Zed Langston
May 12, 2015
Assignment 4: Feedback’s and Path Dependence

Description: 

This is a development model built by combining several sub-models in NetLogo.  This model was built to emulate how the emergence of urban development patterns by agents occur on a landscape over time.  In addition, how these development patterns (spatial structure) are affected over time by feed backs and path dependence.  The parameters (preferences) are the distance to services (range 0 – 1), the aesthetic quality (range 0 – 1), the neighborhood density (range 0 – 1) and the ideal density (range 0.5 – 1).  The sub-models are the aesthetic quality, the distance to service, the utility (function), the resident development, the neighborhood density and a service that will add service centers near the closest available cell next to the newest building after every 20 buildings developed.  The environment was set to 100 x 100 to simulate a landscape that is 10,000 square meters with each patch having a cell size of 4 x 4.  Two points of attraction (yellow) were created and added to the environment P1 at (25, 25) and P2 at (75, 75) as well as a initial service center (green) S1 at (50, 50).  The utility function calculates a weighted average using the aesthetic, service center distance and neighborhood preference values to find the most suitable (highest weighted) site for development based on 16 randomly selected cell locations per time-step (using the numtest) reflective of the stochasticity of real-life decisions, to develop a site, that would be made in the real world.  This random selection (stochasticity) of potential sites can lead to path dependance.  The settings for the model are 0.5 for the aesthetic quality, distance to service and neighborhood density preferences and 0.75 for the ideal density at setup. The video below shows the emergent pattern.

Questions

1) It is important to test each of the sub-models independently (while creating the code blocks) to see what the sub-models do and make sure each one is working as expected.  If you complete the whole model using sub-models and it doesn’t work it is a lot harder to figure out where the problem area is.  It is important to test each of the sub-models independently to look at the effects on the agents and how the parameters change the agents behavior as it relates to the points of attraction and the initial and additional service center(s).  To test the sub-models, a parameter sweep was used using (0, 0.5, 1) and by setting the other parameters at the same value (null).  Using this method each parameter was tested after it was created and verified to test functionality and reasonableness.  The images in the first row show the results of testing a high aesthetic preference sub-models without any development, with development and with development showing the utility.  The second row images show a high aesthetic quality preference sub-model with no initial service center, with a service center and with the aesthetic quality set to 0.  This indicates that the aesthetic quality is based on the two points of attraction.  The lighter color reflects a highest aesthetic quality area.  The third row (down) shows the distance to services sub-model with an initial service center (left) with development (middle) and with development showing the utility (right).  The fourth row (down) shows the distance to services sub-model with an initial service center and both a high aesthetic quality and distance to service center parameter preference (left) and with both preferences set to 0 (right).  As expected in both of these sub-models the most desirable development location (bright spot) occurs at the place(s) that correspond to points of attraction and/or a service center.

However, these patterns would change as development occurs because new service centers are created and the two density preferences (one is include in the utility calculation if the value is above null) leading to undeterministic outcomes.  It should be noted that when the preference for the variables is low or null every patch in the landscape would be equally acceptable for development (the landscape has the same color: right image in row 2 and 4).  The density sub-model is not applicable until development occurs.  When no preferences are selected site development is equally likely to occur in any location of the 16 randomly selected locations over the landscape.  As development occurs, the locations for possible development are influenced by the parameter settings for aesthetic quality distance to service center, neighborhood and ideal density.  If the aesthetic quality is high then development options occur near the points of attraction and so on based on the weight of the utility (the highest calculation result of the 16 randomly selected potential sites).  The result of the independent testing met (conformed with) the expected results.  The diagnostics did conform to expectations because the aesthetic quality preference relates to the points of attraction (Row 1: middle and right image) whereas the distance to service preferences relates to the service center (Row 3: middle and right image).  The utility conformed to expectations because it shows the most suitable areas for development based on the calculation providing a weighted result using the setting of the preference parameters.  The density preference affects location suitability for development.  When density preference is high development is likely to occur in areas that have development.

