Predato Prey model
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1. 10 Autoplot Show legend Plot Pens Choose pen to edit hares v Color B red x Mode Line i Interval 1 0 Show in legend Figure 5 The Plot Editor a When the plot editor first opens the Choose Pen to Edit is set to default Select the Rename option and change this name to something meaningful to your model such as Hares b Choose a color for that pen type c Next select to Create a new Plot Pen for the lynx population Give it an appropriate name and choose another color for that pen 4 Once you ve defined all of your needed Plot Pens click OK 5 Now you must adjust your setup and go procedures to update your plots a Just before the end of your setup procedure add the line update plot This will be a user defined function that tells the plot how to update b Similarly just before the end of your go procedure add the line update plot c At the end of your code add the subprocedure given below to update plot set current plot hare lynx set current plot pen hares plot count hares Note this is the name you gave your plot on the interface and this is the name for one of your plot pens With that pen plot the number of hares in the world now set current plot pen lynx Switch to the lynx plot pen plot count lynx With that pen plot the number of lynx in the world now end To display the number of lynx and hares present at each iterat2. happens in your world If there are any errors in code syntax NetLogo will notify you with an error message at the top of your Procedures tab 2 4 The Go Procedure The go procedure will dictate the behavior of the turtles over time and will essentially specify the code to accomplish the behaviors outlined in Table 1 As NetLogo may not have built in commands or procedures that cause a turtle to Check to see if you landed on a hare to eat you will have to define your own procedures to carry out these actions When actions get complicated it is common to make subprocedures to help make steps clear Accepted syntax for user defined procedures and subprocedures is give it a descriptive name using dashes to separate words For instance you may want to create a subprocedure that tells a lynx how to check to see if it can eat a hare You may name that subprocedure lynx tries to eat which is called in a procedure such as the go procedure and defined below the go procedure Here s a snippet of code that illustrates this point to go lynx tries to eat end to lynx tries to eat this is a procedure for the lynx lt describe actions involved in eating here gt end In our model we will need to ask our different breeds to take different actions When this is the case we must ASK our particular breed to perform a task and those tasks will be outlined between closed brackets When designing procedures it is important to keep in mind whic
3. 0 50 20 Table 2 Possible Parameter Slider Settings Untitled NetLogo Fie Edit Tools Zoom Tabs Help Interface Information Procedures d fe p v view updates 2 Xe ee Cet normal speed continuous Set Up go Md ticks 0 2o a Command Center observer gt Figure 4 Starting to create a model adding buttons and sliders to the interface page 2 2 1 Breeds and Attributes As we mentioned earlier mobile agents in NetLogo are referred to as turtles It is often the case that we have more than one type of moving agent such as with our lynx and hares in this example in which case it helps to specify breeds of agents The breeds keyword which is used to identify breeds of turtles for your model can only be used at the beginning of the Procedures tab before any procedure definitions The breed declaration would look something like breed plural name of breed singular name of breed such as breed mice mouse In addition to specifying different breeds of turtles we can also specify attributes associated with our turtles This is accomplished through the use of the turtles own or breed name own declaration also placed before any procedure definitions Attributes are helpful when we need to keep track of a quantity associated with or the status of a turtle at any point in time As each turtle is handled individually it is possible that two di
4. attributes and location associated with each turtle We will make use of some of the built in NetLogo commands Command Action clear all Clears the world of any previous turtles and patches shape name Changes the default shape for turtle of breed breed to be portrayed using the shape shape name found in the Turtle Shapes Editor create breed name number NetLogo creates number turtles of the type breed name with default color blue size 100 normal value shape turtle and location 0 0 set default shape breed setxy random xcor random ycor Sets the coordinates of a turtle to a randomly gener ated x and y coordinate set attribute value Sets the value of the attribute named attribute to have the value value random pos maz value Provides a randomly generated integer value between 0 and pos maz value random float pos maz value Provides a randomly generated floating point value between 0 and pos maz value To accomplish what we want from our setup procedure we could use the following code to setup clear all set default shape hares rabbit create hares initial hares 33 create the initial number of hares set color white set their color to white set size 1 5 set their size to 150 times the default size setxy random xcor random ycor place them at a random x y position in the world set age 0 set their age at birth to 0 units set default shape l
