6. Conclusions and Best Practice

The discussion of LCP algorithms, cost components and appropriate cost functions as well as possibilities of combining costs shows that no standard procedure exists that successfully addresses all issues in this context. A best practice LCP study should cover the following issues:

1. The accuracy of the topographic data should be discussed, including the effects of erosion, land slides, meandering rivers, bulk material extraction, terracing and change of the sea level since the period considered. Often it will not be possible to reconstruct the past landscape in detail. Adding small errors to the DEM can help to assess the stability of the LCP results.
2. An LCP study relying on standard GIS software should mention the version and parameters used. The user should be aware of the features of the algorithm applied, i.e. the worst case distance between the optimal route and the LCP depending on the number of grid neighbours considered, the way the algorithm deals with anisotropic situations and possibly the effects of a steepest descent approach instead of back-links.
3. It seems advisable to start with a simple cost model and to refine it in an iterative procedure.
4. In most cases, the initial cost model will focus on slope. All slope-dependent cost functions will generate LCPs that choose obvious best routes like mountain passes. But if the best route is less apparent, some care should be taken in choosing the cost function. The results in Sections 5.1.4.2 and 5.1.4.3 show that for pedestrian travel the sixth degree polynomial and the Tobler cost function (if implemented properly) perform well from a theoretical point of view. This agrees with my mostly unpublished work when comparing the LCPs with historical paths. For wheeled vehicles another cost function is more appropriate (Section 5.1.4.1).
5. Focusing only on slope, LCPs will often run in riverbeds. It might be necessary to model rivers as barriers and to identify the fords (Herzog 2013a) in order to generate realistic LCPs.
6. In many situations water travel is more efficient than transport by porters or wheeled vehicles (Section 5.4). Water travel should be taken into account whenever possible.
7. It is often difficult to identify all relevant cost components including social and cultural attraction or repulsion and to combine them in one cost model. Any cost model suggested should be validated by archaeological or historical evidence.

My own studies in the Bergisches Land (e.g. Herzog 2009b; 2010; 2013a; 2013c), Italy and in two regions in Ecuador (unpublished) reconstructed historical routes in most parts quite successfully after adjusting the parameters accordingly, whereas for some stretches, the LCPs suggested another route. When historical routes connecting two locations can be reconstructed successfully, the next step in LCP calculations is to model networks; different least-cost network layouts and methods for generating the corresponding paths are presented in Herzog (2013c).

With a well-calibrated cost model, spatial analysis of archaeological data can rely on more realistic distance calculations and improved results are to be expected in nearly all aspects of spatial analysis.