Distance decay

Abstract

The attenuation of a pattern or process with distance from a central point. Its importance in the evolution of spatial patterns was enshrined in Tobler’s (1970) famous ‘first law of geography’: ‘everything is related to everything else but near things are more related than distant things’. Distance-decay relationships underpin much of the work on spatial structures undertaken within spatial analysis and spatial science, because the costs of spatial interaction are related to the distance travelled (cf. gravity model). Empirical studies have identified a range of distance-decay relationships in which the degree of attenuation with distance is much greater in some situations than others (see figure), in part because of the characteristics of the geometric configurations of the spatial structures within which they are set (Cliff, Martin and Ord, 1975–6).