# Solve for the Following Problems

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Predation Homework                                                     Predation Homework.doc

1. Oystercatchers are wading birds that eat a wide range of food common in intertidal areas. Observation of oystercatchers showed that when feeding on mussels these birds would crack the mussels open with their beaks. The figures to the right show the size distribution of available mussels and the size distribution of the mussels consumed by oystercatchers. The x-axis is mussle length and the y-axis is the frequency of that size of mussle in the population. What accounts for this difference between the two figures? Use the optimal foraging equation to explain your answer.

2. Lotka-Voltera Predation in Populus: In the main menu, select Continuous Predator-Prey Models (Model>Multi-species Models>Continuous Predator-Prey Models), then select Lotka-Volterra in Model Type. The “C” term in Populus is the same as the “a” term in the equations we saw in class. The “g” term is our “fa”. a. While viewing the predator-prey phase plane, examine the consequence of starting with different numbers of predators and prey. Do different initial numbers of predator and prey affect the dynamics? In what way (what is and what isn’t affected)? b. Start with the default values. Leaving other values at their default levels, experiment by increasing the starvation rate (d2) that predators suffer in the absence of prey. Recall that this number is subtracted from dP/dt, so a large value means an increasingly negative effect. What two effects does increasing the predator’s vulnerability to starvation have on predator-prey dynamics? Look at both graph types as you do this. c. Now return to the default values and experiment with increases in the intrinsic rate of increase for prey (r1). This is the rate at which prey would increase (exponentially) in the absence of predation. What effect does increasing the prey’s intrinsic rate of increase have on predator-prey dynamics? d. Now return to the default values and make prey growth density dependent, using the check box (D-D Prey). What does this do to the isoclines? Why? What effect does increasing or decreasing K have? How does the changed isocline due to density-dependence alter the dynamics?

Predation Homework.doc3. Lotka-Volterra on your own (Without Poplus). Suppose that spider and fly populations are descried by Lotka-Volterra dynamics Start with these initial parameters: r = 0.1, q = 0.5, a = 0.001 and f = 1 You start with 200 spiders and Predation Homework.doc600 flies. a. Explain what r, q, a and f stand for and how to translate them. For example – how is f defined, and what does at f of 1 mean for spiders? b. After one generation, how many spiders and how many flies will exist in the community? Show your work. c. Plot the zero-growth isoclines and show graphically how the size of each group is expected to change in both the short term and the long term. 4. Of the Type I, II and III functional responses, which one is modeled by the Lotka-Volterra predator-prey model? Explain the features of the model that generate this type of response.

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