Bio 481 - Problem Set 8 - Predator-Prey Dynamics

General Note: a^b stands for a raised to the b power.

1. Start with the classic Lotka-Volterra predator/prey system. Use some reasonable values for the parameters. Graph the isoclines for this system. Next, using different starting points, project the system in P/V phase-space.
   
   
2. Analyze problem 1 analytically. Find equations for each of the isoclines and solve for the equilbrium point in the system.
   
   
3. Adapt your system from problem 1 to include density dependence in the prey. Use the basic logistic form to do this. Graph the isoclines and again do some projections in phase-space.
   
   
4. What happens if you add density dependence to the predator equation in the previous problem?
   
   
5. Use a type II functional response in a classic Lotka-Volterra system. How have the isoclines changed? What is the dynamics now in phase-space? Can you see these dynamics easily in a time series plot?
   
   
6. Combine the type II functional response and density dependence in the prey. Again, look at the isoclines and dynamics.
   
   
7. Pick some other characteristic that you might think is important in biological systems (eg. type III functional response, refuge effect, seasonality in prey growth, another trophic level, etc.) and analyze this new system the way you have these previous ones. Make sure you understand fully how the parameters affect the system.