Iyolloco in altepetl: Tlapa-Tlachinollan's polity through GIS and spatial analysis.

La Montaña of Guerrero, Mexico

By

Israel Hinojosa Baliño

Dissertation in partial fulfilment of the requirements for the degree of Master of Science

in

Geographical Information Systems and Spatial Analysis in Archaeology

UNIVERSITY COLLEGE LONDON

INSTITUTE OF ARCHAEOLOGY

Note: This dissertation is a unrevised examination copy for consultation only and it should not be quoted or without the permission of the Director of the Institute.

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Abstract:

This paper is about La Montaña and the altepetl of Tlapa Tlachinollan; the former, one of the regions that constitutes the Mexican state of Guerrero, the later, a complex polity that became powerful during the Post-Classic Period (AD 1300-1500). A series of spatial and non-spatial analyses were made in order to depict and try to understand the political unit called altepetl. Which literally means "the waters, the mountains" and is considered the main political unit (polity) in central and southern Mexico. Due to its relation with geography, it is propose that we can recreate how the altepetl used to work during these years based mainly in: 1) a series of viewsheds to identify if the visual affordances of this mountainous region affected the character of the polities. 2) building a network to explore the connectivity of each site. This way we can know to what degree did major routes of communication affect the character of the polities and 3) during these years small polities fought each other in order to control all over the waters and the mountains, so we explore a new method to define regions using cost surfaces and real archaeological areas to simulate a territory.

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Acknowledgements

I would like to thank to all my family for all the support they gave me. I want to show my gratitude to CONACYT for the scholarship that is still maintaining me while I'm writing this as well as CIESAS which allowed me to come and preserve my job in these days of recession, fear and loneliness, we are not alone, we are not afraid. I would like to thank to Gerardo Gutierrez for all the support and the data used in this dissertation. I am grateful with all the friends I met here, specially those that were there until the end of the battle. I want to say Hello, Goodbye, to all the music that maintain me afloat, thank you Enjambre. I want to express my sincere gratefulness to the evanescence people that I met everywhere but never see them again. Thank you because every day I learn a lot from those small details. I would like to say Ciao Italy, Quihubo Mexico, Quema, Que tal, Como estais,, chamo, chavo, chava, tronco, salam, yalabina! And a per a kilo ashera! I would like to thank to Mark Lake and Andrew Bevan for all the patience they had with me and my Espanglish. At the end the problem were my ears. Thank you everyone, I'm sorry if I'm not able to include you all or if I'm being so informal, I'm sorry you know I don't like it, always like a salmon, against the flow, but I'm pretty sure you are include...believe me ;) I also want to thank to the unknown readers! And finally, I would like to thank to the life, I have been so lucky and I really appreciate it. Thank you everyone and everything.

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Table of ContentsChapter One. Introduction....................................................................................................................7

1. Research questions.......................................................................................................................82. Dissertation structure...................................................................................................................8

2.1.Problems................................................................................................................................9Chapter Two. Tlapa-Tlachinollan.........................................................................................................9

1. Its waters and hills: The environment........................................................................................122. Its expansion: The human variable...........................................................................................143. Altepetl: Spatial Social Organization.........................................................................................21

Chapter Three. Viewshed analysis, cumulative viewsheds and Monte Carlo simulations.................241. Viewsheds. Did the visual affordances of this mountainous region affect the character of the polities?..........................................................................................................................................262. The simulations..........................................................................................................................28

2.1.How to perform viewsheds of more than 5000 viewpoints!...............................................333. Analysis......................................................................................................................................35

3.1.First test...............................................................................................................................353.2.Second test..........................................................................................................................40

Chapter Four: Network: Depicting Tlapa-Tlachinollan through nodes and edges.............................461. Network.....................................................................................................................................472. Towards the exploration of significance in network analysis....................................................523. The “Total Network”, Focal mobility Network and Monte Carlo Approach. ..........................55

Chapter Five. Territoriality: Tlapa-Tlachinollan's dependencies and its territories...........................681. Territories and the XTENT model.............................................................................................71

Chapter Six. Conclusions...................................................................................................................74References..........................................................................................................................................77Appendices.........................................................................................................................................83