2) Stochasticity is implemented in this model by the randomness of the selected suitable locations (n-test) for development placing limits on where the agents may develop at each time step (16 is the setting used for most of the images).  The utility value of locations that are part of the selection is specified but the potential sites for development are randomly selected.  Stochasticity is also implemented by where the new service centers are developed because the potential development sites are chosen at random and with every 20 developed buildings, a new service center is created closest to the last development in the nearest available patch.  The parameter that influences the stochasticity is the numtest (n-test).  The images below show the utility of the most desirable development locations over the landscape.  I know that development will occur somewhere in the bright spot but the 16 chosen patches/agents are selected at random within that area and the highest of the random locations is selected for agent development.  The middle image (max aesthetic, distance to service and neighborhood density preference and a minimum ideal density setting) shows the first 20 developments. The first development occurred near P2 while the 2nd service center was developed next to the last development near P1.  This image shows how there is both stochasticity (from the suitable location selections) and uncertainty (development of new service centers) of where the new service centers will be developed.  The utility gives you an idea about development that allows some prediction despite the stochasticity (the Numtest).  The higher the n-test, the more suitable location are selected for possible development.  The right image shows the spatial distribution using the same setting except the n-test was set to 50, meaning at every time step 50 possible suitable locations were selected at random for development.  This image shows a less distributed spatial pattern because the agents have more choices for the desired development location even though possible sites are selected at random.

3) Environmental heterogeneity is implemented in this model by using an initial service center and points of attraction because of the parameter settings relating to the points of attraction (aesthetic quality preference) and initial service center (distance to service center preference).  The distance to service center preference also determines the importance of the service centers (to the agents) that are built in relation to the number of buildings developed.  The parameters that determine its importance are the distance to service, aesthetic quality preferences but density preferences also have an impact (not initially though).  Among many model iterations greater heterogeneity (top images) leads to less variability because there are less options for new developments with every time step.  With less environmental heterogeneity (bottom images) there is more variability between model runs using the same parameter settings.  The upper images below shows 4 iterations with no initial service center, increasing aesthetic and the distance to service center preference parameter preferences (set at 0.0, 0.2, 0.4, 0.6), no density preference, ideal density set at 0.5 (the lowest) and the n-test set at 16.  The lower images below shows 4 iterations with an initial service center, increasing aesthetic and the distance to service center parameter preferences (set at 0.0, 0.2, 0.4, 0.6), no density preference, ideal density set at 0.5 (the lowest) and the n-test set at 16.  In both sets, greater variability is shown with less environmental heterogeneity with and without the initial service center.  It appears that with less initial and overall heterogeneity, there is the most variability because there are more suitable locations that could be developed and less path dependence at each time step in space.  However, as development occurs the agents are more likely to develop closer because the suitable areas chosen at random tend to be closer together (higher path dependence), especially as the parameters are increased.

 

4) In this model, feedbacks are positive when the neighborhood density and distance to service center preference parameters are higher.  The major feedback signal is the development of new service centers (based on the preference setting) because it encourages more development in the vicinity of the created service center.  New service centers are created with every 20 new developments (the setting used) encouraging more development to occur around the service center or developed area.  Path dependence is high when the feedback is high but it is more random when there is no feedback.  The images below show how development is higher near created service centers.  The settings for image one (upper left) were low for the density parameters and high for the service center preference showing the spatial emergence at about 100 developments.  The settings for image two (upper middle) were high for neighborhood density, and service center preference and shows the spatial emergence at 300 developments.

