In a 1969 study, E. R. Leigh concluded that the fluctuations in the numbers of Canadian lynx and its primary food source, the hare, trapped by the Hudson's Bay Company between 1847 and 1903 were periodic. The actual population levels of both species differed greatly from the predicted population levels obtained from the Lotka–Volterra predator–prey model. Use the entire model-building process to modify the Lotka–Volterra model to arrive at a more realistic model for the growth rates of both species. Answer the following questions at the appropriate times in the model-building process:

a. How have you modified the basic assumptions of the predator–prey model?

b. Why are your modifications an improvement to the basic model?

c. What are the equilibrium points for your model?

d. Is it possible to classify each equilibrium point as either periodic, asymptotically stable, or unstable? If so, classify, them.

e. Based on your equilibrium analysis, what values will the population levels of lynx and hare approach as t tends to infinity?

f. How would you use your revised model to suggest hunting policies for Canadian lynx and hare?  You are introducing a second predator–the human–into the system.