5. see if you landed on a hare to eat e Check to see if you should reproduce this time do you have enough energy to have a kitten e Check to see if you ve reached maximum age e Check to see if you re out of energy Table 1 Outlining the Behavior of Our Hares and Lynx Based upon these rules we immediately identify some parameter values we ll need the user to specify hare birth rates minimum energy needs for a lynx to reproduce and maximum ages for each animal We ll also need to know how many of each type of animal we ll need to start our simulation i e upon setup 2 1 Setting Up the Interface Start by opening a new model in NetLogo go to the File menu and select New We can now add some of our needed buttons and slider bars We can start by adding the two buttons common to most every NetLogo model the setup and go buttons e Creating the Set Up Button 1 Choose the button option from the pull down menu and then left click in the white portion of the NetLogo Interface tab to position the new button in the window This will pop open a window like the one below Button Agent s Observer Y Forever Commands setup Display name Set Up Action key 2 In the Commands window type the single word setup This will be the name of the procedure that will define how the world should be populated initially It is important not to use blank spaces in t
6. Individual Agent Based Modeling with NetLogo A Predator Prey Example Differential equations in biology are most commonly associated with aggregate models Aggregate models consider a population as a collective group and capture the change in the size of a population over time Consider for example the classic Lotka Volterra predator prey equations dA me rA aAB 1 dB Tes B BAB 2 where A t represents the size of the prey population at time t and B t represents the size of the predator population at time t Without the presence of predators i e when B t 0 the prey population is dA assumed to experience exponential growth rA Similarly if no prey are present when A t 0 dB the predator population will decrease exponentially F 5B The interaction of predators and prey represented by the AB terms have a negative impact on the prey and a positive impact on the predators This system of differential equations models the change in the size of the prey and predator populations collectively over time Individual agent based models however look at population dynamics from an individual s perspective Rather than modeling the aggregate change to the entire population individual based models track the behavior and number of a collection of individuals in a population Individuals move and interact with their environment based on a set of rules and probabilities and are thus stochastic in nature
7. NetLogo is a freely available individual based modeling environment created by Uri Wilensky at the Center for Connected Learning and Computer Based Modeling Northwestern University Evanston Illinois 1 1 NetLogo Models NetLogo comes with a very nice set of built in sample models from a variety of disciplines Perhaps the best way to become familiar with NetLogo is by investigating one of the models in its Models Library Go to the File gt Models Library menu option and select a sample model in the discipline of your choice For the purposes of this introduction we will use the Rabbits Grass Weeds model in the Biology subfolder Before exploring the Rabbits Grass Weeds model an introduction to vocabulary and concepts associated with agent based modeling and NetLogo would be helpful Definition 1 Agents The individuals or organisms in the model The behavior of a class of agents is determined by a modeler defined set of rules In NetLogo there are two types of agents the mobile agents called turtles and the stationary background agents known as patches Definition 2 NetLogo Tabs NetLogo has three tabs at the top of its window An Interface tab an Information tab and a Procedures tab Wilensky U 1999 NetLogo http ccl northwestern edu netlogo Center for Connected Learning and Computer Based Modeling Northwestern University Evanston IL Untitled NetLogo File Edit Tools Zoom Tabs Help In
8. fferent turtles can have different attribute values For instance we ve mentioned that our lynx need to have a certain amount of energy to have a kitten Thus we need to know how much energy each individual lynx has which will depend on the amount of hares it s eaten again not all lynx will have eaten the same number of hares We can declare the attributes named energy and age to be associated with each lynx by the following command lynx own energy age If all turtles will have the same attribute it can be declared using the turtles own attribute name rather than specifying the same attribute for each breed The code needed to start our lynx hare model could look like this breed hares hare breed lynx a lynx hares own age lynx own energy age 2 3 The setup Procedure After defining our turtles breeds and their attributes we can write the code that will define the actions NetLogo will carry out when the setup button is pushed As with all user defined procedures the setup procedure will have the form to procedure name code for actions to take end We want our setup procedure to populate our world with the desired number of hares and lynx placed randomly in the coordinate plane We d also like to set up any attributes associated with each hare or lynx when it is created In addition to the user defined attributes we noted above with our hares own or lynx own there are color attributes size attributes shape
