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Overview

An important part of the modeling process is the development of simple models to help us train our intuition about the causes and implications of a pattern we observe in reality. These simple models can help us to understand our assumptions about how human decision-making, ecological processes, and interactions among modelled components affect each other and aggregate to produce macro or system level outcomes.

In the presented model (SOME – SLUCE’s Original Model for Experimentation), we considered the question of how different behavioral assumptions affect the extent of sprawl. This website allows the user to explore the SOME model of residential location. Through this website, we hope that you will see this simple model as a tool to help generate and evaluate hypotheses about residential location and settlement patterns, learn about agent-based modelling, and see the utility of simple models that can be used to form the basis of larger and more complicated models.

What follows is a guide through the SOME model, accompanied by a series of experiments and questions that will get you thinking about the behaviour of the model, and agent-based modelling and residential sprawl more generally. While this website was developed by D. Robinson, the conceptual developments and initial NetLogo models were developed by Dr. Daniel Brown and the greater SLUCE research team at the University of Michigan. A list of research papers that have extended this model or used this model as inspiration is given at the end of the webpage.

 

Description of the SOME model

The SOME model has four components that are visible upon setup and watching a model run. The Landscape, Residential Household Agents, Service Center Agents, and a sprawl measurement boundary (a yellow circle). The model is initialized with a Service Center Agent at the center of the landscape (red dot), surrounded by the sprawl boundary, in a landscape of aesthetic quality. Residents that locate outside of the sprawl boundar are counted as sprawled residential settlement units (black squares). The number of sprawled units provides a measurement for comparison between different model settings and the overall level of sprawl. The screen capture below shows the landscape and model components after running a few time steps.

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The model is initialized with a service center located at the center of the landscape. The model moves forward in discrete time steps, whereby each time step could represent a month or a year. The link between the logical time of the model and real-world time has not been made explicit in this simple version of SOME, but has been made in the modelling papers in the reference section of this website. Each time step, 10 residential household agents are create and evaluate some number of locations to settle (numTests parameter). The settle at the location that maximizes their utility for aesthetic quality and nearness to urban service centers. After 100 residential household agents have settled a new service center agent is created and locates near the last residential household agent.

The Landscape

The SOME model is situated in a hypothetical landscape that has a single environmental variable, environmental beauty or as we refer to it, aesthetic quality. The aesthetic quality of each cell is set at the beginning of each model run using a random map that is smoothed to some degree, specified by a smoothness parameter (called “smoothness”). The smoothness parameter creates a coarser grained (i.e. smoother) pattern of aesthetic quality at higher parameter values. With no smoothness, the aesthetic values of the landscape vary greatly and are completely random. With a high smoothness, the values change little from place to nearby place. With the model you can move the slider on the smoothness widget to change the landscape smoothness. (The aesthetic quality map could be read from a GIS data layer if we wanted to evaluate these dynamics in a particular place).

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Residential Households

Residents locate themselves on the cells that maximize their utility. Residents evaluate utility by calculating a score for each sampled cell that is a function of that cell’s distance to nearest service center, that cell’s aesthetic quality, and the importance the resident places on distance and aesthetic quality. All residents prefer cells that are closer to a service center and have higher aesthetic quality.

utility of a cell to resident = ( ( 1 / sddist ) ^ alphaS * quality alphaQ ))

The distance of each cell to the nearest service center (sddist) is calculated each time a new service center enters. The importance residents place on aesthetic quality (alphaQ) and distance (alphaS) is set according to a parameter called “Space-Quality-Tradeoff.” If this value is 1.0, each factor is given equal weight in the calculation of utility. A value of 2.0 places all emphasis on distance, with no consideration of aesthetic quality. Conversely, a value of 0.0, forces the residents to consider only aesthetic quality, with no consideration of service center distance. All residents have the same utility function and parameter values.

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Residents locate themselves on the cells that maximize their utility. However, they only get to sample some small number of cells before selecting one. The parameter “numtests” determines how many cells each resident gets to sample and, in this version of the model, it can be set to any value from 1 to 30 (15 is default). By providing the residents incomplete information about the cells in the landscape, this process represents a form of bounded rationality.

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Measuring Sprawl

Because our interest has been in using ABMs to help understand urban sprawl, we have incorporated a measure of sprawl into the model. The measure is simply the number of developments (residents or service centers) that are located outside a specified distance radius from the center cell. The circle defined by this radius is displayed in yellow on the screen and can be changed using the “radius” parameter. At each time step, the cells that fall outside the specified radius are counted and the number is plotted on the graph. Model settings that locate more residents outside the radius at a given time step indicate a system with more sprawl.

