A Cost-Based Ripley’s K Function to Assess Social Strategies in Settlement Patterning

Most quantitative approaches to distributional analysis in archaeology assume a homogeneous study surface that is amenable to easy generalisations. This framework has been widely used to describe settlement processes, disregarding the spatial heterogeneity inherent to geographic reality. In other words, researchers have often assumed that the correlation between the elements of a spatial distribution is a function of the Euclidean distance (i.e. straight line distance) between them. Other archaeological studies have tested alternative measures to Euclidean distances, such as cost-based ones, both to describe optimal routes and to assess spatial autocorrelation in a point pattern. Nevertheless, until now there has been no suitable model to introduce these measures into spatial statistical equations. In order to overcome this obstacle, we approach the implementation problem inversely by embedding the spatial pattern under study into a Euclidean frame of reference based on its cost-distance pairwise matrix. This paper describes the application of this methodology on one of the main tools used by archaeologists to assess settlement patterns: Ripley’s K function. We present two case studies, covering both macroscale and mesoscale, with significant variations in the results depending on the use of the Euclidean or cost-based approach. Data, functions and results have been R-packaged for the sake of reproducibility and reusability, allowing other researchers to build upon our methods.