1. Why is it important to test each of your sub-models independently? Explain how you tested the sub-components of the main model using images and text to illustrate your methods and explain how your diagnostics conformed (or not) to your expectations.

It is important to test the model parameters and sub-models independently as you develop your model to make sure that your coding and module runs as expected. It is also necessary to do this in order to determine how each separate parameter affects the outcome of the model. Parameters that work together collectively and/or synergistically may have completely different outcomes than individual parameter settings alone.

One way to ensure that your sub-models are working properly is to visually inspect them. In lab we learned how to represent the value of cells with the built in NetLogo function – “scale-color” allowing us to determine if our model was “set up” properly. Take for example the following screenshots of the sub-models where each parameter of preference; distance services preference (DSP), aesthetic quality preference (AQP), and the neighborhood density preference (NDP) was visualized and then tested independently. Also, the “utility” of cells, which was based on the weighted value of both DSP and AQP, was also visually inspected in this manner and it gave an especially predictive power to the observer of where to expect to see development occur under these conditions.

Distance Services Preference – Screenshot of visualization and model results

Aesthetic Quality Preference – Screenshot of visualization and model results

Show Utility Function – Screenshot of visualization and model results

2. The methods for calculating the components of utility are deterministic in this model. How is stochasticity implemented in the model? What parameter influences the degree of stochasticity?

Stochasticity is introduced into this model in at least two ways. One is with the variable “n_test” that sets the number of randomly chosen vacant cells that are available to be developed at the beginning of each time step. While the quantity is determined by the observer the cell’s locations are random and this affects the following distributions of agents depending on what the parameter settings are.

Another way stochasticity is introduced in this model is when the “initial center” variable is not turned on and the beginning developments are assigned a completely random starting location. However, once again, when the model is initiated the process becomes deterministic and the distributions depend on what the parameter settings are for that model. That being said, if there are no parameter settings implemented for the model run then it should produce a completely dispersed and random pattern of settlement. This is indeed what we find when we run the model with no preferences as demonstrated by the following video.

Video of the model running with no preferences or starting center and showing a “random” dispersal

3. How is initial environmental heterogeneity implemented in this model and what parameter or parameters determine its importance? Do you think that greater environmental heterogeneity corresponds to greater variability among replicate model runs, and why? Support your argument with evidence from replicate simulations with and without initial environmental heterogeneity.

For this exercise, Brown et al (2005) test for what they call “extreme path dependence” where they run their model with no initial center and test the parameters of ‘distance to services’ versus ‘aesthetic quality’. This is an attempt to get at part of their larger hypothesis that environmental homogeneity leads to greater path dependence. Basically, they suggest that land-use histories are more “path dependent” where the environment is variable and that if there is less variability in the landscape then people will make choices to live somewhere based on parameters like “distance to service” which have been ultimately determined by the initial settlers (i.e. path dependence). I agree with this statement and the difference between homogeneity and heterogeneity in this model is exemplified, and can be easily visualized, when we look at the DSP parameter with its initial center both on and then off. In this figure a more homogenous environment is displayed with the initial center “off” while a heterogeneous environment has its initial center “on”. Also, multiple runs with visual inspection and graphic analysis support Brown et al’s (2005) hypothesis that a homogenous landscape results in stronger path-dependence and less variability among replica runs and these results are discussed in more detail in Lab 5.

Screenshot of homogenous and heterogeneous environments focused on DSP

4. Explain the roles of feedbacks and path dependence in this model. How are the two concepts related? How do the three parameters for preference relate to feedbacks and path dependence? What parameter settings would you use to eliminate any effect of feedbacks or path dependence?

Two other hypotheses being tested in this exercise are also borrowed from Brown et al (2005) who suggest that “more and stronger feedbacks lead to more path dependence” (no variation in aesthetic quality) and that “spatial variability enhances path dependence” (increased variation in aesthetic quality). I believe this model is capable of exploring this topic adequately and I feel that the two concepts of path dependence and “feedbacks” are related because according to Brown et al (2005) “path dependence arises from negative and positive feedbacks”. Since feedbacks modify processes in a system in ways that either amplify or reduce certain responses, those “paths” whose behavior are reinforced within the system can be considered dependent. For our model this week, three parameters reproduced feedbacks in a hypothetical environment of housing development based on aesthetic quality of the area, the distance to services, and the preference for settlement density. All three affect the distribution of housing to a some degree with the results ultimately being dependent upon the environment and whether it is more homogenous or heterogeneous.

5. Describe at least two of the model assumptions or simplifications and how they could influence your interpretation of model results. Despite these assumptions and limitations, what can we learn from this model?

While I believe this model can show some very basic effects that certain social preferences might have on settlement distributions and certain spatial phenomena, the model is not necessarily “realistic” and makes simplified assumptions such as all agents will behave the same, or rather maintain the same preferences, and that development costs are either non-existent or universal across agents.

Also, in using this model we are assuming that the variable of “nnd” (nearest-neighbor-density) is a realistic measure of the phenomenon we are interested and that it is important for some reason that developers care about. Here, I think Central Place Theory could complement the study in some way but it is important to remember that centralized behavior, although efficient and well-fitted to “laws of maximization” is not universal in human communities. It makes sense to think that the proximity of housing development is somehow related to the parameters we established but proximity, in the form of distance to services or density of habitation, may not always be an important variable in community patterning.

References:

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