1. Appendix – r.cva installation...................................................................................................842. Appendix 2 – Viewshed Random Samples Generator...............................................................863. Appendix – Procedures in R to analyse simulations..................................................................914. Appendix 4 – Closeness centrality.............................................................................................945. Appendix 5 – Territories............................................................................................................98

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List of FiguresFigure 1: Study Area...........................................................................................................................11Figure 2: 1426-1432 expansion..........................................................................................................16Figure 3: 1447-1453 expansion..........................................................................................................19Figure 4: Depiction of province at the end of the 15th century..........................................................23Figure 5: A viewshed generated with VIEWIT on a UNIVAC 1108 computer in 1968 (Amidon & Elsner 1968)........................................................................................................................................27Figure 6: Area 1 .................................................................................................................................29Figure 7: Box plot (ESRI 2009).........................................................................................................30Figure 8: Exploratory analysis............................................................................................................31Figure 9. Area 2 .................................................................................................................................32Figure 10: Densities. Theoretical normal distribution in red..............................................................35Figure 11: Frequencies.......................................................................................................................36Figure 12: QQ plot..............................................................................................................................36Figure 13: Poisson distribution...........................................................................................................38Figure 14: Box plots. As we can see the sites population is clearly above the mean values of the rest of our samples.....................................................................................................................................39Figure 15: Densities of viewshed sizes of archaeological sites in the constrained area. Theoretical normal distribution in red...................................................................................................................40Figure 16: Frequencies of sites...........................................................................................................41Figure 17: QQ plot Area 2..................................................................................................................42Figure 18: QQ plot of sites in Area 2.................................................................................................42Figure 19: Poison distribution Area 2.................................................................................................43Figure 20: Box plot Area 2.................................................................................................................44Figure 21: Full Weighted Network and areas mentioned in Chapter 2 for the non-parametric analysis to show them in comparison with the whole universe of data..............................................48Figure 22: How the values are calculated and the ranks are assigned. Note that depending on the rank, we can “filter” the network to represent it in terms of the accumulated costs, therefore, the lower the rank the lower the accumulated costs and then a better representation of the best hypothetical network according to the nearest neighbouring links....................................................51Figure 23: Threshold 10000 meters....................................................................................................54Figure 24: Weighted network and edges to circled sites....................................................................57Figure 25: Comparison between networks.........................................................................................58Figure 26: Watershed threshold 10000. If we reduce this value when creating the stream lines we can explore the data at a lower scale..................................................................................................60Figure 27: Stages 1 - 5........................................................................................................................62Figure 28: Stages 6 - 11......................................................................................................................63Figure 29: Closeness centrality...........................................................................................................66Figure 30: Closeness centrality...........................................................................................................66Figure 31: Visualizador de perfiles topograficos. AntropoSIG. ........................................................67Figure 32: Hypothetical Organization of the Triple Alliance altepetl in a upward flow of tribute (redrawn after Lockhart 1992 and Hassig 1985)................................................................................69

Index of TablesTable 1: Archaeological sites selected................................................................................................70Table 2: Geology characteristics of territories after with a k value of 0.0000225.............................99Table 3: Geology characteristics of territories after with a k value of 0.000027...............................99Table 4: Geology characteristics of territories after with a k value of 0.00009...............................100Table 5: Geology characteristics of territories after with a k value of 0.00027...............................100

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Chapter One. Introduction

“Le dije la verdad: que lo mejor era que estudiara una carrera universitaria y que la terminara, porque acá (y allá, y en todos lados)

la gente de honor termina lo que comienza; que mientras no dejara de luchar ahí, en su tierra, con los suyos.

[…] Y ahora que la releo antes de enviarla, se me ocurre que todo lo que en ella se dice tal vez no venga al caso en lo que estamos

reflexionando sobre ética y política.” (Subcomandante Insurgente Marcos 2011)1

This dissertation is about the relationship between humans with humans and the space they share,

the ways they use to configure the landscape historically. The main goal is to show how, with a

selective mixture of Geographical Information Systems techniques, is possible to try to understand

the complexity of human societies making it simpler, to study this relationship between human and

space based on statistical and spatial techniques.

