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Modeling geopolitics in Tikal through least cost paths

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Modeling geopolitics in Tikal through least cost paths

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Modeling geopolitics in Tikal through least cost paths

by

Matthieu Munoz

A Thesis Presented to the
Faculty of the USC Graduate School
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
Master of Science
(Geographic Information Science and Technology)

August 2017

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Copyright © 2017 by Matthieu Munoz

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To my Mom and Dad, who have always supported me. Also to my sister, who has always been
there for me, no matter what.

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Table of Contents
List of Figures ................................................................................................................................ vi
List of Tables ................................................................................................................................ vii
Acknowledgements ...................................................................................................................... viii
List of Abbreviations ..................................................................................................................... ix
Abstract ........................................................................................................................................... x
Chapter 1 Introduction .................................................................................................................... 1
1.1. Motivation ...........................................................................................................................1
1.2 Description of Study Area ...................................................................................................3
1.3 Methodology ........................................................................................................................4
1.4 Research Goals .....................................................................................................................6
1.5 Thesis Organization .............................................................................................................6
Chapter 2 Related Work .................................................................................................................. 8
2.1 Epigraphic Analysis of Interactions Between Sites .............................................................8
2.2 Least Cost Analysis in Archaeological Contexts ...............................................................10
2.3 Modeling Cost Surfaces .....................................................................................................12
2.4 Assessment of Results........................................................................................................15
Chapter 3 Methods ........................................................................................................................ 17
3.1 Study Sites .........................................................................................................................17
3.2 Preparation of Project Geodatabase ...................................................................................18
3.3 Preparing the Data for the Least Cost Path Operations .....................................................21
3.4 Least Cost Path Operations ................................................................................................22
3.5 Creating Isochrones ...........................................................................................................24
3.6 Sensitivity Analysis ...........................................................................................................25

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Chapter 4 Results .......................................................................................................................... 27
4.1 Least Cost Path Corridors ..................................................................................................27
4.2 Isochrones ..........................................................................................................................31
4.3 Sensitivity Analysis ...........................................................................................................33
4.3.1. Origin and Destination Location Sensitivity Analysis .............................................33
4.3.2. DEM Resolution Sensitivity Analysis .....................................................................35
Chapter 5 Discussion and Conclusion .......................................................................................... 37
5.1 Discussion ..........................................................................................................................37
5.2 Avenues for Future Analysis .............................................................................................40
References ..................................................................................................................................... 42

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List of Figures

Figure 1 The Maya Region ............................................................................................................. 3
Figure 2 Diagram of Tikal’s Interactions ........................................................................................ 9
Figure 3 Four sites overlaid on the 30 m ASTER DEM...……………...……...…...……………20

Figure 4 Flowchart showing procedures used to calculate least cost paths ………….………….23

Figure 5 Flowchart showing procedure to create Isochrones Isochrones….…….…………...….24

Figure 6 Least Cost Paths between Tikal and Calakmul….………………………...…...………28

Figure 7 Least cost paths between Tikal and Naranjo.…...……….…………...……...…………29

Figure 8 Least cost paths between Tikal and Caracol……...…………………...…......…………30

Figure 9 Isochrones from Tikal to three sites……...………………......……...……….…...……32

Figure 10 Results of origin and destination location sensitivity analysis for Tikal to
Calakmul path………………….……………………..…………………………..….......34

Figure 11 Results of Tikal to Calakmul DEM resolution sensitivity analysis…...........................35

Figure 12 Results of Calakmul to Tikal DEM resolution sensitivity analysis ….……....….……36

.

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List of Tables
Table 1 Location of the sites in UTM Zone 16N coordinates ...................................................... 18
Table 2 Example results of Tobler’s hiking function for different slopes…...…………………..21
Table 3 Path Distance Tool inputs……………………………………………………………….23
Table 4 Cost Path Tool inputs ....................................................................................................... 23
Table 5 Raster to Polyline Tool inputs………….………………………………….…….……...24

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Acknowledgements
I am grateful to my thesis advisor, Karen Kemp, for the direction I needed and my other faculty
who gave me assistance when I needed it. I would like to thank Professor Thomas Garrison as
well for his assistance in helping me decide on a topic for my thesis project, and for agreeing to
be on my thesis committee. I would also like to thank Professor John P. Wilson for agreeing to
be on my thesis committee.

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List of Abbreviations
BCE Before the Common Era
CE Common Era
GIS Geographic information system
GISci Geographic information science
GIST Geographic information science and technology
SSI Spatial Sciences Institute
USC University of Southern California
USGS United States Geological Survey

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Abstract
Since the 19
th
century, excavations at the Maya site of Tikal have continually provided intriguing
archaeological insights into the Maya world. Tikal was one of the most influential powers in the
Southern Maya Lowlands, and maintained wide-ranging relationships with neighboring sites
throughout the Maya area. These inter-site relationships are described extensively in the
epigraphic record of Tikal and its neighbors. As one of the major powers in the Maya region,
Tikal was engaged in frequent warfare with rival cities in the Lowlands. The objective of this
thesis project was to model probable paths for Tikal’s warfare interactions in the region through
the use of least cost path analysis. The study generated three separate sets of points, to the Maya
sites of Caracol, Calakmul, and Naranjo using the Path Distance tool in ArcGIS. Least cost path
analysis expresses the efficiency of each route as a function of time and distance. The study
generated these least cost paths through the use of Tobler’s Hiking function in order to express
how the inhabitants of Tikal would have traveled through the unique terrain of the Maya
Lowlands. This thesis also used sensitivity analysis to test the location sensitivity of the modeled
paths. These analyses determined that the least cost paths diverge significantly if input data is
altered. The least cost path analysis indicated that the modeled routes represented a set of
probable paths from Tikal to its neighboring rival sites.

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Chapter 1 Introduction
GIS has been an invaluable asset for archaeological research since the 1990s (Connolly and Lake
2006, 7). GIS is able to visualize the spatial landscape in a unique fashion that complements the
work performed in archaeology. Least cost path methodology is perhaps one of the best
examples of GIS applications that can be applied to archaeological analysis. Least cost path
methodology operates based on the assumption that people familiar with a landscape will
optimize the costs of travel for frequently used routes. (Herzog 2013, 180). This thesis project
aims to show how least cost path methodology can illustrate human movement between
archaeological sites in the distant past.
This thesis examines the spatial interactions of the Mesoamerican archaeological site of
Tikal. Tikal was one of the most significant Maya cities, which was at the epicenter of a complex
network of relationships during its peak between 200-900 CE. The geopolitical complexity of the
Maya world opened up avenues for a wide range of interactions, chief among them conflict
(Martin and Grube 2008, 21-25). This analysis aims to model the spatial movement of the
inhabitants of Tikal to rival sites which it came into conflict with when Tikal was the dominant
city in the region.
1.1. Motivation
As this thesis was first articulated, it was determined that the focus of this project should
be based on Mesoamerican archaeology, specifically studying the Maya civilization. Inspection
of the existing GIST literature revealed that there had been several spatial analyses within
Mesoamerican archaeology, which could be used as a model for further investigative studies in
the region. GIST would best be able to visualize inter-site relationships among the major
archaeological sites of the Maya area.

