Distance Decay and Its Use in GIS

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Distance decay is a phenomenon observed between locations or populations – 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 can lead 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.

An illustrative example of distance decay using blue points and yellow arrows.
With distance decay, things that are geographically closer tend to be more related than things that are farther apart. Diagram: Caitlin Dempsey.

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.

Technologies and distance decay

Good infrastructure and efficient transit help to mitigate distance degradation between human settlements. If ethnic groups A, B, and C are connected by a bullet train, their proximity to one another is much less important than if they must travel by foot.

If a city can afford to offer well-maintained roads and adequate transit from the center to the outskirts, it will see more equitable development and less difference between the city center and the outskirts.

Inventions like as widespread wireless technology and high-speed internet have helped to further reduce distance decay by reducing the number of scenarios that necessitate travel at all. A person in France can now readily contact a person in Brazil in seconds using a cable internet connection, providing for a simple and speedy exchange of ideas.

Distance decay and ecology

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).  

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.

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 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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1 thought on “Distance Decay and Its Use in GIS”

  1. Two things to consider here: Maybe the decay is in reverse of what is stated. Maybe the dacay can be described as an independance decay from the farthest point out to the city center. Maybe perfection is complete isolation. Cultural decay happens when groups interact more meaning the decay is greatest in the city center. Cultural purity would result from isolation.

    The only distance decay i see from Tora Bora is the radiation levels from the bomb we should have dropped there.

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