Assignment #1: Policy Analysis for the Kaibab Plateau Background Summary Kaibab Plateau: Source: Kormondy, E. J. (1996). Concepts of Ecology. Englewood Cliffs, NJ: Prentice-Hall. p.96. Prior to 1907, the deer herd on the Kaibab Plateau, which consists of some 727,000acres and is on the north side of the Grand Canyon in Arizona, numbered about 4,000. In 1907, a bounty was placed on cougars, wolves, and coyotes all natural predators (over 8,000) and a consequent and immediate irruption of the deer population. By 1918, the deer population had increased more than tenfold; the evident over browsing of the area brought the first of a series of warnings by competent investigators, none of which produced a much needed quick change in either the bounty policy or that deal with deer removal. In the absence of predation by its natural predators (cougars, wolves, coyotes) or by man as a hunter, the herd reached 100,000 in 1924; in the absence of sufficient food, 60 percent of the herd died off in two successive winters. By then, the girdling of so much of the vegetation through browsing precluded recovery of the food reserve to such an extent that subsequent die-off and reduced natality yielded a population about half that which could theoretically have been previously maintained. Perhaps the most pertinent statement relative to the matter of the interregulatory effect of predator and prey is the following by Aldo Leopold, one of the most significant of recent figures on the conservation scene: We have found no record of a deer irruption in North America antedating the removal deer predators. Those parts of the continent which still retain the native predators have reported no irruptions. This circumstantial evidence supports the surmise that removal of predators predisposes a deer herd to irruptive behavior. 1
The Task: Your task is to maintain the environmental balance of the Kaibab Plateau with the focus on the task of controlling of the deer population which has grown alarmingly since the elimination of predators began around 1900.. In addition, you have to take into consideration the voices of various opinion groups of local residents while making policy recommendations. These groups and their opinions are as follows: The Sierra Club argues that the elimination of the predators is mainly responsible for the problem, so reintroduction of the predators, such as cougars and wolves, will solve it. The ranchers, who are worried about their herds to be attacked by the predators, are seriously against the idea of reintroduction of predators. The local hunters want free access to the plateau to harvest predators. Overview of Vensim PLE: Open the Kaibab model in Vensim PLE, and you should see a screen below: a. To change the view of the model, go to the function menu on the top of the window, select View/Zoom/, and use the options to change the size of the view. b. To change the setting for printing out the model, go to the function menu, select File/Print Options, and use the options there to change the setting for print out. c. To change the simulation setting of the model, go to the function menu, select Model/Setting, and use the options to change the simulation setting, such as the simulation time frame. 2
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The Assignment: (1) Draw a causal-loop diagram for the whole Kaibab model. Identify the stocks (a.k.a. levels) by using rectangles to represent them, while leave the rest in simple words and arrows (e.g. represent an inflow/outflow as a variable, which is shown as a word or a set of simple words). Since a model usually contains a number of loops which are difficult for us to identify with our eyes. However, Vensim PLE provides a tool that can help us to identify the loop(s) that a particular variable/stock is in. Use the following procedure: Double click the Deer stock to select it (it should appear in the window bar, the blue bar at the very top of Vensim window, as the variable on Vensim s workbench. ) Use the loop symbol in the vertical bar of tools at the left of the Vensim screen (the 3 rd one on the vertical bar). You will see a list of loops in lengths (the number of other variables around the loop). Start with the loop 1 and draw it. Proceed until you finish drawing all the loops that involve Deer. Use the same procedure on Predator and Food to draw all the loops that involve them. Finally, try to organize your stocks, variables, and arrows to make your diagram clear as possible as you can, but do not waste too much time on it. Identify the polarities of links (arrows) and loops in your diagram. (2) On the menu bar at the top of Vensim screen (see the figure below), there is a text field for you to name each simulation run. In the figure below, the name is Base, but you can name it anything as you wish (it is not case sensitive). Once you name your simulation run (e.g. Base run kaibab ), click to runner button to simulate the model. When the simulation is done you will see a pop-up window wit some warnings. Please ignore them for now and close the window. Click on the dial button at the right-end of the menu bar (see the figure above) to bring up the Control Panel (see the figure below) and choose the Graphs tag. 4
There are two kinds of graphs that are set in advance. Double-click the KAIBAB POPULATIONS (or select it and then click the Display button) to show a graph of Deer, Predators, and Food. Click on the other graph to see some other information. You can also use the Graph button and the Casual Graph button of the menu bar at the left of Vensim window to get some more information to understand and evaluate the kaibab model. A suggestion here is that you can use these two buttons to show graphs of key variables and stocks to help you explain why you think it is appropriate for us to use this kaibab model to test policies for the Kaibab Plateau (use the concept of reference mode. ) You can copy the graphs by using the Export button on the menu bar at the top of the Graph window (see the figures below) and paste them to your Word processing document. 5