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Environmental Feedback

The model also has the ability to incorporate coupled human-environment interaction. You may switch this feature on and off with the ‘LUAB’ switch. With ‘LUAB’ (Land Use Affects Beauty) switched off residents evaluate the landscape but do not change the aesthetic value of the landscape. When ‘LUAB’ is switched on, each development reduces the aesthetic quality of the cells around it. This can result in changing the decisions made by the subsequent residents as they evaluate the aesthetic quality of available cells. This process can reduce desirability of locations selected early in the model run and can serve as a form of negative feedback.

Service Center Feedback

In addition to the influence of environmental feedback on agents location decision making is feedback between agents and service centers. Each time a new set of 100 residents locate in the landscape, a new service center locates by selecting a random direction and moving out from the last resident until it finds an unoccupied cell. This is a relatively crude approach to locating service centers, but it captures our intuition that services tend to locate near people, who can serve as both customers and employees. This process can reinforce the location decisions of early residents as a form of positive feedback.

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Experiments

Experiment 1

Our first experiment considers an environment in which there is no heterogeneity in the aesthetic quality of the land. The sprawl boundary has been set at a 25 cell radius from the initial service center, located at the center of the landscape.  Click here to open a new browser tab with the SOME model or click on an existing browser tab if you have already opened the model webpage. Once the new webpage opens click on the Exp#1. SMOOTH LANDSCAPE, LOW INFORMATION button and then the SETUP button.

The landscape should be initialized with aesthetic quality values, a sprawl boundary, a smooth landscape, luab off, and a sampling of ten locations (i.e., numTests) for each residential household agent. In this experiment, the residential household agents do not look at many locations before choosing a place to live. In fact, they consider only ten random locations, which in a landscape of 6400 locations represents a sample size of less than 1%. The sample size limitation reflects the imperfect or incomplete information that residents have when they choose a residence. Since there are several parameters that can be changed, you may want to create a worksheet in Excel and record the different parameter values and model results as you run the model multiple times and you may want to compare among model runs or between experiments.

When you are ready you can press the GO button and the model will run. If it seems like the model is running too fast to watch you can either run through the model one step at a time using the NEXT STEP button or you can move the ‘speed’ slider at the top of the NetLogo model. Run the model a couple times by repeating the procedure listed above to get a feel for how the SOME model works and how the process represented in the model produces the final outcomes you observe. Run the model at least five times and measure the amount of sprawl by recording the number of developments outside the radius at the end of the model run. You can read the numbers off the graph by pointing your mouse at the appropriate location on the graph. This will allow you to compare model settings for the degree of sprawl they produce. You can calculate the average and standard deviation for each model setting if you like for comparison with the other experiments.

Question 1. Describe the behavior of the model and why you observe the produced settlement patterns for one or two typical model runs?

Question 2. Does each run produce the same number of settlements beyond the urban growth boundary? Discuss why the number of settlements beyond the boundary do not change (or do change) each time the model is run. What is required to make a model stochastic or deterministic and how could we modify the SOME model to be one or the other?

Question 3. Run the model 20 times and record the number of settlements beyond the sprawl boundary. Compute the average and standard deviation. Discuss when you should report the average and standard deviation of model outputs and how this information might be used to determine how many times you should run a model with the same set of parameters.

It is easy enough to run and watch the model 20 times for each experiment because it is a simple model. It would be more efficient if you were able to run the model multiple times using the same parameter settings and have the software automatically record the results of those individual runs for you. It would be even better if you could have the model iterate a number of times for each of several parameter settings! NetLogo has a tool to do this, which is called Behavior Space. If you are feeling keen and want to try to set up Behavior Space for your experiments then you will have to download and install NetLogo on your computer, export the code for the SOME model from the SOME model page, and under the Tools menu item you can find the BehaviorSpace tool. The openABM initiative has a useful Behavior Space tutorial that may be of interest.

Question 4. What mechanisms in the model act as centripetal forces (cause increasing clustering) and which ones act as centrifugal forces (cause more sprawl)?

Experiment 2

Our second experiment investigates the effects of increasing the amount of information (“numtests”) of each resident. In Experiment 1, residents selected the best location from a list of 10 locations. In this experiment residents evaluate 30 locations. We do not change the aesthetic quality of the landscape because we are interested in the effects of increasing information on settlement patterns.  Click here to open a new browser tab with the SOME model or click on an existing browser tab where you have the model open.

Once the new webpage opens click on the Exp#2. SMOOTH LANDSCAPE, HIGH INFORMATION button and then the SETUP button. The landscape should be initialized with aesthetic quality values, a sprawl boundary, a smooth landscape, luab off, and a sampling of 30 locations (i.e., numTests) for each residential household agent. While the evaluation of 30 locations is still a small sample (i.e., less than 1% of the study area) the results are notably different. Again, you should record the different parameter values and model results as you run the model multiple times and you may want to compare among model runs or between experiments. When you are ready, click the GO button and the model will run. Run the model 10-20 times and record the amount of sprawl at the end of each model run. Calculate the average and standard deviation for comparison with the other experiments.