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The main motivation for undertaking the research project was to better understand the
complexity of the geo-political relationships of the sites in the Maya Lowlands. These sites
possessed a very high degree of spatial interaction. Analysis of these inter-site relationships
through the use of least cost paths is vital in order to visualize how the inhabitants of these sites
may have moved throughout the spatial landscape. This project was designed to determine if
there was a means by which these least cost paths might be expressed in order to quantify the
cost effort required to travel between sites. This project’s goal was to model travel paths between
Maya sites in GIS software in order to visualize how the inhabitants of these sites may have
traveled in the distant past. Although archaeological confirmation of these modeled paths may be
unlikely, they would serve as a comparative model for geopolitical movement throughout the
Maya area.
There have been several archaeological studies in the Maya area that have used
geospatial analysis as part of their research. This project was based on those archaeological
studies in particular that used least cost paths in their analysis. Carballo and Pluckhahn used
least-cost paths to model political interactions between Mesoamerican sites (Carballo and
Pluckhahn 2007 612-615). Analysis of these paths would be integral to understanding spatial
movement between sites. Doyle et al.’s analysis featured least cost path analysis to describe the
possible travel corridors between the site of Tikal and other major polities in the region (Doyle et
al. 2012, 796-797). These studies used epigraphic evidence to describe geopolitical relationships
between the sites, and then used the results of this research in geospatial analysis.
As research on this project continued, it gradually focused on the Maya archaeological
site of Tikal as the central origin site for the least cost path analysis. Tikal was chosen due to its
strategic position as the epicenter of Mesoamerican politics during its peak. It was decided that

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this project could advance archaeological study by specifically focusing on conflicts as a means
of analyzing the geopolitical relationships of Tikal through least cost path analysis.
1.2 Description of Study Area
The general area of interest for this project falls on the Yucatan Peninsula, specifically in
the Maya Lowlands of Guatemala, Belize, and southern Mexico as seen in Figure 1 (Criscenzo
2017). The study area is largely within the Guatemalan Department of Petén. The history of
Maya habitation in the Lowlands can be traced through archaeological documentation back to
2600 BCE (Hammond et al. 1976, 579-581). The climate of the study area is semi-tropical with
seasons divided into wet and dry, although this is not constant throughout the entire region. The
study further focuses on the region of the Petén situated on a densely forested limestone plateau
with numerous swamps known as Bajos.

Figure 1 The Maya Region. Source: Criscenzo 2017.

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This project focuses on the Maya archaeological site of Tikal, which reached its political
peak during the Classic Period, c. 200-900 CE (Martin and Grube 2008). The site of Tikal was
one of the most powerful Maya sites in the Petén Basin. Tikal’s influence reached across most of
Mesoamerica with many other Maya sites having archaeological evidence of contacts with Tikal.
Scholars have compiled a body of evidence from the hieroglyphic record of wide-ranging
political interactions taking place between these sites. Martin and Grube describe Tikal as having
a central place in the geopolitical interactions between the majority of the sites in the Maya
lowlands. Tikal’s geopolitical connections with its surrounding sites were expressed in the
epigraphic record in the form of alliances, trade and conflict. More warfare interactions between
Tikal and its neighbors have been recorded than between any other comparable Maya site. These
interactions solidified Tikal’s place as a major power in the Maya region. Tikal was a dominant
power that maintained that dominance through its military prowess.
1.3 Methodology
This thesis project generated least cost paths to visualize inter-site contact between Maya
sites. Multiple least cost paths were calculated to show travel between the Maya site of Tikal and
three other sites in the region, namely Calakmul, Caracol, and Naranjo. This least cost path
analysis was based on an anisotropic cost model and used Tobler’s hiking function to describe
distance as a function of time. Anisotropic cost models are directionally dependent due to the
different costs involved with travel based on the direction and steepness of the slope. These costs
are calculated depending on the path direction from the point of origin, as more effort may be
required for traversal of steep uphill versus downhill slopes. This model is more representative of
the way that people travel through the landscape than an isotropic model as an isotropic model
calculates costs without consideration of slope or direction of travel.

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This project also created isochrones (lines drawn on a map connecting points at which
something occurs or arrives at the same time.) in conjunction with the least cost path models in
order to create an additional perspective. Both the isochrones and the least cost path models were
constructed through the use of anisotropic cost models to ensure that they were complementary
in regards to the distance modeled in each operation. Through the combination of least cost path
methodology and isochrones, this thesis project aimed to show the cost effort required to travel
from the origin point of Tikal to the various endpoints that were selected. The Methods chapter
describes in more detail how the methodology of the project was performed.
The anisotropic cost model was also selected for inclusion in this analysis due to its
frequent use in other archaeological geospatial studies. Anisotropic costs are often used in
archaeological contexts due to the diverse topography often encountered in archaeological
landscapes. An isotropic model would be unsuitable for an archaeological analysis as it imposes
equal costs on the cell regardless of direction of travel (Anaya Hernandez 1999, 78-79; Connolly
and Lake 2006, 316-317). The anisotropic cost model’s use in other archaeological studies
allowed this project to compare its use as a similar isochrones model was prepared. The Related
Work Chapter describes in more detail why anisotropic costs were used in this project over
isotropic costs.
This research project is also making use of an anisotropic cost model which can illustrate
distance as a function of time traveled. Tobler’s hiking function was used as the primary
anisotropic cost model. This function may be able to accurately assess the range of human
motion and provide a more accurate model than simpler isotropic models for the least cost paths
visualized here (Doyle et al. 2012, 794; Katner 2004,5-6). This cost model allows for the
creation of visualization of the movement between sites as a function of time traveled. This

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function allowed this project to determine the length of time required to travel, in order to
compare how the travel times may have differed from the origin to each destination point in the
least cost path analysis.
1.4 Research Goals
In modeling these least cost paths to represent interaction, the project does not aim to
describe paths that are accurate to past spatial movement in the region. The research goal of this
project is to model the most cost-efficient routes between Tikal and its neighboring sites. In the
absence of archaeological documentation of Maya paths, it is impossible to determine how
closely inter-site movement would have resembled the modeled least cost paths. The aim of this
thesis is to use the least cost paths similar to Newhard’s study of inter-regional interaction; to
produce paths that provide a visualization of the relationships between the central sites in the
region (Newhard et al. 2008). This thesis project modeled the least cost paths in order to attempt
to replicate how the inhabitants of Tikal may have moved across the landscape in warfare events.
This model may provide a close approximation of the specific routes that the Maya have taken,
with the idea that the Maya may have chosen paths that required the least effort.
1.5 Thesis Organization
The remainder of the thesis is organized as follows. Chapter 2 covers the necessary
background on the methodology that was used and it describes the use of least cost path models
in other archaeological studies as well. Chapter 3 details the complete methodology for the
current thesis project, so that other users may be able to reproduce the study if given similar data.
In addition, it describes the assessment of results that was performed to ensure the quality of the
results. Chapter 4 details the results from the completion of the least cost path analysis using
visual aids and tabular data to support the textual descriptions of the outcomes. The chapter also

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shows the results of the validity assessments. Chapter 5 provides conclusions and also briefly
describes possible future analyses that may be derived from the results of this research.