(3) Policy analysis: Reintroduction of predators The Predator harvest fraction in Predator Sector of the model represents the fraction of the predator population that ranchers and hunters kill every year. The graph above shows the pattern with points marked every 5 years from 1900 to 1950. The idea of the graph is that the bounty offered in 1905 led within 5 years to enough hunting activity to eliminate 20% of the predator population every year from 1910 on. 6
(a) Simulate the policy of removing the bounty in 1920 and bringing hunting on the Plateau to a stop by 1925. In order to change the setting of the graphic function for policy analysis while keeping the original setting in the model, click on the SET button ( ; the one at the left of the in the top menu bar). Once the SET button is clicked, some of the variables will become blue. These variables are those you can select to change their values for policy testing purposes. Click on Fraction harvest p yr f ; you will see the window shown above containing a graph over time of the fraction of predators we are assuming are being harvested each year because of the bounty placed upon predators. In the table of values at the left, change the 1925 value from 0.2 to 0. Continue for 1930, 1935 and so on to 1950. You should see the graph change accordingly (you can also change these points in the graph itself by moving points with the mouse, but it is hard to be precise). When you are done, click OK. Then name the run ReintroA or some other suitable name and click on the Run (runner) button. Click on the Dial button to see the Custom Graphs, but before viewing them we have to make the new graphs the active ones. Click on Datasets, and then click once on ReintroA to bring it to the top of the list. Then click on Graphs and select the graph(s) you want to see. Looking at the model diagram you can select variables to view in comparative graphs. Double click on Deer, for example, and then click on the Single Graph button (on the left). You should see a graph that shows the deer population in both the Base and ReintroA simulations. You might do this for each of the stocks in the model, and anything else you thinking might be interesting to look at in this comparative way. The Causes Graph tool works the same way here, showing you the two simulation runs together. In your report, discuss what happens in this policy and explain why it happens. (b) Suppose the ranchers delay the implementation of this policy 5 years. Try the same kind of simulation with the zero harvest fraction starting 5 years later (1930). Be sure to rename your new simulation (e.g. ReintroB). Are the results predictable? 7
(c) Try another hunting policy of your own devising. Note that the first 5 numbers in the Predator hunting fraction table must be 0, 0, 0.2, 0.2, and 0.2 since these are history that you are dealing with up to 1920, after which you can take some different action. Hand in a graph of your run and comment on it. As the number of simulation runs increases, it is a good idea to remove some unnecessary or irrelevant datasets so that they don t show up in future graphs. To do so, call up the Control Panel using the Dial button, and then click on the Dataset tab. Use the arrow buttons in the middle to load or unload simulation runs (datasets) as you desire. (4) Policy analysis: Harvesting deer Hunters have urged the hunting of deer to maintain a healthy herd and prevent the collapse. We will test 3 harvesting policies: a constant number of deer per year, a constant fraction of the deer per year, and a harvest whenever the deer population exceeds a chosen target. To test these policies, we have to edit the model. First, in the Deer Sector, we add a new outflow (call it Deer harvest rate ) to the Deer as shown in the figure below. Deer Sector Deer harvest rate Deer net increase Deer Deer predation rate Since the Deer stock has a new outflow, we need to add this outflow to its equation. You can click on the Equations button in the top menu bar and then click on the Deer stock to call up the equation-writing window (or hold down the Ctrl + Shift keys simultaneously and then click on the Deer stock) and then edit its equation. You should subtract the new outflow Deer harvest rate in the original equation, and then click OK. We will set the Deer Harvest Rate equal to the sum of 3 new auxiliary variables: DHR1, DHR2, and DHR3. Since there is not enough room for them in the Deer Sector, we will add 8
them to a new sector named Deer Harvest Sector. The structure of the Deer Harvest Sector is shown in the figure below (although the geometry may be different in your diagram, the arrows and variables should be the same): Deer Harvest Sector Deer harvest year DHR Desired deer pop DHR1 DHR2 DHR3 Constant deer harvest Deer harvest frac <Deer> Time to correct deer pop Add and formulate all the new variables to the Deer Harvest Sector as shown in the figure above. The variable <Deer> is a shadow variable, which is a copy of the defined variable Deer in the Deer Sector. To add this shadow variable to the Deer Harvest Sector, select the Shadow variable button in the top menu bar and click near DHR2 and DHR3; from the list of variables that appears select Deer and click OK. You will have added <Deer> to your diagram. The equations of the new auxiliary variables are as follows: DHR = DHR1+DHR2+DHR3 [units = deer/year] DHR1 = (Constant deer harvest)*(step(1, Deer harvest year)) [units = deer/year] DHR2 = (Deer harvest frac)*(deer)*(step(1, Deer harvest year)) [units = deer/year] DHR3 = MAX(0, (Deer - Desired deer pop)/(time to correct deer pop))*step(1, Deer harvest year) [units = deer/year] (Note: the STEP and MAX in the equations of DHR2 and DHR3 are built-in functions. You can enter them by just typing their names. Make sure the parentheses match.) The initial values of the new parameters are as follows: Deer harvest year = 1920 [units = year] Constant deer harvest = 0 [units = deer/year] Deer harvest frac = 0 [units = 1/year] 9
