Suppose the spotted owls’ primary food source is a single prey: mice. An ecologist wishe...

Suppose the spotted owls’ primary food source is a single prey: mice. An ecologist wishes to predict the population levels of spotted owls and mice in a wildlife sanctuary. Letting M_n represent the mouse population after n years and O_n the predator owl population, the ecologist has suggested the model

The ecologist wants to know whether the two species can coexist in the habitat and whether the outcome is sensitive to the starting populations.

a. Compare the signs of the coefficients of the preceding model with the signs of the coefficients of the owls–hawks model in Example 3. Explain the sign of each of the four coefficients 1.2,−0.001, 0.7, and 0.002 in terms of the predator–prey relationship being modeled.

b. Test the initial populations in the following table and predict the long-term outcome:

c. Now experiment with different values for the coefficients using the starting values given. Then try different starting values. What is the long-term behavior? Do your experimental results indicate that the model is sensitive to the coefficients? Is it sensitive to the starting values?