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Chapter 2 Related Work
The subject of Mesoamerican inter-site interaction has been discussed at length in the scholarly
literature. This thesis uses GIS analysis to analyze the project’s subject. This literature review
examines literature in this area in order to determine the methods generally used in related
academic research. The majority of this chapter focuses on the literature and theory of least cost
paths. This review is of use as background for the thesis project in order to ensure it expands
upon previous research involving least cost paths, cost models, and previous archaeological
studies.
Previous archaeological least cost path studies were examined to determine similarities
between these studies and this project. This comparative analysis was done in order to obtain
insight from the methodology applied in these projects. It was also important to compare the cost
models used in the different studies. The analysis of these cost models is integral to the current
thesis project, as is determining how these other studies assigned weights and how this impacted
their calculations of a least cost path model.
2.1 Epigraphic Analysis of Interactions Between Sites
Epigraphy is the study of texts. In archaeology, examples of epigraphic evidence may be
characterized as textual evidence such as hieroglyphs or engravings. Epigraphic evidence has
been used in archaeological studies to indicate relations between two or more sites. Tobler and
Wineberg (1971, 40-41) detail the results of an archaeological study in which an Assyrian
cuneiform tablet describing a complex exchange network was used to estimate the geographical
position of the 119 towns listed on the artifact. They describe the mention of two site names on
the same artifact as evidence of a relationship between these sites. The authors also speculate that
places mentioned together frequently are closer together or may have a higher degree of contact.

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Tikal was a major Maya center, and contacts between Tikal and other major sites in the
region were recorded in the epigraphic record (Martin and Grube 2008, 21,25). Martin and
Grube visualize the interactions between Tikal and the other major archaeological sites in the
Maya area in Figure 2. As shown in Figure 2, Tikal had familial, diplomatic, and political
contacts with other sites in addition to warfare interactions. Conflict between sites is symbolized
by a bright red line, diplomatic contacts by a thin black line, political contacts were defined by a
bold line, and familial ties by a closely spaced dashed line in Figure 2. The schematic includes
several archaeological sites, however, several of these sites only have a tangential connection
with Tikal.

Figure 2 Diagram of Tikal’s interactions with other Maya sites. Source: Martin and Grube 2008.

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This thesis focuses on archaeological sites that possess a high level of evidence for a
conflict interaction, as shown on the Martin and Grube diagram. Tikal has recorded evidence of
warfare interactions with its surrounding sites in the archaeological record. Many of its conflict
interactions were the result of long-term hostilities involving power struggles with neighboring
polities such as Calakmul, Caracol and Naranjo. These wars were fought over territory or
political control of the region (Webster 2000, 86-96). Warfare was a means through which Tikal
exerted its power and influence throughout the Maya area.
Nolan and Cook (2012, 75-76) describe a least cost path model in their spatial analysis of
prehistoric catchment sites in which the endpoints were chosen via archaeological criteria. The
criteria for the selection of the endpoints was an archaeological site index which recorded known
prehistoric sites in the region. This is applicable to the current project because it also uses a sites
placement in the archaeological record as a criterion for endpoint selection. Although the current
project did not utilize an archaeological site index, it did utilize archaeological evidence to help
further refine possible endpoints. The selection of specific sites included in this research is
further discussed in Chapter 3.
2.2 Least Cost Analysis in Archaeological Contexts
Least cost paths are often used in the context of archaeological research to determine
possible routes between sites. Least cost paths are defined as the most efficient route between
two locations across a landscape in regard to energy or time (Conolly and Lake 2006, 2). These
paths are often used in archaeology due to their ability to demonstrate the quickest route between
two sites or areas. Schild (2016) used least cost paths to evaluate historical trade routes in Turkey
against the known trade routes in the region. He argued that in navigating a landscape, people
typically utilize the path of least-resistance in terms of energy expenditure. According to Schild,

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the inhabitants of a given region generally utilize their specialized knowledge of the region and
are aware of the easiest routes to traverse the area. This tendency to reduce the cost of mobility
results in patterned behaviors of interaction (Schild 2016, 14; White and Surface-Evans 2012, 2).
Schild’s conclusions indicate that archaeological sites that are far away may have significantly
less interaction then those that are closer to the point of origin in the landscape.
Carballo and Pluckhahn (2007, 612) also performed a least cost path analysis in
Mesoamerica using multiple endpoints and one origin point. The study identified the least cost
routes in terms of travel time. To measure this, the study used a hiking function developed by
Tobler (1993, 3) that could create an anisotropic surface which indicated the most efficient path
of travel. This hiking function calculates effort in hours of foot travel across the terrain.
Another example of least cost path modeling was seen in an archaeological study of inter-
regional interaction in the Goksu Valley of Turkey (Newhard et al. 2008, 92-98). The stated
purpose of the least cost path model was to provide a rough understanding of relationships
between sites in the area, not to produce definitive paths that would describe accurately how
people may have traversed the region. The least cost path was performed using a constraint that
the cost of climbing a slope was not proportional to the degree of the slope; this was done to
account for the costs expended while traversing steep terrain. Similar to Newhard’s model, the
least cost paths in this thesis project are not meant to visualize accurate paths, but instead,
visualize a probable path for interactions involving conflicts between the archaeological sites.
Doyle et al. (2012, 795-797) record a least cost analysis in their study of inter-site Maya
exchange route travel that also used Tikal as an origin point. Doyle et al. noted that most Maya
travel in the region was achieved by utilization of footpaths which were created by clearing
vegetation. This suggests that ancient Maya exchange routes were susceptible to land cover

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alterations made by the inhabitants of the region. Their least cost routes were not modeled to
attempt to describe the actual exchange routes of the Maya people, but were instead used to show
how the exchange corridors may have affected settlement in the region. The analysis assigned
weights to the landscape depending on what season of the year it was. These weights were
integral to Doyle et al.’s analysis as some areas of the landscape were impassable depending on
the season. This allowed the cost path to more accurately reflect the actual exchange corridors in
the region. In addition, the study assigned partially anisotropic costs such that it adjusted for
increased difficulty of foot travel through the corridor from the direction of the original origin
point. Similar to Doyle’s project, this thesis used least cost analysis to attempt to model corridors
for potential conflicts between Tikal and these sites.
2.3 Modeling Cost Surfaces
Least cost path models utilize a cost surface that models the energy expenditure that is
necessary to travel between two separate points. Connolly and Lake (2006, 215) define costs as
being separated into either isotropic or anisotropic paths. Isotropic costs are independent of
direction of travel, whereas anisotropic costs are direction specific. Isotropic costs may include
terrain features such as vegetation, land cover, and water. Isotropic cost models assume the cost
would be equal for all directions a path may go in the landscape. Isotropic cost models are more
suitable for areas with little variation in elevation.
Anisotropic models calculate costs that differ based on their initial direction from the
point of origin. This cost model is generally used for archaeological geospatial studies due to its
focus on direction-specific cost modeling. The anisotropic cost model is a suitable model to
accurately estimate the costs that may be incurred during a least cost path analysis of the Maya
area.