The two concepts are related because feedbacks lead to path dependence.  There is feedback that leads to more development (path dependence) in areas with more service centers especially if the distance to service center preference is high and the service centers are created.  The neighborhood density and distance to service center preference parameters relate to the feedback because the distance to service center and density preference lead to path dependence because of the feedback (causing development near the built neighborhoods and service centers).  So, the feedback of the service centers development encourages more building development (path dependence).  To limit path dependence, I would set the distance to service center and neighborhood density parameter preferences to null.  However, randomness also can lead to path dependence and the n-test introduces stochasticity.  Setting this to a lower number will decrease available locations to development at each time step.  This result can be seen in image three (upper right) showing the emergence with minimal parameter preferences (o.2 for neighborhood density and 0.5 for ideal density) , n-test set at 5 and showing the utility (suitability for development).  However, this might be viewed as a negative feedback in a sense but causes a more distributed spatial development patterns (emergence) through time and over space.  The left image on the bottom shows null preferences (except ideal density, set to the lowest setting 0.5) with a higher value for the n-test (set at 16).  The bottom middle image shows the same settings and utility with no neighborhood preference causing the most distributed emergent pattern.

5) The major model assumptions are that the model will better emulate urban development over a landscape if the ideal density preference parameter is at least 0.5 or higher, better reflecting how agents would choose (in the real world) where to develop. Whether that preference is near a service center (distance to service preference), points of interest (aesthetic preference) or in neighborhoods that are growing more rapidly (density preference).  That would influence the environmental heterogeneity and the feedback’s that lead to increased path dependence.  This would decrease the spatial variability and lead to more clustered spatial distribution patterns.  The top left image shows the emergent pattern when the parameters are set to 0.25, there is an initial service center, ideal density is set to 0.5 and the n-test is set to 16.  The top middle image shows the emergent pattern when the parameters are set to 0.50, there is an initial service center, ideal density is set to 0.75 and the n-test is set to 16.  The top right image shows the emergent pattern when the parameters are set to 0.75, there is an initial service center, ideal density is set to 0.85 and the n-test is set to 16.  These images show that preferences have feedback signals that lead to more path dependence, creating tighter spatial groupings over the landscape.  Another assumption is that there is at least two points of interest, that may or may not be the case, and depends on if the landscape area to be developed.  If the area was urban, there would likely be more points of interest.  The bottom three images show an ideal density of 0.5 (lower left), of 0.75 (lower middle) and 1.0 (lower right) with all other setting remaining constant.  As visible in these three images the amount of dispersion and clustering increases as the ideal density is increased.  In addition, the distribution of agents (evenness) of the emergent pattern decreases as ideal density increases.  The assumptions in this model influence the interpretation because we assume that the agents all think the same (based on the calculation weighting from the randomly selected site locations) about choosing a site for development.  However, we introduced stochasticity to reflect different decisions that would be made by differing developers.  This has to be a consideration when interpreting the patterns because, even though there is a random component, development is based on the included preferences, while in actuality decisions made by an agents could vary considerably.  Some agents may choose to live away from other development areas if that was a choice and the constraint on that choice results in less dispersion and, with minimal preferences, more clustering.

A simplification would be that all developments are equal.  If there were a way to emulate certain kinds of service centers, developments or points of attraction, then it would be more likely to have agents that prefer some over others.  This would also change the way that the emergent patterns would be interpreted because we wold need to know the demographics, age ranges, etc. and how important the service center or building developments are to the individual people or households creating another layer needed for analysis and prediction.  Another simplification in the model is that a new service center is developed after 20 buildings are developed.  This is not really reflective of what one would observe normally where neighborhoods or cities go through periods of growth and decline and development often corresponds to these periods.  In a high growth period, may service centers may be developed and may spur new service centers or residential development.  In addition, development often occurs in specific areas (as infill or in areas with available land because other areas have no more room for development).  This simplification does influence interpretation results because every twentieth time step a service center is built near the previous building creating path dependence of upcoming agent development.  The simplified model can help to understand how development preferences change the structure of a neighborhood over time but in some ways it would be hard to fit the development patterns in the real world because things (demographics, economy, available land, zoning, etc.) change and are not constant.