BISC 407 SAMPLE FINAL EXAM QUESTIONS 1. An equation describing the growth of the Spruce Budworm is given below: 3 dN N = r N (1− ) − P ( N ) = f ( N ) dt K 2 P N P ( N ) = 02 A +N 2 2 1 0 0 10 20 30 40 -1 Where, P(N) is the predation term with a fixed number of predators (P0). a) The graph shows f(N) as a function of N. On the graph indicate the equilibria and whether they are stable or unstable. b) What happens to the population if the initial population is 10 units? c) Explain the biological assumptions underlying the P(N) predation term. Name two other types of predation terms and describe the biological assumption for each one of them. d) Sketch the three different predation terms from c) as a function of N and label them. 2. Two sibling species of Bufo are brought together through flooding of a plain that once housed each species in separate ponds. You estimate the carrying capacity of the new pond to be 5000 for each species. While morphologically identical, the species are known to differ in that One species is a voracious carnivore on young larvae while the second species is not. Competition coefficients derived from lab studies are α21 = 2.1 and α12 = 0.8. What is the probable outcome of competition between these two species? Illustrate graphically. Can you predict the outcome without graphing? Explain. 3. Explain the Relative Yield Graphs below. Predict the outcome of competition. 4. You study at an orchard where hosts and parasitoids interact in a mostly typical fashion except for one thing: due to agricultural activities, 8 of the 48 trees are inaccessible to the parasitoids whereas all trees are available to the caterpillar hosts. Provide a Nicholson-Bailey type model that takes this phenomenon into account. What are the implications for this type of system and what might you tell the owner of the orchard? 5. Develop a model for a mechanically-transmitted human viral disease that is vectored by a flea. By mechanically vectored, I mean that the virus does not replicate inside the flea but rather virus particles sit on the flea’s mouthparts and move into the human’s bloodstream during feeding. As such, viral particles are lost from the flea (feeding or otherwise) at the rate δ. Upon transmission from flea to human, there is a 2-day incubation period whereupon humans shed viral particles into their blood stream. Fleas pick up the particles while bloodfeeding. Infectious humans are quite ill and die at a rate that is far higher than for healthy humans. Only a small proportion of infected humans ever recover and those that do develop a lifelong immunity. Explain the structure of your model and any underlying assumptions. 6. In class we examined the effect of fluctuations in carrying capacity on a population following logistic growth. Recall the model we used: N t +1=N t +r d N t (1− N t / κ) where κ ~ N(K0,σ) We can think of these fluctuations in K as arising from process error within the system. a) What is wrong with how this model, in its current form, incorporates error? b) Explain what you would need to do to correct the model, and make the necessary changes.