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A case study by Anaya Hernandez (1999, 78-79, 81, 82-83) of spatial movement between
sites in the Maya area focused on assessing both isotropic and anisotropic cost functions. This
spatial analysis focused on movement as a function of not only distance, but also of time and
energy expenditure and incorporated the isotropic costs as a fixed unit of resistance on the cost
surface. Anisotropic costs are described by Anaya Hernandez as being cumulative as well as
direction specific, with different friction values derived. He hypothesized that to accurately
identify spatial movement over a natural setting, both anisotropic and isotropic cost models
might be necessary. He also detailed the necessity of combining three different raster images in
order to create a workable cost surface image that would incorporate his mixed cost model.
These images were the source image, the friction cost, and a directional image. The DEM was
derived from digitization of several topographic maps which were isotropic source images as
slope was not incorporated into these maps. The DEM was used to generate the slope and aspect
images. Slope and aspect were used together to create an anisotropic directional image, as slope
measures the angle of the terrain and aspect gives the direction of the slope. The anisotropic
friction cost was derived from the slope and aspect. The friction cost increases exponentially
relative to slope.
Least cost paths typically utilize a spreading algorithm across the cost surface in order to
create the accumulated cost surface. This spreading algorithm tallies the total cost of the travel
between the original point and the endpoint in the least cost path analysis (Schild 2016).
Therefore, the selection of this algorithm is crucial for any least cost study. The least cost path
analysis often uses Dijikstra’s algorithm. This algorithm is mathematically based, and focuses on
the determination of the total minimum cost between two points. This calculation uses a graph-
based weighting solution in order to determine the total cost (Dijikstra 1959, 269-271). This

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algorithm is ideal for utilization in the current research project, however, Dijikstra’s algorithm
does not include other factors of measurement besides distance.
A least cost path study by Bell et al. (2002, 106-107) describes several techniques for
calculating the final cost surface. Their study derived the cost surfaces from the slope values and
accounted for movements across the sloped surface through the utilization of an anisotropic cost
computation. The study focused on the magnitude of the slope as well as the direction of the
slope. This model used a strategy that the best way to solve the problem of an excessive slope is
to traverse across the angle of the slope rather than attempting to go against it. In a least cost path
model, a path going around a high elevation area may be faster than one going through it. By
using such cost functions, it ensured that the modeled path was as efficient as possible even in an
area where there are complex slope changes across the landscape.
Tobler’s hiking function is able to model cost paths in a way that minimizes both the time
and energy expenditure required to reach the target destination. Tobler’s hiking function is useful
because it manages to utilize slope in its cost. The function is most efficient when going
downhill at a slope of five to seven degrees, steeper slopes may force a walker to slow down.
(Katner 2004, 6). This would indicate that Tobler’s hiking function is more suitable for least cost
path based analysis in studies where there are significant differences in slope. It is also extremely
useful for indicating the exact time it takes to traverse a path as it will calculate the time cost per
degree of slope in the final cost raster.
Tobler’s hiking function is not the only algorithm that may be used to calculate a cost
surface to determine time and distance in a least cost path analysis. Other methods such as the
one used in Pandolf’s report for the Army, place constraints upon the walker and utilize
assumptions about the starting speed and pace of the individual (Pandolf et al. 1977, 5-10). The

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cost model also imposed load costs which may be only viable in studies where these load costs
can be measured. These studies also may not accurately reflect the full range of human motion,
as an individual’s speed may vary depending on their range of mobility. In an archaeological
context such as this research project, determination of an average load cost is not possible given
the lack of available information regarding individual human movement in the Maya region.
Tobler’s hiking function has been determined to be consistent with independent
assessments of human motion. It was assessed in an anthropological mobility study in South
America and was determined to be a valid indicator of travel times in rough terrain, although
factors such as path condition could affect its accuracy (Aldenderfer 1998,12-13; Katner 2004,
6). The terrain that was assessed in this least cost model study requires a model that realistically
depict human motion through the landscape. In addition, Tobler’s hiking function demonstrated
that it was able to model more accurate paths as it assigns its costs through the landscape.
2.4 Assessment of Results
It is important to assess the results of least cost analysis to prevent errors when modeling
in a GIS. There are several means by which an accuracy assessment may be conducted in a
spatial analysis. Rothley stated that in order for least cost paths to be reliable, the validity of the
data must be demonstrated (Rothley 2005, 2). It is critical to check the input raster data for
errors to ensure that the model is accurate. Second, if there is a mistake in the cost raster, the
output will likewise be erroneous as well. According to Rothley, raster-based spatial data may
have technical issues which may nullify the original results. Therefore, when doing a cost path
analysis, it is necessary to review the cost raster data before generating the final results. It may
also be necessary to do a thorough review of all input and output data to ensure that there are no
mistakes being created through the use of the wrong input for an operation.

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Evaluation of the cost function is integral to the operation of a least cost path analysis.
Herzog suggested that archaeological least cost path analysis should not be stopped after the
initial paths were modeled, and that the paths be tested to determine how they may reflect reality.
(Herzog 2013, 181-182). Herzog stated that the validity assessment of the least cost analysis may
also be performed via alteration of the initial parameters in the cost model. This may be achieved
by introducing different cost components into the model in order to determine the sensitivity of
the final result. Other examples may include alteration of the endpoint or origin to determine if
the cost function is operating correctly. Herzog argued that such minor deviations in the model
parameters could result in a very different least cost path. However, alteration of cost parameters
such as substituting a lower resolution DEM could result in an even more divergent least cost
path from the original.
In the thesis project, one origin-destination pair underwent a sensitivity assessment in
order to determine the potential accuracy of the least cost path. This evaluation took the form of
slightly altering the locations of the original destination and origin points in order to test the
sensitivity of the least cost path.

