Homework Assignment #7: Competition                                           Name:                                    

Due: Monday, 6 November 2006

Note: Need to use graph paper to do this assignment!

1. You are studying two species of rodent, the deer mouse (species 1) and the long-tailed vole (species 2),out at Hells Gate State Park.  For the deer mouse, K₁ = 100 and b = 2.0, and for the long-tailed vole K₂ = 150 and a = 0.5.

Plot the following population sizes for the two species and determine the short-term dynamics given the placement in relation to the isoclines.

            1) Initial population size for the deer mouse is N₁ = 100 and N₂ = 50 for the long-tailed vole.

            2) N₁ = 50 and N₂ = 50

            3) N₁ = 125 and N₂ = 175

            4) N₁ = 25 and N₂ = 175

What is the final outcome of interspecific competition?  Is this a stable equilibrium?

2. If two species have the following competition coefficients, a = 1.5 and b = 1.5 with carrying capacities of K₁ = 100 and K₂ = 100, plot out the isoclines on a state space graph.

Plot the following population sizes for the two species and determine the short-term dynamics given the placement in relation to the isoclines.

            1) N₁ = 25 and N₂ = 150, what are the short-term dynamics of the populations?

            2) If the populations were at N₁ = 10 and N₂ = 70, what are the short-term dynamics of

                the populations?

            3) What if the populations were at N₁ = 70 and N₂ = 10?

            4) Will competitive exclusion occur in this environment given the above data? Why or

                 why not?