The study area is La Montaña (The Mountain) of Guerrero, called after the intricate topography that

prevails in the area where the Sierra Madre del Sur mountain range shape a complex system of deep

gorges, constricted valleys and high mountains. In this scenario, during the Post-Classic Period (AD

1300-1500), Tlapa-Tlachinollan was transformed into a complex polity covering an area larger than

4000 sq. km. Almost all the archaeological sites within this area were related in some way under a

complex political system called altepetl, which, at the end of the 15th centure was subjugated by

Mexico-Tenochtitlan, one of the main polities of this system that sometimes is referred as the Aztec

Empire. Literally, altepetl means "the waters, the mountains" and is considered the main political

unit (polity) in central and southern Mexico, the native state. During the 14th and 16th centuries at

least 35 different polities were distributed in La Montaña.

The ultimate goal of this project is to generate new archaeological information of this area, which

not only archaeologically but historically, has been relegated to a marginal position that is leading it

to misery and poverty even when its famous around the world for its rich geology full of precious

metals. The waters, the forests and the mountains are as important as gold or silver for the

inhabitants of this place and certainly we cannot understand the culture separately from the nature.

In this specific case, the landscape, the modified environment.

1 “I told him the truth: that the best thing was for him to finish his degree at the university, because here (and there, and everywhere) people of honor finish what they started; and that he shouldn’t cease to struggle there, in his land, with his people.And now that I’m rereading this before sending it, it occurs to me that maybe nothing in it has anything to do with what we are reflecting on in ethics and politics.” (Translated by El Kilombo Intergaláctico: http://www.elkilombo.org/third-letter-to-don-luis-villoro-in-the-interchange-on-ethics-and-politics/)

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I hope to contribute with this paper to the studies of the region as well as contribute to the

archaeological science with some innovative methodological procedures to understand what we call

in this project spatial social organization.

1. Research questions

The aims of this projects are based on the following questions.

1. To what degree did major routes of communication affect the character of the polities

in the Guerrero Mountain region between 1300 and 1500 AD. I think that based on the

topography as well as the least cost paths that connect the sites it should be possible to

create a network to reconstruct the communication routes that were used by the polities all

over the region so we can understand the way they organised their space.

2. To what degree did the visual affordances of this mountainous region affect the

character of the polities of this period? It is often said that mountains are very important

for most of the Mesoamerican people, not only because they are/were an intrinsic part of the

altepetl but also as a strategic spot to control or protect an area. In this sense based on the

visibility between sites or along the areas where they are located, I think is possible to

observe analyse if the archaeological sites kept a relationship with the visibility; this period

is well known for its agitation due to the expansion of Mexico-Tenochtitlan but also for the

expansion of subordinates polities like Tlapa-Tlachinollan, is expected to find strategic

archaeological sites with a good visibility in order to control the space.

3. To what extent did the control of particular resources affect the size and configuration

of these polities? According to Gerardo Gutierrez, the nature of the Mesoamerican political

organization could provide a framework to comprehend how these polities interacted and

competed in Guerrero. In this sense in a period of agitation (AD 1000-1521) where small

polities fought each other in order to control all over the waters and the mountains, the

complexity of the human actions can be simplified using GIS so we can understand some of

these processes better according to our human simplicity. I will try to model hypothetical

territories to build a catchment area based on the size of the site as recorded in the field, and

the cost of transit from one place to another.

2. Dissertation structure

I start with a historical and geographical synthesis in the Chapter two. I try first to depict the history

of Tlapa-Tlachinollan altepetl, trying to contextualize it in an intricate system of mountains and

valleys called the Balsas river basin as a background. At the end of the Chapter I talk about the

political organization and the altepetl.

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After Chapter Two, the next three chapters are about the techniques that I used to explore some

things about Tlapa-Tlachinollan's altepetl. In general, each chapter is composed by an introduction

to the technique employed as well as in which way was used. Then I try to talk about the technique

itself and the procedures that were made to analyse the data. After the technique is showed there is a

section in Chapter Three and Two about the analysis and are exposed some conclusions.

Chapter Three is about visibility and simulations. The concept of viewshed is explained as well as

brief review about the technique used to analyse the data. Chapter Four is about networks and how

they are used in the project and the concept of closeness centrality is showed. At the end of this

chapter I show a technique to produce a simple network using watershed analysis based on a cost

surface.

