Answer Happy

Problem 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) Year Moose Wolves 1960 700 22 1961 22 1962 23 1963 20 1964 25 1965 28 1966 24 1967 22 1968 1000 22 1969 1150 17 1970 966 18 1971 674 20 Year Moose Wolves 1972 836 23 1973 802 24 1974 815 30 1975 778 41 1976 641 43 1977 507 33 1978 543 40 1979 675 42 1980 577 50 1981 30 1982 590 13 1983 23 881 570 811 (a) Integrate the Lotka-Volterra equations from 1960 through 2020. Determine the coefficient values that yield an optimal fit. Compare your simulation with these data using a time-series approach, and comment on the results. (b) Plot the simulation of (a), but use a phase-plane 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 phase-plane plots. For this case, as well as for (d), use the following coefficients: a = 0.3, b = 0.01111, c = 0.2106, 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 phase-plane plots.