Distance Decay

Distance decay is a concept linking geography and the occurrence or frequency of a pattern of activity. Some literature uses the term “distance lapse rate” to identify this connection. The underlying principle is that any phenomenon or influence diminishes in intensity as the distance from the point of origin increases. This is due to the effect of friction of distance. The concept is enshrined in the geographer Waldo Tobler’s famous dictum that all things are related, but those that are nearest to one another are more related than those located at a greater distance.

Distance decay is an important precept of spatial analysis, especially for spatial interaction models and notions of cultural diffusion. Distance decay is inherent in various applications of gravity models in economic and urban geography and underlies some of the fundamental theoretical models in these subfields of geography, including Christaller’s Central Place Theory and the Von Thunen model of agricultural development. Gravity model theorists, for example, suggest in their simpler propositions that a precise mathematical relationship exists between the strength of a spatially expressed phenomenon and the distance over which it is distributed, in a formula closely akin to Isaac Newton’s equation defining gravitational force. 

Whereas Newton proposed that the force of gravity is directly proportional to the mass of the objects in question and a mathematical constant, divided by the square of the distance between them, geographers using gravity theory in their work attempt to construct a similar model analyzing labor or trade flows, transportation, shifts in population, diffusion of languages, religions, technologies, etc. Just as Newton’s theorem postulates that the force of gravity between two objects declines with distance, so too do gravity models in geography, based on the concept of distance decay. A simple example would be a model that attempts to gauge the influence of German as a first language used in business transactions. Such a model would likely show a high degree of use in Germany (center of gravity), with moderate use in surrounding countries in Europe (weakening gravity with distance from the center), and little use in North America or Africa (decay of gravitational influence with distance). 

More sophisticated approaches attempt to integrate a geometric component into the model, because in real world applications the rate of decay with distance is dependent to some extent on the geometry of the distance covered, not simply the absolute distance intervening between the two interacting points. A simple illustration of the influence of geometry (or in more accurate terms, topography) would be a mountain range lying between two towns that trade with one another but are separated by a distance of only 5 miles, and the same two towns located on a level plain but separated by a distance of 10 miles. The distance decay rate (as expressed by a mathematical formula or a curve) in the first relationship could likely be higher (a steeper curve when graphed) than in the latter case, due to the physical barrier presented by the mountain range, in spite of the fact that the towns are separated by only half the distance. Some geographers suggest that the impact of globalization and mass electronic communication are weakening the relevance of the distance decay concept.