GEOG 110 – Lab #4 – Modeling Predator-Prey DynamicsGEOG 110 – Lab #4 – Modeling Predator-Prey DynamicsDue Date: 11:59 pm November 4, 2005Objectives: Familiarize yourself with the Lotka-Volterra model of predator-preydynamics by performing some Sensitivity analyses on the provided model.Then, modify the model to include a third population in the model. UsingSensitivity analysis, again vary some of the initial population sizes to seehow producer, prey, and predator population sizes effect all threepopulations.Background: Simulating the interactions of populations of organisms in an ecosystem isanother useful application of modeling to complex systems in theenvironment. The Lotka-Volterra model of predator-prey dynamicsconsiders that the state of these populations is coupled, such that oneinfluences the other, and vice-versa. As was the case with the otherphenomena we have simulated, by constructing such a model for thepredator-prey system, experimenting with its variables can allow us toreproduce trends in these populations that would be quite difficult toobserve in the environment, because it would be difficult or impossible tohold all other factors constant while investigating the effect of a singlefactor. Thus, simulating these sorts of systems gives an opportunity toapproach and understand phenomena that would be extremely difficult tograsp purely through field studies. While field studies are tremendouslyuseful for obtaining the initial values needed to parameterize a modelrealistically, the use of modeling allows us to go significantly further inour exploration of the system dynamics of predator and prey populations.Resources: This lab exercise does not include the background and theory required foryou to understand how to study predator-prey dynamics. For thatinformation, you should look to material from the lectures and the entiretyof Chapter 4 (pp. 95-112) of the course text, paying special attention toSection 4.2.3 onwards. At this point, you should have already successfullycompleted three labs, and you should be getting comfortable with usingSTELLA. You can refer back to the course text’s background material onSensitivity analysis (Section 3.5.3, pp. 84-87) to help you understand howto use Sensitivity analysis to better understand the system dynamics of thepredator-prey model. This lab continues the trend set by the previous labs,where in each successive lab the procedure becomes less step-by-step, andmore open-ended. You are expected to use the knowledge you havealready acquired in previous labs to use STELLA in these lab exercises ina less regimented fashion.1Procedure: Be sure to read Chapter 4 before attempting this lab, in order to familiarizeyourself with this model’s components and how they function.1. Get STELLA started and open up the predator-prey dynamics modelprovided for this exercise. The model (Chap4c.stm) will be inj:/isis.unc.edu/html/courses/2005fall/geog/110/001/data (which youcan also access using a web browser as previously described).2. Let’s take a few moments to familiarize ourselves with the manycomponents of this model. There are quite a few elements that itincludes that we have not seen previously:- You will notice that the model is enclosed in a pink outline, andcannot be edited without clicking on the triangle in the topright corner.- To the right of the model diagram, there is a purple boxcontaining a brief description of the model.- Below the elements mentioned above, we have a set of controlsthat allow us to change some values in the model on the fly, asthe model is running. This model runs in what STELLA termsflight simulator mode, meaning that if you move the controls asthe model is running, you can have an impact on what it does(see Section 3.9.2 on p. 94 for a description).- The Dd (Deer death rate as a function of the Wolf population)and Wb (Wolf birth rate as a function of the Deer population)parameters are represented graphically in two controls thatallow you draw different functional relationships for them withyour mouse.2- There are sliders for r (controls inflows to Deer stock), Kd(death rate as a function of carrying capacity constraint), andWd (decline in Wolf population assuming there is no availableprey) that also allow numerical input by clicking on the numbershown. The dashed circle r is the “Ghost” of the solid circle r ina different position as this makes the diagram looks better (it isthe same r).- There are two dials that control the initial values of the Wolfand Deer populations3. Leaving all of the values at their initial values, try running the model.Click on the graph tools first to create a time series for the Deerpopulation and the Wolf population. Move the graph to the bottom ofthe page and click on the pin to the upper left corner. First run themodel as with the default values as set and see how the two populationchange with time. Copy the graph into your lab report and explain.Then run the model a second time. As the model is running, you canmove the sliders to represent a change in those conditions as timepasses. Change the slider bar one at a time and see how the modeloutputs change. You may see many different graphs here. Copy one of3your favorite into your lab report, and explain what you did and howwhat you did translate to what you see [note: You can go into the RunSpecs and change the Sim Speed if you’d like it to go slower or faster,but do not change the DT as this will affect the models performance ina way that we do not want to examine].4. Now unpin your graph and then double click on it again, the graphspecification dialog comes out. Change the graph type from time seriesto scatter [recall what a scatter plot is]. In the empty space to the right,you will see X and Y. First click on the Deer in the window to the leftas X and then click on the Wolf in the window to the left as Y. Nowrun the model with its default values and see what happens. Copy thegraph into your lab report and explain the graph. 5. In order to get a feel for how the initial sizes of the Wolf and Deerpopulations affect the behavior of the model,