Modeling Assignment

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North Carolina State University *

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360

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Economics

Date

Apr 3, 2024

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docx

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3/27/2024 Modeling Assignment An important aspect of managing a fishery resource, such as that of scallops, is determining the maximum sustainable catch. This is the amount that can be taken from a fishery without causing the ecosystem to collapse. In reality, determining the maximum sustainable catch is difficult and has many uncertainties. It is usually not feasible, or even preferable, to perform experiments on the fishery. Modeling, or performing mathematical simulations, is an important tool for studying the impact of harvesting. In this exercise, you will use a modeling program to simulate a simple predator-prey relationship. First you will simulate how the populations of scallops (prey) and their predators (cownose ray and man) respond to changes in predation rate. Then you will investigate how scallop fishing impacts both prey and predator numbers. Finally, you will make recommendations concerning catch allowances so as to maintain a sustainable scallop population (stock). You will use the modeling software program ‘pop_dynamics’ in Matlab to simulate the populations of scallops and a general predator, the cownose ray. The Matlab calculations are based on the Lotke-Volterra predator-prey model. The model is not specific to scallops and will have some inaccuracies. Even so, you will see some general trends that are often seen in simple predator-prey relationships. The model solves two simultaneous equations describing the changes in the number of scallops ( S ) and the number of predators ( P ): dS dt = R reprod × S R pred × S × P C (1) dP dt = R birth × R pred × S × P R death × P (2) Where S : the number of scallops P : the number of predators C : total catch by scallopers ( catch per scalloper times the number of scallopers ) R reprod : scallop reproduction rate R pred : scallop predation rate by predators R birth : predator birth rate R death : predator death rate 1
3/27/2024 Step 1. Open and start the Matlab app following the steps below. 1. Download the files popdyn.m and popdyn.fig from Moodle if you have not already. 2. Open Matlab, either from the Math tab in the Admin Launcher, or by using the Finder (Applications). Click on the Editor tab. 3. The script to be run has be in the correct folder path. If not in the correct folder, drag and drop the files popdyn.m and popdyn.fig into the current folder window. Double click on the popdyn.m file and the file should open in the editor window. 4. To run the transport script, click on in the menu on the editor tab. The app should open a dialog box that you will use for the rest of the assignment (Fig. 1). Figure 1. Screen shot of population dynamics app in Matlab. In the popdyn application, check the default parameters for predator death rate, predation rate, scallop reproduction rate, predator birth rate, total catch by scallopers and the starting contents of scallop population and predator population. The settings should be as pictured above in Figure 1. 2
3/27/2024 Step 2. Run the simulations. In this simulation, there are no scallop fishermen. Run the model by clicking on “Plot” with these preset conditions. The blue curve represents the scallops and the red the predator (cownose ray). Use the plot to answer Questions 1-3 in this document. The plot should look like this: Question 1. How do the populations of scallops and predators vary with time? Describe how the populations interact and why they vary the way they do. Question 2. As a manager of a scallop fishery, you need to decide the length and timing of the fishing season as well as the amount of scallops that can be taken. Explain how knowledge about the natural population dynamics might influence these decisions. Question 3. Without predation pressure, humans would have little competition for scallops, yet user groups usually want to avoid causing a collapse in the predator population. Why might it be important to conserve the scallop predator? Now, imagine it is a good year for cownose rays- the population is healthy. Change the birth rate of the predators to 0.1. This has the effect of increasing the number of rays (predators) that reproduce each year. Run the app and use the plot to answer Question 4. Question 4. How did changing the predator birth rate affect the population fluctuations? Explain why. 3
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