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Chapter 3 Methods
This chapter describes the methodology used in the creation of the least cost paths for this
project. The least cost paths developed for this thesis focus on paths between prominent Maya
sites in the Maya Lowlands: Tikal, Caracol, Calakmul and Naranjo (Figure 1). This methodology
uses Tobler’s hiking function when determining the least cost paths in order to model the paths
in the most time and cost-efficient manner. Least cost paths were implemented from Tikal to
each destination site as well as vice versa. Isochrones were modeled for this project to represent
travel time between Tikal and the destination sites. Sensitivity analysis was conducted on the
least cost paths in order to determine the sensitivity of the results to variations in the input data.
This was performed using DEM and site placement sensitivity analysis.
This chapter is divided into several sections. The first section briefly discusses the
selection of the origin and destination points. The following section covers the data acquisition
process. The third section describes the process by which the least cost path was executed. The
fourth section describes the processes by which isochrones were created for this analysis. The
last section of this chapter outlines how the sensitivity of the model results was assessed by
alteration of input variables.
3.1 Study Sites
The sites used in this project were all located in the Maya Lowlands as seen in Figure 1.
A vital step in this project was choosing the origin and destination points that would be modeled
in the least cost path analysis. The selection of these sites was based on published epigraphic
evidence without the use of GIS. This study used textual evidence given in Chronicle of the
Maya Kings and Queens: Deciphering the Dynasties of the Ancient Maya (Martin and Grube
2008). A reading of this book led to the conclusion that Tikal was the most viable origin for the

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least cost path analysis due to its wide range of interactions with other archaeological sites in the
Maya region as can be seen in Figure 2.
The decision was made for this analysis to focus on conflict-based spatial interactions
between Tikal and its neighbors. In Figure 2, red lines indicate each spatial interaction signifying
conflicts between Tikal and neighboring sites recorded in the epigraphic record. Multiple lines of
the same interaction type in the diagram signify that there are multiple forms of this contact
between the two sites. For the purposes of this analysis, three destination sites were selected to
showcase the spatial interactions of Tikal. Naranjo, Calakmul, and Caracol were selected
because they each possess evidence for conflict-based spatial interactions with Tikal.
The coordinates for Tikal, Naranjo, Calakmul, and Caracol were discovered by searching
for these sites in Google Earth. These site locations were recorded in UTM coordinates. Table 1
shows these values. An Excel spreadsheet was created to record these site locations. This Excel
sheet had to be rendered spatially compatible, and so it had four columns: ID, Description,
Northing and Easting. This spreadsheet was then saved as a comma separated values file in order
to make it compatible with ArcGIS.
Table 1 Location of the sites in UTM Zone 16N coordinates
ID Name Northing (m) Easting (m)
1 Tikal 1906017 220984
2 Caracol 1854642 274016
3 Naranjo 1895735 259427
4 Calakmul 2004115 202519

3.2 Preparation of Project Geodatabase
This project required a surface model of the region surrounding the site of Tikal. This
digital elevation model (DEM) was obtained from the United States Geological Survey (USGS)

19
through one of its tools called the Global Data Explorer. This allowed me to visualize the entire
world in the Data Explorer viewer, and narrow down my study area for the project. By selecting
an appropriate box around these sites of interest, an ASTER Global DEM V2 and an SRTM
DEM in GEOTIFF format were downloaded.
The ASTER DEM was produced in part by NASA using data gathered from the ASTER
remote sensing program. The ASTER DEM has a vertical accuracy of 7-14 m. The horizontal
resolution of the ASTER DEM is approximately 30 m. The SRTM data was collected by the
Shuttle Radar Topography Mission. There are two SRTM products available, one with a 30 m
and one with a 90 m resolution, the second of which was used for this project. The vertical
accuracy of the SRTM is 10-16 m (Ramirez 2017). The ASTER DEM was selected as the
primary digital elevation model for this project and the 90 m SRTM was used for the sensitivity
assessment at the end of the process.
The ASTER and SRTM DEMs were imported into ArcMap via ArcCatalog. The ASTER
DEM was originally obtained in a geographic coordinate system of GCS WGS 1984. The SRTM
was also available in the GCS WGS 1984 coordinate system. It was later projected into a
projected coordinate system of WGS 1984 UTM Zone 16N. I projected both the ASTER and
SRTM DEMs from a GCS to a UTM projected system due to my decision to implement my site
coordinate data in UTM coordinates.
The .CSV file containing the site data was uploaded into ArcGIS via ArcCatalog. Once
the file was opened in ArcMap, the tool Display XY data allowed an events layer for the point
file to be created. The events layer was then exported into a shapefile so that the points could be
used in the least cost path analysis. Figure 4 shows the location of the sites in the context of the
Maya area.

20

Figure 3 Four sites overlaid on the 30 m ASTER DEM

21
3.3 Preparing the Data for the Least Cost Path Operations
Use of the Tobler’s hiking function is key in this analysis since it allows for both the
determination of anisotropic paths and the calculation of path time. A vertical factor table was
used in the path-distance tool to operationalize the Tobler’s hiking function. It is calculated via
the following equation:
Time (hours) to cross 1 meter =
0.000166666*(exp(3.5*(abs(tan(radians(slope_deg)) +0.05)))) (1)

For use in the Path Distance tool, a discretized version of this equation is necessary. Table 2
shows a range of possible results from the equation, for values with slope degrees between -40
and 40. An extended version of this table, called “ToblerAway”, with values for all degrees
between -70 and 70, plus +/-80 and +/-90 was used in the Path Distance tool as the vertical factor
table.
Table 2 Example results of Tobler’s hiking function for different slopes
Slope (degrees) Vertical Factor
-40 0.001610753
-30 0.000822629
-20 0.000474721
-10 0.000257717
0 0.000198541
10 0.000365717
20 0.000673661
30 0.001240899
40 0.002285767

The origin and destination feature classes were transformed into individual feature
classes for the least cost path analysis. This was accomplished by means of the Feature Class to
Feature Class tool for each of the sites. As this analysis used three paths that were analyzed
separately, three path specific feature geodatabases were created to store the data. The Path

22
Distance and the Cost Path tool requires data from both the origin and the destination for the
main input in the least cost path operations. The first path point pair to be modeled in this
manner is Tikal to Naranjo, then Tikal to Calakmul, and finally, Tikal to Caracol.
Prior to the start of least cost path operations, I created buffers around each one of the
sites. The buffers are used to represent an area of origin because the actual physical origin would
not be a zero-dimensional point on the landscape. The area of central Tikal, for example, was
approximately 4x4 km (Thomas Garrison, personal communication, May 8, 2017). Using the
Buffer tool, I created a buffer for each site point of 1000 m diameter, saving each output as a
separate file. Then this vector buffer was transformed into a collection of contiguous raster cells
by using the Polygon to Raster tool in ArcToolbox since the Cost Distance tool requires one or
more raster cells as origin and destination points. I used both of these buffers in the analysis and
mapping steps so that there was a total of eight buffers created. The naming convention for the
buffers follows this form: ‘TikalBuffer’ for the polygons and ‘Buffer Tikal’ for the raster
versions of these buffers.
3.4 Least Cost Path Operations
The least cost path operation uses a combination of the Path Distance and Cost Path tools
in ArcToolbox. The least cost path operations were performed not only to each destination site
from Tikal, but also from each destination site to Tikal. This resulted in a total of six paths, with
the objective to determine how the paths may have been altered depending on their point of
origin. These paths were performed in both directions in order to better model a conflict
interaction path for Tikal invading a site as well as being attacked by rival sites.
Figure 4 shows these input, tools and output for one destination through a flowchart to
illustrate how the least cost path process would work for each path. Tikal’s buffer and the

23
destination buffer are switched for each reversed path. Tables 3 through 5 show the inputs and
outputs for the Path Distance, Cost Path and Raster to Polyline operations. The Vertical Factor
input shown in Figure 4 for the Path Distance tool is how Tobler’s hiking function is
implemented in the least cost path operation. The DEM provides the elevation extent over which
the cost surface is calculated for that path.

