enemy-free-space?
  4. What are fixed resources?
  5. What is the basic idea behind Royama's geometric model for competition and what is the mathematical result (I want the logic of Royama's analysis not mathematical details)?
  6. Describe the Ricker spawner-recruit model and its corresponding R-function.
  7. Describe the discrete logistic equation and its corresponding R-function.
  8. Derive Thompson's equation for survival from parasitoid attack.
  9. Describe the logistic model for any species in a food chain.
  10. Why is the logistic model considered to be ratio-dependent?