Question 5. Describe the behavior of the model and how the parameter settings influenced the settlement patterns that were produced?

Question 6. How do the settlement patterns from this experiment differ from those in Experiment 1, were the patterns more or less clustered? Use both quantitative (mean and standard deviation) and qualitative (visual interpretation) results.

Question 7. Why is the graph initially flat? Is the number of settlements beyond the urban growth boundary increasing linearly, exponentially, or taking some other form? Can we expect this trend to continue in the modelled landscape (why or why not)?

Question 8. The decision-making approach used by the residential household agents in the model is called bounded rationality. Each residential household agent is making a rational decision to maximize its’ utility from a subset of study area locations (i.e., numTests). Because the residential household agents are basing their rational decisions on a subset of locations the decision-making process can be referred to as bounded rationality. Describe what we can learn from changing the level of information available to an agent and relate it to the concepts of bounded rationality and rational decision making, which is sometimes referred to as homo economicus.

Experiment 3

Up to this point our experiments have explored the effects of changing the the level of agent information (as represented by the number of evaluated locations) in a relatively smooth landscape with little variation in aesthetic quality (grey cells in table below).  In this 3rd experiment, residential household agents will continue to evaluate 30 locations, but they will do it in a landscape with greater variation in aesthetic quality.

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Click here to open a new browser tab with the SOME model or click on an existing browser tab where you have the model open. Once the new webpage opens click on the Exp#3. ROUGH LANDSCAPE, HIGH INFORMATION button and then the SETUP button. When you are ready, click the GO button and the model will run. Run the model 10-20 times and record the amount of sprawl at the end of each model run. Calculate the average and standard deviation for comparison with the other experiments.

Question 9. Compare and contrast this model behavior to the two previous experiments. Describe the differences or similarities among the experiments using the number of settlements beyond the sprawl boundary, the landscape patterns, and the shape of the graph.

Question 10. “All models are wrong but some are useful” (Box 1979, pg. 2) highlights the fact that by definition a model is a simplification of reality and inherently has flaws in the representation of reality within the structure of the model. However, this does not exclude the fact that a model can be useful and that models may ultimately be judged based on how useful they are. Conceptualize two or three uses that could demonstrate how or why this model, its results, or the agent-based modelling approach are useful. If you do not think the model is useful then argue why it is not. In either case try to provide some literature justification for your argument.

Box, G. E. P. (1979), “Robustness in the strategy of scientific model building”, in Launer, R. L.; Wilkinson, G. N., Robustness in Statistics, Academic Press, pp. 201–236.

Experiment 4

You should now have completed the first three experiments (grey cells in the figure below), where you varied the number of search locations (i.e., numTests) and started to look at variation in the landscape as represented by aesthetic quality values. Each of these experiments had been predefined for you and the buttons at the top left of the model have set the parameters accordingly. We leave Experiment 4 and its analysis for you to create and conduct on your own. Click here to open a new browser tab with the SOME model or click on an existing browser tab where you have the model open. Run the model 10-20 times and record the amount of sprawl at the end of each model run. Calculate the average and standard deviation for comparison with the other experiments.

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Question 11.  To answer this question develop a research question related to landscape variability and describe in 2-4 paragraphs the relevance of answering this question and how modelling can help answer this question. Use peer reviewed literature to help establish some context or identify research gaps that answering your research question may help to fill. If you’re in the University of Waterloo GEMCC 630/GEOG 653 Land use and the carbon cycle then relate this back to some aspect of landscape variability that affects the carbon cycle or climate processes. If you’re in another course using this website then think about the course content and the broader concepts in the course that are driven by or affected by landscape variability.

Experiment 5

Until now we have explored only the effects of information and landscape variation on residential settlement patterns and the amount of sprawl (as represented by settlements beyond the 25 cell radius sprawl boundary). Residential household agents have indirectly interacted with each other by occupying locations that could be settled by other agents and may even be more preferred by other agents. In this experiment we expand on this type of interaction by incorporating additional environmental or aesthetic impact from settlement by degrading the aesthetic quality locations that have been settled. To focus on this effect we use a smooth landscape with little aesthetic variation and focus on only one or two parameter changes so that we can interpret and learn about the different mechanisms in the model. If we were changing many parameters at once it would be very difficult to understand and learn from the model.

Question 12. Before you run the model make a hypothesis about how you think the pattern of settlement and the amount of sprawl will compare to the previous experiment. Include this hypothesis and your logical reasoning for it as an answer to this question.

