Spatial Simulation: Exploring Pattern and Process, By David O’Sullivan and George L. W. Perry

Question 1: What potential new forms of knowledge can spatial simulation provide to your discipline, and more importantly, to your specific graduate research topic?

Asking why our world is the way it is, and how it got to be that way, are some of humankind’s most enduring questions. To cope with the diversity and complication of the world, the human brain evolved a subconscious mental strategy of building models to reduce the intractable complication of the world into simplified and manageable representations of reality (O’Sullivan and Perry, 2013 p. 1). Consciously duplicating this process of abstracting reality into explicitly defined models of the world is the essence of science, and it has revolutionized the way we question our world. Humankind’s collective body of knowledge generated through the scientific enterprise as we know it is a testament to our use of models.

Modeling has long had purchase with Geographers who have understood the explanatory power of a good map in making sense of the world. Studying and interpreting the world’s spatial patterns is essential work in modern Geography; this primacy has spawned a language of pattern to describe the distribution of features and numerous methods for quantifying their placement in space–hoping to reveal the underlying causes. Yet, despite the technological improvements afforded by modern computing to previously available modeling techniques, like empirically derived statistics, the knowledge produced has methodological limitations. Describing a spatial pattern, like clustering with a statistically significant Moran’s I value, leaves two important questions unanswered: Is the role of space in the observed pattern significant in a practical sense; and what is the causal mechanism responsible for creating the pattern?

One reason behind the inability for Geography, and the social sciences in general, to provide definitive answers to the some why questions is, in part, an effect of the methodological legacy and historical dominance of reductionist science and the privilege given to knowledge produced by controlled laboratory experiments. The expectation that follow from this ethos, that all science should approach questions in this same fashion–and with the same models, fails to recognize the frequency in which the world cannot be fit to these models of scientific enquiry (O’Sullivan and Perry, 2013 p. 15). Spatial simulation models, though, hold an opportunity for the discipline to approach questions about the role of processes and space that past modeling could not. The discovery of non-linear systems have further weakened the assumption of reductionism, that the whole of a system can be understood by understanding its lesser parts. Even the most simple spatial simulation models, like Conway’s “game of life” (O’Sullivan and Perry, 2013 p.18), have shown that complete understanding of component behaviors cannot be extrapolated to an understanding of system behavior. A primary expectation of reductionism is that scientific experiments have repeatable outcomes. For a significant set of Geographical enquiry, these laboratory experiments are impossible for reasons of scale, temporal limitations, and ethical considerations. These reasons aside, laboratory experiments sill have trouble addressing the role of history in system behavior, a fundamental weakness that spatial simulations can help to alleviate.

For my own research on the experience of people with mobility challenges negotiating pedestrian network in Eugene, it’s difficult to say how spatial simulation will be relevant in my work. The first chapter of the book, though, did give me some interesting things to think about. The framework language of system dynamics modeling (p. 5), and organizing the parts of a system into variables is a new way for me to consider the actors in my system, especially changes in the state of a system. Using this framework as a lens may give me a new perspective on a way to conceptualize the interactions between my population of interest and their environment. However, it feels too soon to know. One of the main reasons for my uncertainty is whether the system I am looking at has a non-linear dynamic that produces emergent patterns, especially at the scale I plan to work. However, since the system is contained in an urban area, and cities themselves have emergent properties (Johnson, 2002), there may be a dimension of this project that will lend itself to a spatial simulation model. Thinking of how spatial simulation analysis could address the theme more broadly; some social theorists have forwarded a position that disability is a product of societal preference for a built environment that reflects societal attitudes on the values of people with physical impairments (Kitchin, 1998). A question I’d ask would read something similar to this: To what degree does the physical configuration of a pedestrian network disable those with certain physical impairments, and what is the threshold for a configuration that would cause a change in state to an enabling network?

References:

O’Sullivan, David, and George L. W. Perry. Spatial Simulation: Exploring Pattern and Process. Sumerset: Wiley-Blackwell, 2013.

Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities and Software. London: Penguin, 2002.

Kitchin, Rob. “‘Out of Place’, ‘Knowing One’s Place’: Space, Power and the Exclusion of Disabled People.” Disability & Society 13.3 (1998): 343-56.

 

Question 2: Describe the difference between models of aggregation, mobility, and percolation. Provide an example for each.

In the effort to understand systems that exhibit complex, emergent macro-scale behaviors driven by simple rules of local interactions spatial simulation modelers often employ three important classes of models: aggregation models, movement models, and percolation models. While no model class has an entirely exclusive domain of applications, in their most orthodox forms, each model excels at exploring unique aspects of complex systems  behavior. Aggregation models look at the processes in which neighboring elements become more similar. Movement models are interested the sequential nature of agent travel and what can be learned from retracing an agent’s steps. The patterns generated by percolation models themselves, rather than their defining rules, are what garner the interests of simulation scientists.