Figure 4 Flowchart showing procedures used to calculate least cost path
Table 3 Path Distance Tool inputs
Path # Input Vertical Factor
1 (Tikal to Calakmul) BufferTikal CalakmulTikal
2 (Calakmul to Tikal) BufferCalakmul CalakmulTikal
3 (Tikal to Caracol) BufferTikal CaracolTikal
4 (Caracol to Tikal) BufferCaracol CaracolTikal
5 (Tikal to Naranjo) BufferTikal CaracolTikal
6 (Naranjo to Tikal) BufferNaranjo CaracolTikal
Table 4 Cost Path Tool inputs
Path # Input Output
1 (Tikal to Calakmul) CalakmulBuffer Path1
2 (Calakmul to Tikal) TikalBuffer ReversePath1
3 (Tikal to Caracol) CaracolBuffer Path 2
4 (Caracol to Tikal) TikalBuffer ReversePath2
5 (Tikal to Naranjo) NaranjoBuffer Path3
6 (Naranjo to Tikal) BufferTikal ReversePath3

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Table 5 Raster to Polyline Tool inputs
Path# Input Output
1 (Tikal to Calakmul) Path1 LeastCostPath1
2 (Calakmul to Tikal) ReversePath1 ReverseLCP1
3 (Tikal to Caracol) Path2 LeastCostPath2
4 (Caracol to Tikal) ReversePath2 ReverseLCP2
5 (Tikal to Naranjo) Path3 LeastCostPath3
6 (Naranjo to Tikal) ReversePath3 ReverseLCP3
3.5 Creating Isochrones
Isochrones are lines of equal time. Isochrones were created to determine how far an
individual could travel in a set interval of time. Three sets of isochrones were created, one set
from each of the three non-Tikal sites. For this operation, I used the path distance output for the
calculation, using the output backlink from the Path Distance tool. Then the Contour tool from
the surface analysis section of ArcToolbox was employed. From the Contour tool, the ‘output
backlink’ was used as the input surface. Figure 5 shows the input, tools and outputs for one site.
In this analysis, this process was repeated only twice, as the output backlink for Tikal to Caracol
overlaps with that for Tikal to Naranjo.

Figure 5 Flowchart showing procedures to create isochrones

25
As the isochrones are created, it was necessary to set the interval between them. After
some trial and error, the interval was set to four hours from Tikal, an interval that would show
sufficient time resolution for visualization purposes. The isochrones are meant to be used in
conjunction with the least cost modeled paths and not as an exclusive means of determining the
time required to travel the given distances. Thus, overlaying the isochrones with the line features
that are created in the final step of the least cost path analysis allows visualization of these
isochrones in comparison to the least cost paths. A slope map was created from the Aster DEM
for this project to be used as the background for the isochrones. Since the path distance surface
was calculated using the Tobler Hiking Function table, the isochrones represent the distance
traveled as an anisotropic time-distance, allowing a visualization of the approximate cost effort
required to travel away from each site. This helps to demonstrate the possible range of motion
for an individual in the given time frame that is expressed in the result of the original least cost
path model.
3.6 Sensitivity Analysis
In order to determine the validity of the least cost path, it was necessary to perform a
sensitivity analysis. The sensitivity analysis was performed using two methods: an origin and
destination location sensitivity analysis and a DEM resolution sensitivity analysis. The origin
and destination location sensitivity analysis used a new pair of origin and destination points. The
new origin point is near the site of Tikal, but moved 1500 meters east. The destination point
selected for this sensitivity analysis is Calakmul. It was repositioned 1500 meters east. For this
assessment, new buffered points were created using the repositioned site features. Least cost
paths were generated from these points and these were compared to those modeled in the original
methodology.

26
The DEM resolution analysis was completed by using the original methodology, but
substituting the SRTM DEM instead of the ASTER DEM as the base digital elevation model in
all procedures. This check helped to determine if there were discrepancies between the modeled
paths when performed with the SRTM DEM as the base instead of the ASTER DEM. For this
comparative analysis, the SRTM replaced the ASTER DEM specifically for the extent of the
path between Calakmul and Tikal.

27
Chapter 4 Results
This chapter presents the results of applying the methodology outlined in the preceding chapter.
Results include an inspection of each pair of paths and the isochrones, and a discussion of the
results of sensitivity testing.
4.1 Least Cost Path Corridors
Figure 6 shows the multiple paths generated between Tikal and Calakmul. The Tikal to
Calakmul path merges with the Calakmul to Tikal path throughout the majority of its path except
at the ends. As noted earlier in Chapter 3, origin and destinations were modeled as 1000 m
buffers to allow the least cost paths to begin in raster cells over a larger area than a zero-
dimensional point which causes all of the paths to split into multiple branches as they approach
the destination.
The Tikal to Calakmul path initially descends to a lower elevation then travels across this
low elevation until starting a climb up to a higher elevation, eventually declining on its way to
Calakmul, ending with a short uphill slope. The reverse path begins on a downward slope to a
slightly lower elevation before the path treads upwards again, wherein it stays on the higher
elevation until it reaches the green lower elevation point. There, the reverse path splits off into
two branches, both of which stick close together.
In Figure 6 the buffers create multiple destination points for both the Tikal to Calakmul
path and the reverse path. Both paths split as the path travels downhill into a lower elevation
area. The Tikal to Calakmul path overlaps with the reverse path throughout the majority of its
course. The maximum distance that the paths deviate from each other as they travel in opposite
directions is 1 kilometer as the Tikal to Calakmul path initially descends downhill into the lower
elevation region.

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Figure 6 Least cost paths between Tikal and Calakmul

29
The Tikal to Naranjo path, shown in Figure 7, has several different routes, some of which
merge with the reverse route at various points along the paths. The single path from Tikal merges
with one of the reverse paths near the beginning then bifurcates and begins to deviate as the path
heads towards a downhill slope in the yellow lower elevation area. The Naranjo to Tikal path
flows an original path until a lower elevation area is reached, wherein it deviates to the south
until the path goes uphill as it returns to the higher elevation area and rejoins one of the Tikal to
Naranjo routes.

Figure 7 Least cost paths between Tikal and Naranjo
In Figure 7, the buffers create multiple routes at the destinations for both the Tikal to
Naranjo path and the reverse path. In both paths, the routes split into two separate branches. The
maximum distance that the original and reverse paths deviate from each other is in the yellow

30
lower elevation region; the separation between the paths going in opposite directions is 2.3
kilometers.
The Tikal to Caracol Path and its reverse path, shown in Figure 8, both split into two
branches as the paths go downhill towards lower elevation regions. The buffers create multiple
destination points for both paths. The maximum distance that the paths in opposite directions
deviate from each other is 3.7 kilometers in the white higher elevation area where the Tikal to
Caracol path heads downhill as the reverse path makes its way uphill.

