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Lotka–Volterra competition models applied to LA street gang territories

A mathematical model previously used to determine the hunting range of animals in the wild, namely the ‘formal spatial Lotka–Volterra competition model’, apparently holds promise for mapping the territories of street gangs.

Lead author P. Jeffrey Brantingham is quoted in a press release saying: “The way gangs break up their neighborhoods into unique territories is a lot like the way lions or honey bees break up space”.

The press release explains the findings that

the most dangerous place to be in a neighborhood packed with gangs is not deep within the territory of a specific gang, as one might suppose, but on the border between two rival gangs. In fact, the highest concentration of conflict occurs within less than two blocks of gang boundaries.

This finding is potentially important, according to a quote from co-author George E. Tita, because “maps of gang territories provide police with a better understanding of how to allocate resources”.

For details of the model, the press release offers this:

The equations are based on the principle that competition between groups determines where the boundaries between rivals form, and even a tiny amount of competition is enough to cause territories to form.

The model the researchers derived from the equation predicted that gang boundaries would form midway between the home bases of rivals and would run in a perpendicular line between them.

To validate the model the researchers used results about an area of Los Angeles and 563 known gang crimes that occurred between 1999 and 2002 that had been attributed by police to at least one of 13 gangs. The press release explains that “most of the crimes fell on the borders that the model laid between gang territories” and “when crime locations did deviate from the borders, they did so in a configuration that was consistent with the model”.

The full paper is available in the journal Criminology.

Press release: Remapping gang turf: Math model shows crimes cluster on borders between rivals.

Paper: The Ecology of Gang Territorial Boundaries. (Brantingham, P.J. et al. (2012). DOI: 10.1111/j.1745-9125.2012.00281.x.)

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