Modeling Assignment

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 Now imagine that the conditions are just right for scallop reproduction: Change the scallop reproduction rate to 10. Change the birth rate of the predator back to 0.01 because the rays are experiencing typical conditions. Run the app and use the plot to answer Question 5. Question 5. How does increased scallop reproduction change the population cycles? Why? So far you’ve run the model with only one predator involved, the cownose ray. Now let’s introduce another predator: Humans. Change the scallop reproduction rate back to 1. Set the number of scallopers (fishing vessels) to 10 and the catch to 1000. Keep the other parameters the same as the original values shown in the screen shot at the beginning of Exercise 3 . Run the model. Run the app and use the plot to answer Question 6. Question 6. How did the populations respond to scallop fishing? Is the result qualitatively similar to those in Exercise 1? Adjust the number of scallopers down incrementally to simulate reductions in fishing effort. Either take notes on each incremental run or archive screen shots of each to use as you answer questions 7 and 8. Question 7. How many scallopers can safely fish in these waters at the current allowed catch without causing the scallop population to collapse? Question 8. The maximum sustainable catch is equal to the number of scallopers that can fish without causing the population to collapse times the catch per scalloper (= scallopers  catch). What is the total maximum sustainable catch? Set the number of scallopers back to 10. Now simulate the effect of catch limits (how much each vessel is allowed to catch each season) by adjusting the catch per scalloper until the population approaches natural levels. Again, you will want to either take notes on each incremental run or archive screen shots of each to use as you answer questions 9 and 10. Question 9. What is the maximum sustainable catch per scalloper? What is the total maximum sustainable catch? Question 10. Imagine you are a manager of this fishery and answer the following: a) How would you adjust the number permits for scallopers? b) If you decide to allow 10 scallopers, how would you set their catch limit? 4

3/27/2024 a) What other factors would you have to consider before you could make these decision (list three)? Step 3. Save your work and upload it for grading. 5