Problem Set 13:

Predator-Prey Interactions

Scenario

 In a study of mink and muskrats on a 130-km2 study area in central Iowa, it was observed that the maximum intrinsic rate of increase was 1.2 for muskrats and 0.18 for mink. Research biologists estimated that approximately 450 muskrats were required to support one mink for one year. The carrying capacity for muskrats on the study area was estimated to be 100,000.

Use the Predator-Prey Model in program POPEC (based on Tanner's Model A) to answer the following questions.

1. If there currently are 20 mink and 60,000 muskrats on the study area, describe what will happen to the 2 populations over the next 40 years?  Hint: what outcome does Tanner's Model A predict?   Create a phase plane graph with prey abundance on the x-axis and predator abundance on the y-axis. Why, according to Tanner, do you see this behavior in the two populations? How does this outcome differ from the Neutral Limit Cycle predicted by the Lotka-Volterra model of predation?

2. Suppose this area was subject to a prolonged drought and intensive agricultural practices, which ultimately reduced the carrying capacity of muskrats to 25,000. Using the population levels observed at year 40 (from question #1), predict what will happen over the next 40 years? Is the outcome the same as above (Q1)? If not, explain why it is different.

3. Use the same initial population sizes as in question #1, but alter one of the input parameters (except K) in some way to get a similar outcome to question #2 (i.e., similar in terms of Tanner's predictions based on Model A). Describe what you did and explain why it resulted in a similar outcome to question #2.

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Revised: 03 December 2001