Predator/Prey with Functional Response
Questions

The Homework has the assignment to hand in. These Questions are basically drill to build an intuitive grasp of functional response and isoclines, so that you expect the answer you get.

  1. On Scenario | Functional Response, look at Types I and II. With the preset parameter values (killrate 0.05 and handling time 0.02), the Type I and II responses seem colinear for a little ways. At what prey population do they appear to diverge?

  2. Using the same Scenario, set Type II killrate to 0.1. What happens?

  3. The difference between the predator/prey Scenario | Linear Codependent and Scenario | Saturated Predator is their functional responses (Type I vs. Type II). To simplify your comparisons, the preset parameters match (i.e., both have killrate 0.05.) Now look at (in sequence):
    1. "Linear Codependent" with its default killrate 0.05.
    2. "Saturated Predator" with its default killrate 0.05. (How many cycles are there on the time series?)
    3. "Saturated Predator" with killrate 0.1. (What happens to the phase plot (top) trajectory shape? How many cycles on the time series?)
    4. Back to "Linear Codependent".
    Tell yourself a story about what this means. Based on your story, predict what will happen with a Saturated Predator killrate 0.01 and 0.2. Test your theories.

  4. Play the Question 2/Question 3 game again, this time varying only the handling time. (Set parameter "predator saturation" to killrate times handling time. See Details.) Again, what does this mean? Does the handling time affect the number of cycles on the time series?

  5. Pick Scenario | Saturated Predator again, to make sure you've got the default parameters. Now try doubling and halving the prey birthrate. What happens?

  6. Now try doubling and halving the predator deathrate. What happens?

  7. The number of cycles is determined by the period, or length of each cycle. Are the cycles of equal length in the Saturated Predator system? Which parameters affect the period? Why would that make sense?

  8. The quantities Prey and Predator are population densities. Let's say you wanted to scale these. For instance, you have data from Idaho on a one-meter-square map and data from Wyoming on a ten-meter-square map. How do you adjust your parameters to scale the one-meter data down two orders of magnitude? (0.01 per (10m)2 = 0.01 per 100m2 = 1.0 per 1m2.)

  9. In the natural world, there are extremely few predators who depend on a single sort of prey. What aspects of these models do you think would be relevant in practice? Which are probably less useful?

  10. Take a predator/prey ecosystem you're familiar with, like cats catching mice and baby moles in Connecticut, but include the cat's food bowl. Pick one of the models here and describe its fitness to describe your sample ecosystem. What ought to happen when you add more prey types? What do you think the equations suggest about adding prey types?

Ginger Booth, revised April 2005, orig. December 1998, for oswald.schmitz@yale.edu