Consider the competition between bluegill and redear mentioned in 6. Suppose that 2/2 >

Chapter 9, Problem 7

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Consider the competition between bluegill and redear mentioned in 6. Suppose that 2/2 > 1/1 and 1/1 > 2/2, so, as shown in the text, there is a stable equilibrium point at which both species can coexist. It is convenient to rewrite the equations of in terms of the carrying capacity of the pond for bluegill ( B = 1/1) in the absence of redear and its carrying capacity for redear ( R = 2/2) in the absence of bluegill. a. Show that the equations of take the form dx dt = 1x_1 1B x 1 B y_, dy dt = 2 y_1 1R y 2 R x_, where 1 =1/1 and 2 =2/2. Determine the coexistence equilibrium point ( X, Y ) in terms of B, R, 1, and 2. b. Now suppose that an angler fishes only for bluegill with the effect that B is reduced. What effect does this have on the equilibrium populations? Is it possible, by fishing, to reduce the population of bluegill to such a level that they will die out?