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Predator-Prey Models

Part 6: Summary

  1. What features of the lynx and hare data suggest that the Lotka-Volterra model might be an appropriate mathematical description of the interaction? What features suggest this would not be an appropriate model?
  2. How do you find an equilibrium solution to a system of differential equations? What does an equilibrium solution mean for interacting populations?
  3. What is the biological meaning of each of the four parameters in the Lotka-Volterra Model?
  4. For solutions x(t) and y(t) of the Lotka-Volterra equations, explain why the peaks of the y(t) graph should lag about a quarter-period behind those of the x(t) graph.
  5. What special characteristic is shared by all trajectories of the Lotka-Volterra Model? What is the biological significance of this characteristic? Is this biologically reasonable?
  6. (Optional) What is likely to happen to the trajectories if the model is altered, say, by hunting or stocking one of the populations?

There are many extensions of the Lotka-Volterra model to make the equations more realistic. For example, one might add a carrying capacity constraint for the prey population, as in logistic growth models for a single population. Here are some links to other sites at which you can study other models of interacting populations.

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