Figure 8 Least cost paths between Tikal and Caracol

31
4.2 Isochrones
Figure 9 displays isochrones of walking time from Tikal calculated for both the northern
and southern extents of the study area. They are shown over the slope raster instead of elevation
in order to better represent the costs involved in travel. Visualizing slope in this map provides a
clearer picture of the cost-effort required to travel than simple elevation. The time to walk from
Tikal to Calakmul was estimated to be over 20 hours, Tikal to Naranjo at 8 hours, and Tikal to
Caracol at 16 hours.
The four-hour intervals used here are intended to represent an average continuous
walking period between rest stops. This interval is integral as this project models conflict
interactions between sites, these routes would be traversed by large groups of people carrying
heavy equipment. This would necessitate multiple rest stops, most likely more than an individual
would require for the same distance. The approximate distance between each four-hour interval
is 17.5 kilometers.
The intent of creating the isochrone map was to illustrate the travel time from Tikal to the
destination sites. In this analysis, the isochrone lines are not consistently smooth across the entire
area, with the lines showing the most irregularities in areas of higher slope. These irregularities
typically occur in regions where there is a sudden change between higher and lower slope. This
shows how the actual horizontal distance covered will vary between individuals who approach
the location of a particular isochrone at a different point. The isochrone lines are smoother in the
green areas as these represent lower slope, indicating decreased cost effort required to travel
through the region. Although the majority of the region has low slope, there are some red higher
slope areas throughout the region, which is the ultimate cause of the isochrone lines not forming
perfect concentric circles moving outward from the point of origin.

32

Figure 9 Isochrones from Tikal to three sites

33
4.3 Sensitivity Analysis
The following section presents the results of the origin and destination location sensitivity
analysis as well as the DEM sensitivity analysis that used the SRTM DEM instead of the ASTER
DEM. The first sensitivity analysis was conducted by comparing the original Tikal to Calakmul
paths against paths performed using modified origin and destination points. This was done to
determine if the results were sensitive to repositioning of the original points. The DEM
sensitivity analysis uses the extent between Calakmul and Tikal, substituting the SRTM DEM for
the ASTER DEM. The objective of this DEM analysis was to determine whether the lower
spatial resolution of the SRTM DEM would lead to significantly different paths.
4.3.1. Origin and Destination Location Sensitivity Analysis
This sensitivity analysis was performed by moving both Tikal and Calakmul points 1500
meters to the east. The least cost path methodology for the original paths was repeated using the
new placement of the points. As the distance between the original and shifted points is
significant, and crosses a higher elevation, it was expected that this path might diverge
significantly and cause the path to shift as it reaches a lower elevation area.
Figure 10 shows how the sensitivity path behaves when compared to the originally
modeled least cost path. The new placement of Tikal and Calakmul buffered points, shown in
yellow, resulted in a path that is similar to the original, but deviates at key points. The paths
initially follow simple separate paths, going relatively straight north from the origins until they
merge at the same canyon at the north side of the green low elevation area. From this point, they
overlap until they deviate again as they gradually head downhill on their final approaches to
Calakmul. The maximum distance that the paths deviate from each other in the same direction is
5.0 kilometers as the paths began to head downhill in the central region of the map.

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Figure 10 Results of origin and destination location sensitivity analysis for
Tikal to Calakmul path

35
4.3.2. DEM Resolution Sensitivity Analysis
Using the SRTM DEM, the least cost path methodology was repeated for each direction
between Tikal and Calakmul. In Figure 11, it can be seen that the original path from Tikal to
Calakmul is very close to the SRTM DEM path. The original path is very similar to the new path
with short deviations in the low green elevation area and in the higher elevation area. The
maximum distance that the paths deviate from each other in the same direction is 2.5 kilometers.

Figure 11 Results of Tikal to Calakmul DEM resolution sensitivity analysis

36
In Figure 12, the SRTM DEM path is split into two branches from the origin point and
then splits again in the high elevation area, although the original ASTER DEM path follows the
eastern branch of the SRTM path. The buffers create multiple destination points for the paths,
although in the reverse SRTM DEM path, the presence of a lower elevation region near the start
of the path causes the path to split as it initially heads downhill. The two western branches of the
SRTM DEM reverse path avoid the original path entirely. The maximum distance that the paths
deviate from each other in the same direction is 11.0 kilometers.

Figure 12 Results of Calakmul to Tikal DEM resolution sensitivity analysis

37
Chapter 5 Discussion and Conclusion
The objective of this thesis project was to model least cost paths across the Maya Lowlands. The
paths model possible military thoroughfares between Tikal and its neighboring rival cities in the
Maya region. This analysis used Tobler’s hiking function to evaluate the modeled routes. This
chapter discusses the significance of the results and describes possible future applications for
least cost path analysis in the Maya region.
5.1 Discussion
In the least cost path analysis shown in Figures 6 to 8, a reverse path was modeled for
each path-pair, interchanging the origin and destination pairs. The two paths for each path-pair
intersect each other at some points along the routes. The path intersections in Figures 6 and 7 are
in areas of high elevation where there is no lower elevation course for the path to take. Figure 8
shows the opposite where as soon as the Caracol to Tikal path reaches the lowest elevation area,
the two paths intersect until a higher elevation is reached. This is due to least cost paths always
being driven towards the area of least resistance. However, in Figures 7 and 8, although there
were some points of convergence between the paths, at least one branch from each path did not
converge with the opposite path. Reverse paths may significantly diverge from the original path
due to these paths being modeled in the opposite direction over high slope regions where the
vertical factor imposed by the Tobler’s hiking function varies considerably.
The isochrones provide useful visual aids when overlaid over the least cost paths as
shown in Figure 9. The labeled isochrone lines enable quick reference to the approximate length
of time that it would take for an individual to cross the terrain. Deviations in the isochrones lines
are more pronounced where the isochrones pass through sudden changes in slope from high to

38
lower elevations. The time to walk from Tikal to Calakmul was estimated to be over 20 hours,
Tikal to Naranjo at 8 hours, and Tikal to Caracol at 16 hours.
As the specific point locations for the endpoints of paths used in this project were
uncertain in terms of their exact positions, buffers were created to simulate the full extent of each
site. Thus, rather than using zero-dimension points, the origins and destinations of these paths
were modeled using the contiguous set of raster cells contained within these buffer polygons. In
each of the modeled least cost paths, the buffers resulted in the creation of multiple destination
points for the modeled paths, although as seen in Figure 12, the buffer results in the creation of
branching paths from the origin. The sensitivity analysis illustrated in Figure 10 revealed the
insensitivity of the precise placement of the buffers around the approximate site locations. The
difference in slope in the areas around the new origin and destination was marginal enough to
cause the paths to follow parallel routes that merged where the terrain forced travel up a canyon.
In the DEM sensitivity analysis, least cost paths were remodeled on the Tikal-Calakmul
extent using the SRTM DEM, with a 90 m cell resolution, as the elevation base. These paths
were then compared to the original paths modeled using the ASTER DEM, which has a 30 m cell
resolution. The DEM sensitivity analysis showed that the DEM resolution did impact the least
cost paths modeled. Although the SRTM DEM path did not deviate substantially from the
original when Tikal was used as the origin (Figure 11), the path did deviate considerably from
the original when Calakmul was used as the origin (Figure 12). The SRTM DEM path in
Figure 12 is split into three sections, the first adhering closely to the original modeled path from
Calakmul to Tikal; however, the other paths are situated very far apart from the original. This
marked divergence from the original path is likely due to the lower spatial resolution of the
SRTM DEM. Comparing Figures 3 and 11, it can be seen that the original ASTER DEM is

