2. Why least-cost path calculations?

In archaeological studies, LCPs are often calculated to reconstruct ancient routes or a route network (e.g. Fábrega Álvarez and Parcero Oubiña 2007) or to identify the principal factors governing the construction of known roads or road segments (e.g. Bell and Lock 2000; Polla 2009). Parslow (2009) identifies possible routes of interaction for the pre-Neolithic sedentary Natufian culture in the Eastern Mediterranean by clustering the artefacts and creating LCPs within and between the clusters. When a site is located on the LCP connecting two other sites, some authors assume that the midpoint site was founded later (e.g. Bell and Lock 2000; Batten 2007) i.e. LCPs also play a role in relative dating.

In general, for landscapes heavily structured by geographical features such as steep slopes or streams, cost distances should be substituted for the simpler straight-line distance calculations in all algorithms applied for spatial analysis. In fact, circular site catchments are hardly used any more but have been replaced by irregularly shaped areas that take the cost distance into account (e.g. Conolly and Lake 2006, 224–5). Some archaeological applications of least-cost buffers were published as well (e.g. Fábrega Álvarez and Parcero Oubiña 2007; Whitley and Burns 2007). The most common formula for spatial autocorrelation includes a weighting function to reduce the impact of distant points (e.g. Wheatley and Gillings 2002, 131–2; Conolly and Lake 2006, 158–9), and replacing the map distance by the cost distance is straightforward. Algorithms for hierarchical spatial clustering require a distance table that stores the distances between all points considered (e.g. Conolly and Lake 2006, 168), so a least-cost adjustment is possible but computationally intensive for a large set of points. Ripley's K was designed to test if points are clustered spatially, and the formula also includes the map distance (e.g. Conolly and Lake 2006, 166–8). However, the method requires many iterations and therefore is computationally intensive. So currently, least-cost Ripley's K is not a feasible option in spatial statistics. However, most other spatial analysis tools allow a least-cost adjustment and therefore should be extended accordingly in non-uniform terrain.