Chapter Five is about territoriality and try to explain how the main political units in The Mountain

shared the space or fight for it. The concept of altepetl is taken again in order to produce an abstract

idea about how was structured then, using a computational model, a series of hypothetical

territories were created to delineate the boundaries of this particular type of polity.

At the end of this work a series of general conclusions are drawn in Chapter Six. The conclusions

do not have to be considered as definitive results of this project since during its development several

questions arose and for now, cannot be answer.

2.1. Problems

Many problems made this work difficult and certainly this is not the place to enunciate them.

However, I need to say that due to time pressure and above all, the manipulation, management,

production and analysis of the data, some proposals were left apart. There are some tasks that need

to be done in the future. The wide gamma of possibilities that GIS and Spatial Analysis give you

make you feel with the necessity to try everything in your own project but unfortunately the bast

source of techniques and analysis go beyond our power to manage them; some of the problems in

this dissertation have their roots in this insatiable human desire to want to do everything.

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Chapter Two. Tlapa-Tlachinollan

“Geography in this context is no longer an end in itself but a means to an end. It helps us to rediscover the slow unfolding of structural

realities, to see things in the perspective of the very long term” (Fernand Braudel, 1972)

Let us start with the foundation of Tlachinollan, a relatively small polity settled in one of the valleys

that shape the complicated structure of the mountain range called Sierra Madre del Sur. According

to a series of documents found in a small town called Azoyú near to the Pacific Coast in the

Mexican State of Guerrero, Tlachinollan was founded by lords Death-Sun?2 and Ten Deer

in the year 3 Ollin of the Tlapanec Calendar, that is AD 1299-1300.

The valley mentioned above was named after the small village of Tlapa, which became important

years later since an Aztec calpixque (tribute collector) was settled there after AD 1461. Due to the

economic importance of Tlapa as an administrative center, not only the valley but the main river

that irrigates the lands of the whole basin and also the modern town settled on top of the ancient

ruins of Tlapa-Tlachinollan as unified entity, are named after what was once a small village.

During the Post-Classic Period (ca. AD 1300-1500) Tlapa-Tlachinollan was transformed into a

complex polity (altepetl3) that had power over other polities (altepeme plural of altepetl4). Almost

all the archaeological sites within its area of influence are related in some way due to the nature of

this native state. The area of influence is understood as the area where Tlapa-Tlachinollan claimed

to have controlled in a tributary based system where “expansive Mesoamerican polities forced

subject polities to pay tribute” (Gutierrez 2002: 307), being Mexico-Tenochtitlan the core of the

system, the main altepetl, with tributary provinces like Tlapa-Tlachinollan which, at the same time

spread its power over the Sierra and dominated at least eight altepeme and several villages.

2 The symbol “sun” probably was painted later to hide the symbol “death”3 See the section Altepetl: Spatial Social Organization4 According to the Nahuatl Dictionary by Wired Humanities Projects, University of Oregon (2011), this form appears

in the Techialoyan manuscript of Ocoyacac, nonetheless, Lockhart says that Altepetl shows no plural in Nahuatl since it is an inanimate noun (Lockhart, 1992:478).

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Figure 1: Study Area

To have a general idea about how this altepetl used to work, we have to consider the its complexity

in historical and organization terms as well as the area that belong to it. Since it is not possible here

to talk about it extensively but only as an overview, not least because we pursue a different

approach and interests, I will try to characterise the study area in geographical terms in a few words

and then summarise the main events related to the polity following the sequence proposed by

Gerardo Gutierrez Mendoza (2002)5, which will help us to have a better idea of what was happening

during those years.

1. Its waters and hills: The environment

All the sites that were used to perform the analysis -except those utilized to develop the hypothetical

transport network- are within the limits of the Tlapaneco River basin which cover an area of ca.

