Q1: What is the difference between a variable and a parameter?

Variables are properties of objects, or changes in state, which vary when during model runs. Parameters are settings or conditions that do not vary during model runs and are used by the model’s formulas to calculate the output variables. In this model, the variable being measured is the Nearest Neighbor Distance (how ever utility is also a variable being calculated during runs), the parameters are aesthetic quality preference, distance to service preference, ideal density, and neighborhood density preference. In this sensitivity analysis the parameter settings were: aesthetic quality preference (0, 0.33, 0.66, 1); distance to service preference (0, 0.33, 0.66, 1); ideal density (0.5, 0.75, 1); and neighborhood density preference (0, 0.33, 0.66, 1). For each parameter the model was run 10 times for a total of 1920 runs. The graphs below show the nearest neighbor distance as a function of each parameter value (Figures 1 – 4).

 

 

 

 

Q2: Which parameter is the nearest-neighbor distance most sensitive to? Why do you think this is the case?

In this model nearest neighbor distance (NND) was most sensitive to the effects of two parameters rather working in concert rather than just one. The parameters, aesthetic quality preference (AQP) and distance to service preference (DSP), in essence had a binary effect on the model. When these parameters had a both had a value of 0 the highest NND values were recorded. Over 1920 model runs the range of mean NND values was 4.24 cells (5.93 maximum to 1.79 minimum), when the AQP and DSP both had a value of 0 this accounted for 60% of the variance in the data (2.55 cells). The plots for AQP and DSP show NND values were widely variable only when these parameters were set to 0. However, neither of these parameters were able to account for the effect alone. When AQP was set to 0 the maximum and minimum NND values were recorded. The results were almost identical when DSP was set to 0, the range of recorded NND values encompassed 99% of the spread of the data.

The AQP and DSP parameters are responsible for creating a heterogenous utility landscape in the model, when they are set to 0 the utility landscape is homogenous allowing the other parameters to dictate the results of the model.

Q3: Which parameter is the nearest-neighbor distance least sensitive to? Why do you think this is the case?

The Ideal Density (ID) parameter was the least sensitive parameter in this model. Each of the three parameter settings produced very similar looking graphs. No one setting produced an appreciable difference in the NND.
The portion of the utility equation that involves neighborhood density preference and ID includes the value parameter values for neighborhood density which never falls below .5, this portion of the equation stable and reduces the effect of ID has on the NND.

Q4: In our parameter sweep we used the mean nearest-neighbor-distance as an output descriptive statistic. Describe why nearest-neighbor-distance may be important to homeowners. List at least one other measurement that we could have used and explain how it differs from mean nearest-neighbor-distance.

Of almost universal interest to homeowners is how their land can be used, and how land adjacent to their own can, and may be used, and what opportunities may arise or be precluded by current or alternative uses. People (who have the agency to act by choice rather than desperation–a big caveat) often choose a place to live because it is close to the things that are important to them, in this model, and in life, people desire access to the services that support their lifestyle. In many circumstances settlement density is linked with certain types of services. Dense urban populations have the critical mass needed to warrant public transit systems, make efficient use of energy compared to their rural counterparts, attract diverse businesses, and foster numerous rich cultural movements. In turn, these spaces often become more desirable locales and attractors of further settlement perpetuating the demand for more services and ultimately the patterns of growth and densification illustrated by this model. Antithetical to the density of compact urban spaces, the rural lifestyle, too, is predicated on a critical threshold for population to maintain its character and benefits. Nearest neighbor distance must be high to allow for space between homes, and distance to services can shift in meaning as the services derived from space supersede the importance of euclidean distance to business services.

An alternative way to measure urban growth would be to look at settlement density in each agent’s immediate neighborhood as a percentage of neighbors to potential total neighbors. Instead of looking at the distance from each agent to its nearest single neighbor, which tells us something about the closest neighbor but nothing about the next nearest, and so on. If all agents settle immediately adjacent to each other yet not near to another pair the nearest neighbor distance will be very low even if the pairs of nearby agents are dispersed from each other. When looking at the neighborhood density, the ID parameter, which before was the least sensitive parameter may become the most sensitive parameter. When the ID is set to its lowest value (0.5) the neighborhood density is very low despite the nearest neighbor distance remaining in a typical value. However when the ID is increased by just 20% the neighborhood density value can quadruple (Figures 5 & 6). Low ID values can result in a 0% neighborhood density, this can be observed when the general pattern of settlement is highly dispersed or relatively clustered around the points of attraction (Figures 7 & 8). Similarly, when the ID is high, higher levels of neighborhood density are seen when the general pattern of settlement is both highly dispersed or relatively clustered around the points of attraction (Figures 9 & 10).

 

Measuring neighborhood density gives further insight to the neighborhood clustering patterns that the model produces. This new look helps to show that despite very similar general patterns of settlement produced by the model, the immediate neighborhoods of the agents actually has more variability than may be initially apparent when looking at the visual patterns and the nearest neighbor distance data alone.

Q5: Provide a 100 word summary of what the model describes with regard to how residential decision making leads to specific patterns of urban growth.

The residential growth patterns had three main pattern characteristics, there were very dispersed clusters of settlements, clustered settlements around the points of attractions, and local patterns of clustering and dispersal were seen in both the former conditions. In general when agents considered the points of attraction they were likely to group near to these points to some degree. Essentially this says that settlements generally aren’t random and once the early settlers begin to arrive the next arrivals are likely to begin following the existing pattern of settlement. This model exhibits the role that path dependence has in settlement patterns and how the decisions made by the initial settlers feed into decisions made by those who follow.