39
shown to have higher elevation in this area; thus, the lower resolution SRTM DEM has smoothed
the elevation range, creating lower peak heights. The alternate paths in Figure 12 are the result of
the lower spatial resolution of the SRTM DEM, which caused this region to have a lower overall
slope through which viable least cost paths could be modeled.
These results support the observations of Doyle et al. (2012, 794) who noted the
unsuitability of the SRTM DEM for least cost path analysis. In particular, they observed that a
path created using an elevation raster with 90 m resolution would calculate a path that would be
90 m wide. A higher resolution DEM such as the ASTER DEM provides a better representation
of the least cost path.
The least cost paths modeled in this analysis were not meant to describe actual paths that
the inhabitants of the Maya region took during inter-site travel. The aim of this thesis was to
utilize Tobler’s hiking function in the least cost path process in order to approximate the
cost-effort of human travel across the terrain. The least cost paths modeled were intended to
provide a visualization of the relationships between the prominent sites of the region in a manner
similar to Newhard et al. (2008)’s study of inter-regional interaction in archaeological contexts.
As Schild (2016) suggests, inhabitants of a region typically preferred to use the easiest routes to
traverse a given area. The paths modeled in this project are only possible reconstructions of the
lowest cost effort of travel from the origin to destination. In the event of conflict interactions, the
parties involved might be expected to seek the quickest and easiest routes available to them in
order to possess the advantage in the warfare event, though other characteristics of the terrain,
notably vegetation cover and visibility, might lead to different choices. Although the least cost
paths depicted in Figures 6 to 8 are only approximations, they may represent some realistic paths
between rival sites.

40
5.2 Avenues for Future Analysis
Future least cost path analyses for this region may include additional destination points in
the least cost path analysis. The number of destination points in a future project could be
expanded from three to as many as eight additional sites for a more comprehensive study of the
social dynamics of the region. These sites could be selected using Figure 2 which shows all local
known rival sites that had conflicts with Tikal. Analysis of these paths could provide insight to
the possible routes that may have been used between these sites. Further studies may also be
used in order to determine if the possible least cost routes overlap when additional sites are
added into the analysis. As this analysis would encompass sites that did not have as frequent
conflict interactions as those in the original study, a comparison might also be made as to the
cost-effort of travel to these sites from Tikal.
A more thorough version of this study may be able to compare inter-site travel based on
other documented interactions between Tikal and its neighboring sites. Figure 2 shows Tikal also
maintained diplomatic contacts and familial ties with many sites in the Maya area. Tikal also
subjugated several cities in the Lowlands that were situated near the destination points modeled
in this project. The analysis could cover all three interaction categories—conflict, diplomacy and
subjugation—using least cost path analyses. These diplomatic contacts would have constituted
an area of safe travel while subjugation might have required additional administrative travel.
Expansion of this least cost path analysis would also include vegetation as a cost factor.
The Maya Lowlands were subtropical and contained numerous swampy regions that may have
created natural obstacles to travel. In addition, although these paths modeled in this project may
represent the route of least cost-effort, it is possible that they may not have been ideal for a
warfare party. Future analysis could analyze these paths in terms of the area visible from the path

41
through Viewshed analysis. Viewshed analysis creates a raster of visible and non-visible areas
from a vantage point based on elevation (Doyle et al. 2012,794). Viewshed analysis could be
used to determine the visibility of the route as well as blind spots.
A possible future extension of this least cost path analysis may be to display results using
ArcGIS 3D Analyst. Using this tool, the terrain that the path travels through could be visualized
in a three-dimensional view. This would allow for a better understanding of the terrain, in
particular where the paths go through multiple slope changes along the route. In addition,
ArcScene allows for complex line symbology, which is integral to displaying the least cost paths
as some of the modeled paths are split into several branches. ArcScene’s animation capacity for
moving an object along a path would also be useful for visualizing traversing the path from the
origin to the destination.
Overall, this study was successful in achieving its stated goal of generating least cost
paths between Tikal and some of its rival sites. The use of Tobler’s hiking function to simulate
the cost-effort caused by changes in the steepness of the terrain produced credible routes through
the Maya Lowlands that could plausibly function as paths along which the warring parties might
travel. Further least cost path analysis may be able to expand on this study using the suggestions
for future studies outlined above.

42
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Abstract (if available)

Abstract Since the 19th century, excavations at the Maya site of Tikal have continually provided intriguing archaeological insights into the Maya world. Tikal was one of the most influential powers in the Southern Maya Lowlands, and maintained wide-ranging relationships with neighboring sites throughout the Maya area. These inter-site relationships are described extensively in the epigraphic record of Tikal and its neighbors. As one of the major powers in the Maya region, Tikal was engaged in frequent warfare with rival cities in the Lowlands. The objective of this thesis project was to model probable paths for Tikal’s warfare interactions in the region through the use of least cost path analysis. The study generated three separate sets of points, to the Maya sites of Caracol, Calakmul, and Naranjo using the Path Distance tool in ArcGIS. Least cost path analysis expresses the efficiency of each route as a function of time and distance. The study generated these least cost paths through the use of Tobler’s Hiking function in order to express how the inhabitants of Tikal would have traveled through the unique terrain of the Maya Lowlands. This thesis also used sensitivity analysis to test the location sensitivity of the modeled paths. These analyses determined that the least cost paths diverge significantly if input data is altered. The least cost path analysis indicated that the modeled routes represented a set of probable paths from Tikal to its neighboring rival sites.

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Asset Metadata

Creator Munoz, Matthieu (author)

Core Title Modeling geopolitics in Tikal through least cost paths

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 07/10/2017

Defense Date 07/10/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag least cost path,Maya,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kemp, Karen (committee chair), Garrison, Thomas (committee member), Wilson, John (committee member)

Creator Email Matthiem@usc.edu,matthieudavidmunoz@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-396776

Unique identifier UC11265108

Identifier etd-MunozMatth-5495.pdf (filename),usctheses-c40-396776 (legacy record id)

Legacy Identifier etd-MunozMatth-5495.pdf

Dmrecord 396776

Document Type Thesis

Rights Munoz, Matthieu

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA