Here are some additional math-type questions to help you study for the exam:
- Three years in a row, the Biology 203 class takes a field trip to New Zealand to determine the population size of tuataras. In the first year, they discover 200 individuals. In the second year, they find 175 individuals, and in the third year, they find 181 individuals.
- Does this population show density-dependent, or density-independent population growth. Defend your answer quantitatively.
- At what population size would you keep these tutataras if you were interested in collecting tuatara eggs to sell to pet shops?
- You are studying competition between red (N1) and black (N2) scorpions, characterized by the set of competition equations:
dN1/(dtN1)=.5-.005*N1-.01*N2
dN2/(dtN2)=1-.01*N2-.03*N1 - Suppose the initial population sizes are 25 red scorpions (N1) and 50 black scorpions (N2). Graph the phase-plane isoclines and plot these initial population densities.
- Predict the short-term and final outcome of the interspecific competition.
- In a paper published in the journal Science, Kareiva et al. (2002) used age-structured models (analogous to life-tables) to evaluate management strategies for Chinook salmon in the Columbia River Basin. Salmon are both semelparous and anadromous. After hatching in freshwater, Pacific salmon migrate to the ocean to feed until maturity. Ultimately, they return to their natal stream to spawn and then die. Salmon can reach maturity in their 2nd year, but typically reach maturity in their 4th year. Using the Nx values, 1000, 13, 10, 8.25, 5.5 and the mx values, 0, 0, 0.33, 5, 40 corresponding to the age classes 0, 1, 2, 3, 4:
- Calculate R0 for this population. Based on your answer, what is the current status of this population?
- Calculate the approximate generation time to estimate r.
- Use sensitivity analysis to evaluate the alternative management strategies of dam removal (which would increase the fecundity of spawning salmon by a factor of 1.5) vs. increasing open-water survival (all age classes) by a factor of 2. Note: Base your answer on R0, but indicate why this may not be ideal.
