ECOLIGICAL MODLLING. MODELLING METHODScompartment V. COMPARTMENT MODELS. Compartment. modelling

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1 ECOLIGICAL MODLLING V. COMPARTMENT MODELS 1 1 MODELLING METHODScompartment modelling Compartment modelling 2 3 1

2 3C modelling 3C modeling a) Compartments (state variables) b) Connections (parameters) c) Controls (forcing functions) 4 Compartments 1. Give verbal description: - of the problem, - of the system under study - of the system at hierarchical +1, and major subsystems at level List state variables of the system! 3. List the inputs and outputs from the system! 5 Connections 1. Make adjacency matrix of your system. 2. Make box (blok) diagram of your system 3. Make signed matrix and insert + and signs in your conceptual (block) diagram 6 2

3 Control 1. For each direct interaction indicted in adjacency matrix list state variables or forcing functions that have the control (influence) on the interaction. 7 Conceptual model to computer model: 1. INTRODUCTION TO THE TOOL 1. STOCK 2. FLOW 3. CONNECTORS 2. MODEL 3. TO SUM UP 4. GROWTH FORMS 8 1. STELLA modelling tool Stella opens with a graphic menu that contains a number of icons. The first four are the main building blocks for your model 9 3

4 1.1 Stock The rectangles: state variables (Stocks in Stella) They describe the elements in your system. These are the quantities that change in the system, that you analyze and report as a result of the modeling exercise. For each of the state variable a differential (difference) equation is to be created in Stella Flow The flows represent the processes in which materials (or quantities) are taken from one state variable and added to another. The cloud is used to show that material is exchanged with the outside of the system Converters Circles represent parameters or auxiliary variables (Converters" in Stella) The quantities that are either constant in the model or will be calculated based on the values of the state variables. 12 4

5 1.3 Connectors Lines with arrows are to show what depends upon what. They are to feed the value from one Stella icon into another. They cannot move material or quantities, they only convey information. 13 Click on the State variable icon, then click somewhere in the window, where this variable will be located on the diagram. The variable appears with a "Noname" name. Click on this title - type the name of the variable 14 Click on the Flow icon and place it such that the flow will go into of from the state variable. Hold on the mouse button and drag the cursor from where the flow starts to where it goes. (to attach flow with the state variable, latter must get highlighted if not cloud will appear). To make angle of the flow line hit the Shift key. This is useful to keep the diagram tidy and clear. Name the "Noname" flow 15 5

6 Add an auxiliary variable (parameter) place and name it (click and hold the name then drag it around the icon) Use the connector arrows to link variables, flows and state variables - like with flows drag the arrow to connectit with the recipient of the information. With this diagram you have formulated the following differential (or rather difference) equation: S_VARIABLE(t)=S_VARIABLE(tdt)+FLOW*dt 16 Switch the model from "Mapping Mode" to the "Modeling Mode > "?" will appear on all elements in the diagram that need further definition. Specify: the actual size of FLOW the initial condition for S_VARIABLE. 17 Double-click on the parameter icon Give the value for the parameter that you want to use in your model (0.01) Type that value (or use numerical pad ) You can use some arithmetic expressions, like 1/100, or choose some of the built-in functions that are listed there. 18 6

7 Click on the flow icon and open this dialogue box You are to "place the right hand side of equation here". The required inputs are listed above (click on any of them they will be copied into the equation field) Describe the flow as a product of the available stock in S_VARIABLE and the rate coefficient that we have already specified in PARAMETER: 19 PARAMETER*S_VARIABLE Double click on the State variable icon (stock). specify the initial conditions. The list of "Allowable Inputs" is somewhat confusing (flows, parameters, rare used to specify initial conditions). In most cases you will simply type a constant, say 10. Note that there is a check-box that says "Non-negative" >By default all state variables come checked as non-negative. By clamping them with this check-box, you loose track of what is really happening in your model - keep this box unchecked, unless you really know what you are doing 20 Double click on the State variable icon (stock). specify the initial conditions. The list of "Allowable Inputs" is somewhat confusing (flows, parameters, rare used to specify initial conditions). In most cases you will simply type a constant, say 10. Note that there is a check-box that says "Non-negative" >By default all state variables come checked as non-negative. By clamping them with this check-box, you loose track of what is really happening in your model - keep this box unchecked, unless you really know what you are doing 21 7

8 All the question marks are gone (modelling mode) >The model is ready to run. Check out the equations that you have generated >click on the downward arrow in the upper left corner Specify how the output should look like: output tools Click on Graph icon and double click to locate the graph No more then 5 selected variables Scaling highlighting (clicking once) a variable: change the minimal and maximal values for this variable that will define the scale in the graph. 24 8

9 Click on Table icon and double click to locate the graph. Output values that variables take during the simulation. Choose the variables, specify the characteristics of the Table. Output for an individual variable is possible to generate (to get the value that it attains by the end of the simulation) 25 Run the model: choosing "Run" from the Run menu or click the running boy icon 26 Editing tools: Navigation cursor: mostly using to open and close windows and to arrange elements of the diagram Color-paintbrush icon: to add some colors to the diagram (individual elements or change the color the graphics) Delete-dynamite is to delete things in the diagram. No undo in Stella! 27 Ghost: to connect elements that are very far apart in the diagram 9

10 Three tools not essential to create models. The first one :to place buttons in the diagram > handy for navigation or for model runs: get something done by simply pressing a button right in the diagram. The second: to group certain variables and processes into sectors: to put some more order into the diagram, to run only certain parts of the model. The third: to wrap certain details about processes and display 28 them as one icon in the diagram. 3. To sum up Covers only some of the basics of Stella. Please note that: You cannot connect two Stocks with an information flow: only material Flows can change a Stock. The information about a Stock can affect a Flow, but not the information flow. You cannot connect auxiliary variables (parameters) with material Flows. Only information flows are appropriate in this case. A material Flow is assumed positive. If it becomes negative Stella will clamp it to zero. If you need a Flow that can become negative, use the Biflow option. A Biflow can go in both directions To sum up Keep diagram tidy. Avoid long connectors and confusing names. Avoid criss-crossing flows => The easier it is to read your diagram the less errors you will be making, the more appealing it will be to anyone else you need to explain the model to. There is no such thing as too much documentation. Every variable or flow in Stella has a Document option, which is useful to record your ideas and comments about what you are modeling and the assumptions you are making. It is extremely important both for the model developer and the model user

11 4. Growth forms Linear growth Exponential growth Convergence Sigmoid growth Oscilation Linear model - increasing Linear model decreasing 33 11

12 4.2 Exponential growth Exponential decreasing Convergence - up 36 12

13 4.3 Convergence - down Sigmoid growth Oscillation 39 13