Isle Royale National Park is a 210-square-mile archipelago composed of a single large island and many small islands in Lake Superior. Moose, arrived around 1900 and by 1930, their population approached 3000, ravaging vegetation. In 1949, wolves crossed an ice bridge from Ontario. Since the late 1950s, the numbers of the moose and wolves have been tracked. (Dash indicates no data.)

(a) Integrate the Lotka-Volterra equations from 1960 through 2020. Determine the coefficient values that yield an optimal fit. Compare your simulation with the data using a time-series approach, and comment on the results.
(b) Plot the simulation of (a), but use a state-space approach.
(c) After 1993, suppose that the wildlife managers trap one wolf per year and transport it off the island. Predict how the populations of both the wolves and moose would evolve to the year 2020. Present your results as both time-series and state-space plots. For this case, as well as for (d), use the following coefficients: a = 0.3, b = 0.01111, c = 0.2l06, d = 0.0002632.
(d) Suppose that in 1993, some poachers snuck onto the island and killed 50% of the moose. Predict how the populations of both the wolves and moose would evolve to the year 2020. Present your results as both time-series and state-apaceplots.