HW 8 - • At high prey densities, the predator population...

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HW 8 1) For the following phase plane, isoclines, and starting conditions (the purple dot): a) tell me what type of interaction is being depicted (are the two species mutualists? Competitors? Predator- prey? Etc.). b) Plot the dynamics on the phase plane and on the N vs. t figure. c) Is the system stable; if it’s stable is it locally or globally stable? HINT: just do this by hand on these pages – no need to struggle with drawing on your computer. N 1 or 2 Time dN 1 /N 1 dt=0 dN 2 /N 2 dt=0 N 1 In this region, Sp 1’s abundance decreases, Sp 2 decreases 25 20 35 15 40 20 30 10
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N 1 N 2 10 25 15 Sp. 2’s isocline Sp. 1’s isocline In this region, Sp 1’s abundance decreases, Sp 2 increases 2) Repeat what you did in the first problem, except for the following phase plane. 1 or Time 20 30 10
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3) Draw a phase plane for a predator prey system. Label it as accurately as possible (e.g., by adding numbers on the x- and y- axes). Keep it as simple as possible, but assume the system has the following characteristics:
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Unformatted text preview: • At high prey densities, the predator population is limited by nest sites , and as a result, the predator’s density can never exceed 30predators/km 2 . • The prey population exhibits logistic growth in the absence of the predator. In the absence of the predator, the prey achieve an equilibrium of 100prey/km 2 . • At low predator densities (densities below the limit placed by nest sites), the predator has a per capita mortality rate of 0.10 d-1 . • A predator have a type one functional response. A predator achieves a feeding rate of 1 prey / day at a prey density of 20prey/km 2 . • A predator has to consume 10 prey before it can produce 1 new predator. • The prey have a per capita growth rate (r) of 0.5 d-1 at very low prey densities. Predator density Prey density 30 20 10 150 50 100...
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This note was uploaded on 07/13/2011 for the course PCB 4034C taught by Professor Osenberg during the Spring '11 term at University of Florida.

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HW 8 - • At high prey densities, the predator population...

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