9. h type of turtle breed patch etc is going to be asked to perform each action and choose the action commands accordingly Here s one possibility for outlining the behavior of our lynx and hares once our simulation has started i e the user has hit the go button to go if not any turtles stop If all of our turtles are gone stop the simulation Everyone starts the new time period by moving ask turtles Note that this procedure is for all turtles breeds both hares and lynx take a step telling the turtles to take a random step This is a user defined procedure Defined below Now we see about eating reproducing and aging hares first ask hares try to make bunnies a set age age 1 is This is a user defined procedure made especially for hares see below Increase in age by one unit ask lynx set energy energy 1 try to eat This is a user defined procedure for lynx see below try to make kittens Another lynx specific user defined procedure set age age 1 Before we end this time iteration see if anyone grew too old and must die ask hares Ask the hares if they re too old to die if age gt max hare age die ask lynx Ask the hares if age gt max lynx age die if energy lt 0 die 33 if they re too old to die or if they re out of energy die tick end You ll notice this requires the definition of several
10. his name though underscores or dashes would work 3 In the Display Name window type the name of the button as you would like it to appear to the user for example Set Up 4 Click OK when done e Creating the Go Button In a similar manner add a button that has associated with it the command go Note that if you would like hitting the go button to cause the simulation to run continuously rather than for just one step in time click the Forever button at the top right portion of the pop up window e Adding slider bars for the parameters 1 Choose the slider option from the pull down menu to the right of the Add icon then left click in the white portion of the NetLogo Interface tab to position the slider bar in the window This will pop open a window like the one below Global variable TORE Minimum Increment Maximum 0 Ja 200 min increment and max may be numbers or reporters Value 35 Units optional vertical 2 In the Global Variable line type the single word used to represent the parameter such as hare birth rate Note once again that this should not have any blank spaces in the name This will be the name of the parameter representing the hare birth rate in the code 3 NetLogo gives default minimum maximum and initial values for this slider bar as well as an increment measurement For rabbit birth rate we ve set the minimum value to 0 the maximu
11. ic user defined procedure set age age 1 Before we end this time iteration see if anyone grew too old and must die ask hares Ask the hares if they re too old to die if age gt max hare age die ask lynx Ask the hares if age gt max lynx age if they re too old to die or die if energy lt 0 if they re out of energy die die tick update plot end to take a step A turtle procedure rotate anywhere between 50 degrees CCW to 50 degrees CW right random 50 Turtle rotates right CW a random number of degrees b w 0 amp 50 degrees left random 50 Turtle rotates left CCW a randome number of degrees b w O amp 50 degrees forward 1 Move forward one unit in that direction end to try to make bunnies This is a procedure for hares if random float 200 lt hare birth rate Generate a random number between 0 amp 200 If it s less than the birth rate have a bunny hatch hares 1 Hatch one new hare at your location rt random float 360 Pick a direction for it to take fd 1 It moves forward one unit set age 0 Set its age to 0 newborn 33 end hatch T end if end to try to eat This is a procedure for lynx let prey one of hares here Look for a hare at this location if prey nobody If you got one not a nobody then ask prey die kill the hare prey and set energy energy energy per hare eaten end get energy fr
12. ion you can use monitor boxes To do this 1 Go to the Interface tab and select the Monitor option to add Place the monitor in the white space of your Interface tab and a Monitor Editor pops up Monitor Reporter count lynx Display name Number Lynx Decimal places 17 Font Size 11 full precision is 17 2 In the reporter box type count lynx This will ask NetLogo to count the number of turtles of the lynx breed and report it out to that monitor You can choose the display name you want to go on the monitor box itself 3 Click OK Now you can watch your populations of hares and lynx change in size Have fun HaresLynx NetLogo C Documents and Settings emcnelis My Documents Workshops Shodor Houston_July08 NetLogo File Edit Tools Zoom Tabs Help Interface Information Procedures 7 p v view updates 8 x Bees ae re slower continuous rS N P a mber of Individu Number Hares Number Lynx 264 3 lt Command Center observer clear all observer gt Figure 6 See what happens when you adjust your parameter values A Appendix of Completed Procedures Code breed hares hare breed lynx a lynx hares own age lynx own energy age to setup clear all set default shape hares rabbit create hares initial hares 33 create the initial number of hares set color white set their color to white set s
13. ize 1 5 set their size to 150 times the default size setxy random xcor random ycor place them at a random x y position in the world set age 0 set their age at birth to 0 units set default shape lynx cat create lynx initial lynx create the initial number of lynx set color brown set their color to white set size 1 5 set their size to 150 times the default size setxy random xcor random ycor place them at a random x y position in the world set age 0 set their age at birth to 0 units set their intial energy level to a random value between 0 and 3 energy per hare eaten set energy random 3 energy per hare eaten Note parenthesis and spaces important here update plot end to go if not any turtles stop If all of our turtles are gone stop the simulation Everyone starts the new time period by moving ask turtles Note that this procedure is for all turtles breeds both hares and lynx This is a user defined procedure take a step telling the turtles to take a random step Defined below Now we see about eating reproducing and aging hares first ask hares try to make bunnies This is a user defined procedure made especially for hares see below set age age 1 Increase in age by one unit ask lynx set energy energy 1 try to eat This is a user defined procedure for lynx see below try to make kittens Another lynx specif