Desired deer pop = 1e6 [1,000,000; units = deer] Time to correct DP = 1 [units = year] The next step is to link the DHR variable to the outflow Deer harvest rate you created in the Deer Sector. Again, use the Shadow variable button to create a shadow variable of DHR near the Deer harvest rate and then add an arrow from <DHR> to the Deer harvest rate (as shown in the figure below). Deer Sector <DHR> Deer harvest rate Deer net increase Deer Deer predation rate Now click on the Equations button and you will find that the Deer harvest rate shows up black. This means that it is an unspecified variable (a variable which has not been assigned a proper equation). You should fix the equation in Deer harvest rate (equation = DHR; units = deer/year) and all the other unspecified variables (if there are any) in your diagram. Now you have created all the necessary changes and the model should run with the new sector present. However, in order to make sure that every equation in the model has been properly specified, go to Model/Check Model (or click Ctrl+T) in the Vensim s main function menu at the top of the screen. You hope to get the message Model is A.O.K. Otherwise, fix the error(s) that the Check Model identifies. Once everything is fine, save your model. If you want to look at all the equations in the model, click on the Document Model button at the left of the screen and you should see all the new equations just as you want them. There are some more things you should know. First, the parameters (the variables with NO arrows coming into them, as known as exogenous variables) are set so that the policies are all initially inactive. You will change these constants in reruns to test the policies. If you run the model in this condition, it should behave exactly as before, since the new deer harvesting structures are not active. Try to run a simulation and name it DHR0. The strip graphs or the 10
single graph tool will show both runs, so you can easily compare. If DHR0 behaves differently from the Base run, go back over your changes to fix them until the model behaves just as before. Do not continue unless it does. Save your model. Print out a model diagram (click in the diagram to make it the active window and select Print from the File menu). Print out an equation listing by clicking on the Document Model tool in the tool bar on the left of your screen and clicking on the little printer icon in the window bar of the model listing. Or, you can use the Export window contents tool (see the figure below) to copy the equations and paste them in your word processing document. Hand in a model diagram and an equation listing with your new equations highlighted somehow. (5) Deer harvest policy 1: (a) Draw a stock and flow diagram of the deer population and the structure of the first deer harvesting policy (DHR1). There should be no feedback loop in this structure. (b) Simulate the deer harvesting policy 1 by clicking on the SET button and clicking on the Constant Deer Harvest parameter. Set its new value to 1,000. Name the run DHR1 and click on the Run (runner) button to simulate. Check the resulting predefined custom graph and any strip graphs you like, and include them in your written report. (c) Try other values for the constant number of deer harvested per year in order to understand what this policy 1 is likely to do. Determine whether DHR1 is a good or bad policy and why. (d) Summarize your results (include any illustrative graphs you wish for question (5) or the 11
remaining questions in this assignment). (6) Deer harvest policy 2: (e) Draw a stock and flow diagram of the deer population and the structure of the second deer harvesting policy (DHR2). Use the loops tool to help you if necessary. There should be a feedback loop in this structure. Determine the polarity of this loop. (f) Simulate policy 2 by changing the fraction of deer harvested per year from zero to 0.1 (Change the constant by clicking on the SET button and the constant, as before). (g) Try other values of the fraction of deer harvested per year until you think you understand this policy 2 well. Finally, summarize your findings about the policy 2. (7) Deer harvest policy 3: (a) Draw a stock and flow diagram of the deer population and the structure of the third deer harvesting policy (DHR3). Use the loops tool to help you if necessary. There should be a feedback loop in this structure. Determine the polarity of this loop. (b) The case description of the Kaibab Plateau indicates that 30,000 would be a sustainable size for the deer herd. Simulate policy 3, trying a Desired deer population equal to 30,000, and then try 35,000. Try other values of Desired deer population if you want. Explain what happens and why. (c) Try Desired deer population = 30,000 with the Deer harvest year to 1926, simulating implementation of the 30,000 deer limit in 1926 instead of 1920 (you have to change to constants in the SET mode). Explain what happens in the simulation runs and what you learn from it. (d) Summarize your findings about this third policy. (8) Policy recommendations: There are two key questions as follows: (a) What policy would you recommend to the government and why? (b) How would you plan to implement your policy recommendation? 12