Distance Decay and Its Use in GIS

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Distance decay is a phenomenon observed between locations or ethnic groups- the further apart they are, the less likely it is that they will interact very much. In essence, distance decay describes how things like communication and infrastructure break down relative to distance from a cultural center. This leads to cultural differences between an urban center and its outskirts, or between two distant, neighboring settlements.

Geographically speaking, distance decay can be explained by Waldo Tobler’s First Law of Geography. This is the assertion that “Everything is related to everything else, but near things are more related than distant things,” and can be applied to a range of different geographical concepts, from human settlements, to geolinguistics, to ecology.

The simplest way to look at distance decay as it pertains to human culture is like this: Pretend you have three different ethnic groups, called A, B, and C. Groups A and B live relatively close to each other, along a river that allows for easy trade and travel. Group C lives farther from group B, and very far from group A. As a result, groups A and B will come into contact with each other frequently, groups B and C will come into contact with each other occasionally, and groups A and C will come into contact with each other only rarely. This can have far-reaching implications when it comes to the history of these groups- groups A and B might begin to develop common customs and a pidgin dialect, while group C will diverge widely, and remain linguistically distinct. The further these groups are from each other, the less frequent their interactions become.

Distance decay doesn’t just happen to ethnic groups, though. It’s also very easily observed in any city, in any country, anywhere in the world. In the center of the city, there are likely to be more businesses, better public transit, better sanitation services, and better quality roads. As you move further from the city center, these services begin to break down- businesses give way to residential areas, public transit runs less frequently, septic tanks and wells replace sewage systems and municipal water, and roads aren’t as well-maintained. The further you move away from the urban area, the more evidence this decay becomes. Eventually, the very outskirts of an area may have only a few small businesses, no transit system, rudimentary sanitation, and dirt roads. Property tends to be cheaper the farther you move away from an urban area, and buildings tend to get smaller, as well.

Distance decay between human settlements is somewhat alleviated by things like good infrastructure and rapid transit. If ethnic groups A, B, and C are connected by a bullet train, then their proximity to each other matters a lot less than if they have to rely on traveling on foot. If a city can afford to provide well-maintained roads and adequate transit from the center to the outskirts, then the city will experience more even development, and less disparity between the city center and the fringes. Inventions like widespread wireless technology and high speed internet have helped cut down on distance decay even more, by cutting down on the number of situations that require traveling at all. Now, an individual in France can easily contact an individual in Brazil in seconds via a cable internet connection, allowing for an easy, rapid exchange of ideas.

The distance decay phenomenon is also experienced by biomes. The physical distance between two geographic locations is directly related to a loss of similarity between them in terms of ecology and biodiversity. Increasing the physical distance between two areas increases the odds that climate and geological features like lakes and mountains will influence weather patterns in one area and not the other, which, in turn, will influence which species can inhabit them. Longer distances also make seed dispersal more problematic for plants. As a result, a stand of maple trees in one location is not likely to have any relatives in a forest a hundred miles away, and will definitely not have any in a desert a thousand miles away.

Though the “decay” part of distance decay carries a negative connotation, distance decay isn’t always a bad thing. Distance decay between two groups of people is what gives rise to things like languages and regional customs, and the distance decay between biomes is part of what makes the earth such an ecologically diverse place.

Use of Distance Decay in GIS

A UCLA paper that generated interest after it published the results of a GIS study on highlighting the likely location of Osama bin Laden used distance decay as part of the analysis performed.  Published in MIT’s International Review, the study incorporated a distance-decay model based on Osama bin Laden’s last known location in Tora Bora.  Calculating the probability of a 99% chance that bin Laden was near Tora Bora and a 1% chance that the terrorist would be found in Washington D.C., individual circles of probability were calculated in intervals extending away from Tora Bora (see image below).  In additon to distance decay theory, the study also incorporated island biogeography theory, and life history characteristics in making a prediction about Osama bin Laden’s location.  The study had 88.9% that bin Laden was hiding within 300km of Tora Bora and named Kurram, Pakistan as the most likely location.  While ultimately, Osama bin Laden was located and killed in Abbottabad, at 268 km it was within the same distance range and country as the study had predicted.

Distance decay model showing the probability of Osama bin Laden's location. From a UCLA study, 2009.

Distance decay model showing the probability of Osama bin Laden’s location. From a UCLA study, 2009.

Distance decay theory in GIS can be used for other purposes such as the effects of time and distance on public transportation ridership, crime analysis, and health care.

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