Click here to open a new browser tab with the SOME model or click on an existing browser tab where you have the model open. Once the new webpage opens click on the Exp#5. Smooth LANDSCAPE, HIGH INFORMATION, LUAB On button and then the SETUP button. When you are ready, click the GO button and the model will run. Run the model 10-20 times and record the amount of sprawl at the end of each model run. Calculate the average and standard deviation for comparison with the other experiments.

Question 13. Describe why you think the model behaved as you hypothesized or  behaved differently from your hypothesis in Question 12.

Question 14. Compare and contrast this model behavior to the previous experiments. Describe the differences or similarities among the experiments using the mean and standard deviation in the number of settlements beyond the growth boundary, the landscape patterns, and the shape of the graph.

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Additional Questions

If you download the model and run it in NetLogo then you can add a couple lines of code to get NetLogo to create output files of the spatial pattern. You could then measure those patterns and compare them using landscape pattern indicies (LPIs), which are also sometimes referred to as landscape metrics. What would this enable you to do that you can’t do visually?

What is a random seed, how could it be used in the SOME model, and why would it be useful to record a random seed?

You could run a regression on your results and model parameters with your dependent variable being the amount of sprawl and your independent variables being the parameter values. If you applied this to all the data you created from the experiments above, what would it tell you?

Experiment 5 asks you to make a hypothesis about the model outcome before running the model. This challenges the model user to think critically about the model and their conceptual understanding of the system being modelled. For me, I find it useful in that 1) when the model acts as I hypothesized I typically don’t believe I can be correct about these sorts of things and it forces me to interrogate the model further to be sure the outcome is correct (e.g., there are no coding errors, incorrectly set parameters, other modelling artifacts), and 2) if my hypothesis is incorrect then I get worked up because I was wrong and find myself driven to figure out why I was wrong. Either way, I end up double and triple checking everything, which makes for a robust outcome. This story highlights an important question, can you use this type of model for predictive purposes? Discuss why this model can or should be used for predictive purposes or why it should not.

Remember that all residential agents have the same parameter values in this model, including preferences for nearness to service centers and high aesthetic quality, which are equally weighted. Since distance and aesthetic quality are equally important to the agents, they will not sacrifice a lengthy distance for higher aesthetic quality. The Space-Quality-Tradeoff slider alters the relative importance residents place on distance to a service center versus aesthetic quality of a location.One thing we did not do, and should often be a first step is to set a parameter like this to the extreme values and ensure that the model behaves as you would expect. So if you set the Space-Quality-Tradeoff to zero what happens and what happens when you set it to two? Did the model perform as you expected?

Think about the factors driving your preferences for a good location to settle at or why you like some places more than others. What other drivers of residential location are essential and missing from this model and the papers that expand on this model? How would you collect data to empirically inform and justify the inclusion of these additional drivers.

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References

2013. Robinson, D.T., Shipeng, S., Hutchins, M., Riolo, R.L., Brown, D.G., Parker, D.C., Currie, W.S., Filatova, T., and S. Kiger. Effects of land markets and land management on ecosystem function: A framework for modelling exurban land-changes. Environmental Modelling and Software, 45: 129-140. DOI: 10.1016/j.envsoft.2012.06.016

2012. Rounsevell, M., Robinson, D.T. and D. Murray-Rust. From actors to agents in socio-ecological systems models. Philosophical Transactions of the Royal Society B 367: 259-269. DOI: 10.1098/rstb.2011.0187

2009. Robinson, D.T. and D.G. Brown, Evaluating the effects of land-use development policies on ex-urban forest cover: an integrated agent-based GIS approach. International Journal of Geographical Information Science 23(9): 1211-1232.

2008. Brown D.G., Robinson D.T., Nassauer J.I., An L., Page S.E., Low B., Rand W., Zellner M., and R. Riolo. Exurbia from the Bottom-Up: Agent-Based Modeling and Empirical Requirements. Geoforum 39: 805-818.

2006. Brown, D. G. and D. T. Robinson. Effects of Heterogeneity in Residential Preferences on an Agent-Based Model of Urban Sprawl. Ecology and Society 11(1): 46.

2005. Brown D., Riolo R., Robinson D.T., North M., and W. Rand. Spatial Process and Data Models: Toward Integration of Agent-Based Models and GIS. Journal of Geographical Systems (7)1: 25-47.

2005. Brown, D.G., Page, S.E., Riolo, R., Zellner, M., and W. Rand. Path dependence and the validation of agent-based spatial models of land use. International Journal of Geographical Information Science 19(2): 153-174.

2004. Brown, D.G., Page, S.E., Riolo, R., and W. Rand. Agent based and analytical modeling to evaluate the effectiveness of greenbelts. Environmental Modelling and Software 19(12): 1097-1109.