The idea of combining crisis mapping and agent based modeling has been of great interest to me ever since I took my first seminar on complex systems back in 2006. There are few studies out there that ground agent based models (ABM) on conflict dynamics within a real-world geographical space. One of those few, entitled “Global Pattern Formation and Ethnic/Cultural Violence,” appeared in the journal Science in 2007.
Note that I take issue with a number of assumptions that underlie this study as well as the methodology used. That said, the study is a good illustration of how crisis mapping and ABM can be combined.
The authors suggest that global patterns of violence arise due to “the structure of boundaries between groups rather than the groups themselves.” In other words, the spatial boundaries between different populations create a propensity for conflict, “so that spatial heterogeneity itself is predictive of local violence.”
The authors argue that this pattern is “consistent with the natural dynamics of “type separation,” a specific pattern formation also observed in physical and chemical phase separation. The unit of analysis in this study’s ABM, however, is the local ethnic “patch size,” which represents the smallest unit of ethnic members that act collectively as one.
A simple model of type separation assumes that individuals (or ethnic units) prefer to move to areas where more individuals of the same time reside. Playing the ABM yields progressively larger patches or “islands” of each ethnic group over time. The relationship between patch size and time follows a power law distribution, “a universal behavior that does not depend on many of the details of the model […].”
In other words, the model depicts scale invariant behavior, which implies that “a number of individual agents of the model can be aggregated into a single agent if time is rescaled correspondingly without changing the behavior at the larger scales.”
To model violent conflict, the authors assume that both highly mixed regions and well-segregated groups do not engage in violence. The rationale regarding the former being that in highly mixed regions, “groups of the same type are not large enough to develop strong collective identities, or to identify public spaces as associated with one or another group. When groups are much bigger, “they typically form self-sufficient entities that enjoy local sovereignty.”
To this end, the authors argue that partial separation with poorly defined boundaries fosters conflict when groups are of a size that allows them to impose cultural norms on public spaces, “but where there are still intermittent violations of these rules due to the overlap of cultural domains.” In other words, conflict is a function of population distribution and not of the “specific mechanism by which the population achieves this structure, which may include internally or externally directed migrations.”
The model is therefore founded on the principle that the conditions under which violent conflict becomes likely can be determined by census.
The authors used 1991 census data of the former Yugoslavia and the Indian census data from 2001 and converted the data into map form (see figure below), which they used in an ABM simulation. “Mathematically, the expected violence was determined by detecting patches consisting of islands or peninsulas of one type surrounded by populations of other types.”
A wavelet filter that has a positive center and a negative surround (also called a Mexican hat filter) was used to detect and correlate the islands/peninsulas.
The red overlays depicted in Figure D above represents the maximum correlation over population types. The diameter of the positive region of the wavelet, i.e., “the size of the local population patches that are likely to experience violence,” is the main predictor of the model.
To test the predictive power of their model, the authors compared the locations of red overlays with actual incidents of violence as reported in books, newspapers and online sources (the yellow dots in the crisis map below).
Their statistical results indicate that the Yugoslavia crisis map model has a correlation of 0.89 with reports. Moreover, “the predicted results are highly robust to parameter variation [patch size], with essentially equivalent agreement obtained for filter diameters ranging from 18 to 60 km […].”
The statistical results for the India crisis map model indicate a correlation of 0.98. The range of the patch size overlapped that of the former Yugoslavia but is shifted to larger values, up to 100km. This suggests that “regions of width less than 10km or greater than 100km may provide sufficient mixing or isolation to reduce the chance of violence.”
While the authors recognize the importance of social and institutional drivers of violence, they argue that, “influencing the spatial structure might address the conditions that promote violence described [in this study].” In sum, they suggest that, “peaceful coexistence need not require complete integration.”
What do you think?