5000km2 and is part of the Balsas hydrological region. Tlapa-Tlachinollan is settled in the

beginning of the Tlapaneco river which irrigates the fertile valleys of Tlapa and Huamuxtitlan,

where the rivers Coicoyan, Tlaquiltzingo, Igualita and Atentlcuixatl pour their waters to make it one

of the most caudal river that drains the upper Balsas. The Tlapaneco river basin finishes at about 60

kilometers from Tlapa, as the crow flies, between the municipalities of Ixcamilpa in Puebla and

Olinala in Guerrero where converges with the Atoyac river (Figure 1; INEGI 2011a6; Toledo 2003).

During the rain season the river is also feed by secondary streams called jales or xales which

basically are alluvial fans that during the dry season, can be used as roads since the flat sand-bed

surface is easily passable. During the past these streams may also have used since the “road”

-according to Nahuatl writing conventions showing a series of feet- from Tlapa-Tlachinollan to

Cozcatenango (On the Wall of the Jewels) as depicted in Codex Azoyú 1 and 2, is marked with a

silhouette representing a river where small points fall within its boundaries7. It is possible that this

“road” was used by the lords of Tlapa-Tlachinollan when they moved to Cozcatenengo to negotiate

their surrender to the Spanish conquerors (Gutierrez & Medina 2008: 85-86; Gutierrez 2002: 176),

after all, the least cost path as calculated in this dissertation shows that, in order to travel from Tlapa

to Cozcatenango the best route is precisely by the xale, a route that even these days is still used,

where not only persons but cars and animals pass every day.

5 His doctoral dissertation could be considered as the first archaeological study in the area.6 Based on the information provided by the Red Hidrografica escala 1:500007 See Hinojosa Baliño (2009:92-97) for a quick reference about Aztec symbology in mapping.

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The basin -often called depression- of the Balsas river, is located between the Cocos and the

American Plate, in a continental collision coast that makes it a very active earthquake-prone region.

The area includes volcanic rocks like Granite or Rhyolite from the Miocene to the present,

sedimentary and metamorphic rocks such as Gypsum or Siltstone from the Paleozoic, Mesozoic and

Cenozoic periods as well as Limestone mainly from the Cretaceous age, all together exposed in the

mountains (SGM 1998; Toledo 2003; Fisher 1961).

Specifically, the study area is covered by alluvium from the Quaternary along the asymmetric

valleys of Tlapa and Huamuxtitlan whose morphology is related to the depression itself or the

karstic character of La Montaña8 where a series of anticlinoriums and synclinoriums shaped

spectacular configurations (SGM 1998). Also, according to the Servicio Geológico Mexicano, the

complex geological history of the region accounted by mechanisms of brittle and ductile

deformation of rocks could explain the diversity of minerals, for instance, around 43% of the metal

occurrence in the whole area covered by Chilpancingo map9 are polymetalic-epithermal deposits

where 81% constitutes precious metals like gold and silver (SGM 1998), the former, one of the

main goods that Tlapa-Tlachinollan province used to tribute to Mexico-Tenochtitlan as noticed by

Codex Mendoza (Berdan & Anawalt 1992; 1997: 86).

Framed by two main features, the Balsas depression is characterised on the one hand by an oceanic

trench called Middle American Trench including the Acapulco and the Petacalco Trenches and, on

the other hand, two continental mountain ranges, the Trans-Mexican Volcanic Belt and La Sierra

Madre del Sur. In general all these mountains are higher than 1000 meters above the sea level and

certainly close to the coast. Steep slopes and deep canyons characterise the whole area and play an

important role in the erosive processes that model the hills, the planes and the valleys (Toledo 2003;

Fisher 1961).

Nonetheless, the area of this altepetl is connected to the coast and not precisely because it is

possible to follow the river until its river mouth, which by the way is a little bit far from the

Tlapaneco valley. According to Gutierrez the patterns of rainfall and air temperature,

geomorphology features and certainly the geology of the Balsas depression that I mentioned

briefly, create a mosaic of different ecological tiers that can be found from/and within the limits of

8 For a comprehensive definition of La Montaña see Gutierrez 2002: Chapter 29 Chilpancingo map (INEGI E14-8), scale 1:250000. Central region of the mexican state of Guerrero between paralels

17º and 18º N and meridians 98º and 100º W.

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Tlapa-Tlachinollan's altepetl to the immediate south coast in the Pacific ocean, La Costa Chica10.