14. l in motion with rabbits moving randomly through the world and eating and rabbits and grass reproducing and dying The arrows h on the bottom right hand corner of the go button indicate that this button toggles off and on To stop or pause the simulation simply click on the go button again Stop or pause the simulation and right click on one of the rabbits in the world and select the inspect rabbit option This will bring up a window that displays the information on that rabbit agent In the example in Figure 3 a we can tell we right clicked on rabbit 619 Each agent has its own identification number so it s possible to send instructions to an individual agent The information presented also gives the rabbits x y coordinates in the world which defaults to a two dimensional coordinate system with 10 lt a lt 10 and 10 lt y lt 10 Values of any attributes default or user defined are also presented in this information For instance rabbit 619 has 7 285 units of energy associated with it at the instance we paused the simulation Populations i 299 Horass 6 SSe M rabbits E T 64 95524225280767 0 012767888996712439 rabbits 159 count rabbits 239 ommand Center bserver gt ask rabbit 619 set color blue Le EE EAS bserver gt ask rabbit 619 set color red ie a a aserver gt a Inspecting An Agent b Interacting through Command Center Example The Ob
15. m value to 200 the initial value to 35 and indicated to put a unit of on the slider bar 4 When all needed values are identified click OK Repeat this process for all of the parameter values needed For our lynx hare model we ll also need a slider bar for the initial number of hares initial number of lynx maximum age for hares maximum age for lynx the amount of energy needed for a lynx to be able to reproduce and the amount of energy a lynx gets from eating a hare Some possible values for minimum maximum and initial values for each parameter are presented in Table 2 An initial view of our Interface tab could look like Figure 4 Notice that the Set Up and go labels are in red because we have yet to define the procedures commands associated with clicking on these buttons That s next 2 2 Writing the Procedures In order to write the procedures for your model it is often helpful to open a NetLogo model from the Models Library that shares some of the characteristics of your model and look at it s Procedures tab for ideas NetLogo also has a good set of tutorials a user s manual and a dictionary of NetLogo commands available under the Help menu at the top of your NetLogo window Parameter Name Minimum Value Maximum Value Initial Value initial hares 0 1000 100 initial lynx 0 100 20 hare birth rate 0 200 35 max hare age 0 20 6 lynx energy to reproduce 0 100 30 energy per hare eaten 0 30 10 max lynx age
16. new kitten at your location Note each 3 kitten is identical to its parent attributes and all Everything in here refers to kitten attributes rt random float 360 3 Pick a direction for it to take fd i 3 It moves forward one unit set age 0 Set its age to 0 newborn set energy energy 2 Kitten starts with 1 2 of the parents energy 33 end hatch set energy energy 2 Set the parents energy to 1 2 original energy 3 end if end Now go back to your Interface tab and hit the go button to see what happens If everything was typed in correctly you should be able to see movement of the turtles though it s hard to spot when new ones are added or others die Because it s hard to notice the change in numbers of our turtles we use plots and monitor boxes to provide us with a graphical display of this information 2 5 Presenting Data with Graphs and Monitors In order to create a plot follow the steps below 1 First go to the Interface tab and under the pull down tab select the Plot option and click on a blank location in the Interface This will pop open a plot editor box See Figure 5 for an example 2 You will need specify the name of the plot and the labels for your axes 3 Next you ll need to add your Plot Pens each plot pen corresponds to a different curve line on the plot Name hareblynx X axis label Time x min 0 x max 10 Y axis label Number of Individuals Ymin 0 Y max
17. om eating it to try to make kittens This is a procedure for lynx if energy gt lynx energy to reproduce Check to see if energy level is high enough to reproduce hatch lynx 1 rt random float 360 fd 1 set age 0 set energy energy 2 end hatch set energy energy 2 end if end to update plot set current plot hare lynx set current plot pen hares plot count hares set current plot pen lynx plot count lynx end If it s high enough have a kitten Hatch one new kitten at your location Note each kitten is identical to its parent attributes and all Everything in here refers to kitten attributes 3 Pick a direction for it to take It moves forward one unit Set its age to 0 newborn Kitten starts with 1 2 of the parents energy Set the parents energy to 1 2 original energy Note this is the name you gave your plot on the interface and this is the name for one of your plot pens With that pen plot the number of hares in the world now Switch to the lynx plot pen With that pen plot the number of lynx in the world now
