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  3. 2 consider an island that is colonized by mainland species...

Question: 2 consider an island that is colonized by mainland species...

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2. Consider an island that is colonized by mainland species. Suppose that there are S species on the mainland and N(t) species on the island at time t. Assume that the rate of colonization of the island is proportional to the num ber of species, S - N(t), on the mainland but not on the island, with propor- tionality constant I. On the island, species go extinct at a rate proportional to the number of species on the island, with proportionality constant E (a) Write the differential equation for the number of species on the island. (b) Determine the equilibrium solution for your equation. Is this equilib- rium (asymptotically) stable or unstable? (c) Sketch solutions, N(t), for your differential equation. Your sketch should show the correct slope and concavity.

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