Aggregation models develop clustered regions of similarity through the application of simple rules of summation and averaging that govern the transition of individual state variables (p. 64). The Shelling model, Segregation, is among the most influential of all the aggregation models. Segregation is predicated on the notion of individual preference and the self-interested desire to be surrounded by like individuals. Individuals experiencing displeasure with the proportion of others in their immediate neighborhood react based by changing their state, moving elsewhere in this case, to look for a new, more preferable neighborhood. Its worth noting, although the term segregation connotes difference and exclusion rather than similarity or likeness, here it can be considered a plural condition of similarity.

Movement models are interested with patterns of individual movement and what the sequence of their travel paths can tell us about the aggregate behavioral patterns of the population. Flocking models, like aggregation models look at entity-entity interactions. Flocking models also are concerned with immediate neighbor relations, yet there are important differences. The implementation of the Flocking model differs from aggregation models by introducing the mobile agent that traverses the cellular model space that confines aggregation models. Additionally, individuals in the movement models actually represent individual autonomous entities, whereas entities in aggregation models often represent a more abstract individual, like a household. Mobile agents are designed to explore the logic of movement itself as a driver of pattern development. Movement models that incorporate additional complexity may go further and seek to explain how the dynamic interactions between individual movement patterns over the heterogeneous structural environment generate emergent global patterns (p. 111).

Processes are the critical dimension in both aggregation and movement models, percolation models depart from that trend in a significant way; the interest for scientists is understanding the phenomena of “flow or spread” and diffusion through the structure of the model space (p. 142). A characteristic shared by all percolation models is a critical threshold in the proportions of the model structure, that once crossed, results in a total system change. Many percolation models exhibit a significant degree of path dependence and history contained in the patterns of the model that is not present in the other models. Additionally, it seems, as is the case for the invasion percolation model, many percolation models have a high level of sensitivity to initial conditions which intensifies the path dependence witnessed by observers.

Aggregation, movement, and percolation models all share the defining characteristic of bottom-up complex models; localized interaction composite into a high level macro scale pattern that cannot be explained simply by the investigation of the small scale interactions. Yet, the subtle differences in implementation strategies lead to a wide variety of niche applications in many sectors of social and environmental science.

Question 3: How do spatial simulation models incorporate and handle real world system uncertainty?

The world is an uncertain place; there are some things that can never be understood or may not be understandable. For modelers producing useful knowledge about the processes that animate our uncertain world entails grappling with a combination of data uncertainty and epistemic uncertainty about the system of interest. An incomplete understanding of a system, due to measurement inaccuracies (random sampling variation, etc.) or partial understanding of a system’s processes can pose a significant challenge to the enterprise of modeling. However, careful and thoughtful incorporation of this uncertainty can provide fertile opportunities for the discovery of new knowledge about a system.

A researcher aiming to build a spatial simulation model of a real world system can represent the inherent uncertainty by incorporating stochastic elements into the formal structure of the model. Incorporating stochasticity into models of real world systems is a significant conceptual and methodological departure from modeling the world via deterministic processes. This shift is important because information produced by deterministic models and simulation models hinge on very different assumptions and philosophies of knowledge production. Deterministic models have generally been constrained by the epistemological perspective of empirical positivism–that the world is knowable through empirically derived data, or the technical capacity to include stochastic variability into the model, or a combination of both. Both of these constraints limit the realism of the model. Before the advent of modern computers, and since technical limitation are equally prejudiced against all epistomologies, early on computational limits were likely a more significant hindrance to the inclusion of uncertainty into modeling frameworks. While tractability remains a present challenge to some efforts, in a practical sense modern computing has all but removed the limitation of including some degree of stochasticity into most models.

The implications of adding stochasticity to improve model realism are important; the authors illustrate this by comparing a deterministic version of Maximum Sustainable Yield (MSY) model (for a hypothetical crop) to a similar model that represents uncertainty via a single stochastic element. When the stochastic population growth MSY model is parameterized with a harvest rate determined to be optimal by the deterministic MSY model, the system inevitably collapses reveling the maximum “sustainable” yield to be anything but sustainable. This example doesn’t simply just an illustration of the flaws of determinism, instead it shows how uncertainty in both the variability attributed to exogenous sources affecting growth rate (like climatic conditions) and measurement uncertainty (due to the technical limits in the capacity to measure growth rates beyond a certain level of precision) are operationalized in the modeling context to expand the understanding of possible futures. Incorporating uncertainty into the model accounts for both what is unknowable due to variations of external factors, and what is unknowable due to the limitations in capturing and representing all aspects of the system with absolute realism. Formalizing and representing this variability into the model result in a richer picture of the possible permutations of the system as it persists over time.

Incorporating stochastic representations of uncertainty into models of real-world systems allows researchers to grapple with the variability both external to the system and intrinsic to the limitations of human understanding. Operationalizing uncertainty provides an opportunity to transform uncertainty into new insights about system behavior and provides researchers with a more nuanced understanding of how what we don’t know affects the knowledge we produce.

 

References:

O’Sullivan, David, and George L. W. Perry. Spatial Simulation: Exploring Pattern and Process. Sumerset: Wiley-Blackwell, 2013.