18. server asks a rabbit to change its color Figure 3 Inspecting and Communicating with Agents The user as the observer can directly interact with the agents through the command window For example with the simulation stopped we can ask rabbit 619 to change it s color by typing the appropriate commands in the Command Center at the bottom of the NetLogo window Figure 3 b illustrates the result of typing ask rabbit 619 set color red The Procedures tab gives the collection of commands and procedures that define the rules for behavior and attributes of each agent in relation to the buttons sliders graphs etc that are found on the Interface tab This is where the modeling takes place and it will be the focus of building your own predator prey model in the next section 2 Building a Simple Predator Prey Model Let s suppose we would like to model the Canadian lynx and snowshoe hare predator prey dynamics with NetLogo Note we are making the simplifying assumption that the snowshoe hare is the only food source for the Canadian lynx in keeping with the Lotka Volterra predator prey system dynamics Before starting our model we must identify the rules that determine the behavior of the lynx and hares outlined in Table 1 Agent Rules Hare e Move randomly in the world e Check to see if you should reproduce this time e Check to see if you ve reached maximum age Lynx e Move randomly in the world e Check to
19. subprocedures take a step try to make bunnies try to eat and try to make kittens Those could be defined after the end of the go procedure as follows to take a step right random 50 left random 50 forward 1 end to try to make bunnies if random float 200 lt A turtle procedure rotate anywhere between 50 degrees CCW to 50 degrees CW Turtle rotates right CW a random number of degrees b w 0 amp 50 degrees Turtle rotates left CCW a randome number of degrees b w 0 amp 50 degrees Move forward one unit in that direction 239 This is a procedure for hares hare birth rate Generate a random number between 0 amp 200 If it s less than the birth rate have a bunny hatch hares 1 Hatch one new hare at your location rt random float 360 Pick a direction for it to take fd 1 It moves forward one unit set age 0 Set its age to 0 newborn end hatch end if end to try to eat This is a procedure for lynx let prey one of hares here Look for a hare at this location if prey nobody If you got one not a nobody then ask prey die kill the hare prey and set energy energy energy per hare eaten get energy from eating it end to try to make kittens This is a procedure for lynx if energy gt lynx energy to reproduce Check to see if energy level is high enough to reproduce If it s high enough have a kitten hatch lynx 1 Hatch one
20. terface Information Procedures Figure 1 The NetLogo Tabs e Interface Tab The Interface is the main tab where you interact with your model and see your agents behavior and visualize data It can contain buttons slider bars switches monitor boxes and plots in addition to the world the agents live in the larger black window e Information Tab The Information tab simply contains textual information for the user on how to best understand and use the model e Procedures Tab The Procedures tab is also a textual environment that contains the code the defines the rules that determine the behavior and attributes of the agents in the model Rabbits Grass Weeds NetLogo File Edit Tools Zoom Tabs Help Interface Information Procedures a m v view updates B p l normal speed on ticks v moe ticks 0 setup go M grass M ribbits weeds 100 count rabbits 150 a Command Center observer gt Figure 2 The Rabbits Grass Weeds model after clicking the setup button Returning to the Rabbits Grass Weeds model in order to get ready to investigate the model click the setup button This adds rabbits grass and weeds to our world as illustrated in Figure 2 The number of agents in this world is based on the number of rabbits the grass grow rate and the weeds grow rate specified by the user through the slider bars Hitting the go button sets the mode
21. ynx cat create lynx initial lynx create the initial number of lynx set color brown set their color to white set size 1 5 set their size to 150 times the default size setxy random xcor random ycor place them at a random x y position in the world set age 0 set their age at birth to 0 units set their intial energy level to a random value between 0 and 3 energy per hare eaten set energy random 3 energy per hare eaten Note parenthesis and spaces important here end Note that actions that have more than one line of code are grouped using square brackets and the semicolon is used to indicate the start of line of comments Carefully commented code can be a great help to the user who chooses to adjust some of the rules in your model and it helps you remember why you may have chosen to include certain commands or procedures Also note that not all turtle shapes are loaded to the default library of the Turtle Shapes Editor To see what shapes are available go to the Tools menu and select Turtle Shapes Editor If you can t find an image that suits your purpose you can try importing an image from the library or another model or creating your own image The rabbit and cat shapes were imported from the NetLogo library Once you have this typed into your procedures tab below our breed and attribute declarations you can return to your Interface tab and click on the Set Up button to see if what you intended to happen indeed
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