Least Cost Pathways

One of the predictive modeling techniques I employ in my research is least-cost pathway analysis, or LCP analysis. A LCP is a route that minimizes the total cost of moving between two locations across an accumulated cost-surface (Figure 4-9). Least-cost paths in GIS are also called “Optimum Paths” and are frequently used to calculate the optimum path for power lines,

highways, and other linear features crossing the landscape (Batton 2006). In archaeology, the calculations of least-cost paths cannot only help to predict known or unknown past travelling or transport routes, but they can also be used to explain the location of monumental art, to predict prehistoric economic boundaries around central places, and to predict the economic interrelation of sites (Batton 2006).

Least Cost Path

Analysis Model

A _B

What is the accumulated cost (based on terrain danger, need, gain etc.) of leaving point A?

What form of transportation is used?

Possible Routes

Which route provides the least cost from point B back to point A?

Figure 4-9: Least cost path analysis model (by Jennifer Weber)

GIS software usually implements a two stage process to calculate a LCP. First, it creates a cost-surface that models the accumulated cost of traveling outward from the origin, using a relevant transport technology. Here, one (preferable for unknown routes) or several (preferable for known routes) variables can be used. Second, the calculation traces the route of steepest reduction in accumulated cost from the destination back to the origin (Conolly and Lake 2006:252).

In ESRI’s ArcGIS Spatial Analysis program, this model requires digital elevation data in a raster data format. One then creates a friction surface grid, based on the accumulated

information on the environment (topography, etc.). This means creating a slope file from the raster data in ArcGIS. The program then assigns every cell between point A (source) and point B (destination) a value, so it can calculate the accumulative cost to move over the surface (Figure

4-10). This concept might be better explained in its actual computational context: In computer science each cell on a raster surface is called a node. Nodes are connected by links. The LCP algorithm is calculated based on the node value at each end of the link (Figure 4-11). It searches the lowest node value at the end of each link, on the most direct way to the destination cell.

A B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 2 1 1 1 1 1 1 1 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1

Direct Path = 1+4+1= 6

Lowest Cost Path = 1+1+1+1+1 = 5

Figure 4-11: LCP algorithm (by Jennifer Weber)

This is an example of a very simple function that runs solely on one value, for example data derived from elevation levels. This of course can be tricky, for example when the data includes waterbodies with low elevation levels, which the algorithm will not recognize. Rather, it would mistake the sea or lake as a valley or other type of terrain that is easily accessible, when in truth, it is not. Therefore, other variables can be added to various spatial analysis tools to provide more complex analysis methods. An example of applying other variables to this analysis process is demonstrated by Batton (2006), who used LCP’s to explore the role trade and communication links played in the location of three prehistoric settlements in east Central New Mexico. He was investigating whether exchange was a factor in decisions about community location. Following extensive environmental and historical research, Batton (2006) started out with the cost surface, which is, as mentioned above, a raster map where the z-dimension is the least accumulated travel

cost of each cell from a specific source point. Arguing that he did not know enough about the prehistoric values in his research area to implement multiple variables (e.g. water sources, shelter, fuel sources, defensible locations), he used the walking speed on a terrain or varying steepness, also called the “Hiking Function” developed by Tobler in the 1970s (Batton 2006;

Tobler 1993) (Figure 4-12).

Tobler’s Hiking Function

V=6(-3.5 X |S+0.05|) V = Walking Velocity (kms per hour) S = Percent Slope (rise over distance dh/dx) Elevation values (from DEM) must be converted into slope values (via ArcGIS or GRASS), then converted to the cost of crossing each cell. Thus, allowing slope values to be converted into time required to traverse a cell of the raster.

Figure 4-12: Tobler’s Hiking Function (by Jennifer Weber, after Tobler 1993)

Based on the predicted pathways Batton (2006) derived from the LCP analysis, he was able to gain important insights and create testable predictions. He created hypotheses he could now investigate by implementing ground-truthing of likely pathways, spatial analysis of site distributions around LCP’s, assessing the relationship of LCP’s with rock art, and refining the algorithm with additional environmental and social variables (Batton 2006). An example of a similar research approach conducted in Mesoamerica was led by Carballo and Pluckhahn (2007)

who also implemented least-cost path analysis in order to quantify the utility of the Tlaxcala Corridor for interregional transportation relative to other corridors, as well as spatial distributions between sites. They also utilized the Hiker Function by Tobler (Carballo & Pluckhahn 2007).

Aside from employing functions like Tobler’s Hiking Function, ArcGIS’ spatial analysis tool also offers options to add so called “offsets” to environmental data. Here, the cells of a raster dataset can be given certain offset values by the researcher, depending on knowledge of

environmental factors. For example, a waterbody in the landscape between point A and point B could be manually given a very high value, indicating that it would have presented an obstacle that most likely would have not been crossed by foot. Or, the cells next to the waterbody could be given a low value, indicating that a path running by here would have been likely as a source to collect water, as indicated by previous research. In addition, researchers are actively trying to create new ways to incorporate the uncertainty in our inherent knowledge about past human behavior and natural processes.

An example of this is Dempster-Shafer-Theory, a mathematical theory that incorporates this uncertainty by assigning various weights of evidence to defined variables, in that way estimating the probability for supporting a specific hypothesis. Here, each domain of knowledge entails uncertainty and the complement of a hypothesis must not automatically be assigned to its negation, but has to be assigned an uncertainty factor (Boos et. al 2010). An aggregation rule is used to include numerous pieces of information (evidence) with varying weight into a decision making process thus supporting or excluding defined hypotheses (Boos et. al 2010). Boos and colleagues (2010) of Mainz University have successfully applied this theory in order to predict

prehistoric settlement structure and land use surrounding the Celtic oppidum “Hunnenring” in Saarland, Germany. Examples like this show that GIS applications are steadily developing and will become more and more sophisticated to help archaeologists interpret the past.