Eventually, since the environment is so dynamic and variable, different types of soils and vegetation

spread all over the surface. In geopolitical terms, different altepeme competed to control trade

corridors from/to the Costa Chica to/from La Montaña in order to have access to these resources

(2002:30).

Is not a coincidence, taking this into account, that this coast is one of the twenty areas with more

biological productivity in the world, and by its fish diversity, just the second. This, due to the fact

that the region is between the tropics, as well as in the middle of two rich biota provinces

(Californian and Panamic) but also because of seasonal deep water intrusions through the

submarine canyon of the Petacalco Trench where chemical and physical events between the months

of April and May, bring every year chemical nutrients (nitrogen and phosphorus) good for

phytoplankton and for water fertilisation (Toledo 2003:55).

2. Its expansion: The human variable

According to the information available, after its foundation11 Tlachinollan played a pacific role

maintaining its formative extension during the first years. Its expansion starts possibly with the

pacific annexation of some towns in the immediate surrounding area and then, with more power and

an aggressive strategy, started to conquer another polities. In the year 1349 Tototepec was

conquered and two years later Teteltipa starts to be besieged and subjected.

The destiny of this Tlachinollan is uncertain the next years and apparently suffered of distress due

to a series of succesions of governors that fought for the power. The story became clearer by the end

of the 14th century; Lord Lizard, who is depicted in the Codex Azoyu 1, was trying to get the power

of Tlachinollan which, by dynastic rules, belonged to 3 Monkey. Nonetheless, the former got the

power and the later was vanished from the records. Then, is possible that political and social

pressure fell on Lizard who appears conquering several places. From now on, Tlachinollan started

to expand quickly and ferociously. In seven years of expansion between 1412 and 1418, were

conquered and/or attached to Tlachinollan, Tlazallan, Ocoapan and Huiltepec (Gutierrez 2002: 184-

188).

10 For a comprehensive definition of the Costa Chica see Gutierrez 2002: Chapter 211 According to Gutierrez there are two missing pages in the Codex Azoyu 1 and probably the year of foundation could

be wrong: “To be honest, there is no sure basis to claim that this was the year in which the polity was actually or mythically founded. Indeed when one examines the reverse side of the codex, it is easy to realize that the folio 1 was not actually the first page of the codex. What is found is a late Colonial scene on the reverse side that is incomplete because some pages were ripped off. This means that at least two pages at the beginning of the codex are missing.” (2002: 169).

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Figure 2: 1426-1432 expansion.

Lord Calandra Lark-Arrow took the power after Lizard and kept the expansionist policy. During the

years 1426 and 1432, Yoso None, Tlaxco And Atlixtac were conquered, and the last helped to

reinforce the frontier from the growing Nahuatl pressure from the northwest (Figure 2).

Tlazallan revolted between 1433-1439 but was reconquered by Lord Flag-Eagle-Fire, however, in

1439 Mexico-Tenochtitlan, the growing altepetl in the Basin of Mexico which became the core of

the Aztec empire, defeated Azcapotzalco and started incursions into Guerrero. Only 2 years later,

the province of Tepecuacuilco was subjected as well as all of the northern Guerrero between 1441

and 1468, although, according to folio 20 of Codex Azoyú 1, Tlachinollan was able to defeat Aztec

forces and its encroachment over the area (Gutierrez 2002: 191-192; Hodge 1984: 109-110;

Oettinger & Horcasitas 1982:21; Litvak 1971; 67-70).

Between 1440 and 1446, Totomixtlahuaca and Fields of Cacao (Cacahuamilpa?) were conquered by

Tlachinollan without a fight but probably as a by-product of blood linkages12. Notwithstanding

Aztec incursions in the area and raids over Tlachinollan are depicted in Codex Azoyú 2 with a

“temple” in flames, Tlachinollan's answer was the consolidation of the northern territory after Lord

Calandra Lark-Arrow attacked Petlacala13 and Axoxuca-Oztocingo. These places were starting to be

occupied by Nahuatl settlers that before the raid were at certain point accepted but after these events

at least 15 settlements were supposedly conquered by Tlachinollan between 1447 and 1453 which

significantly changed its policy with them (Figure 3; Gutierrez 2002: 194).

12 For instance, Lord Deer-Antler's mother was related to the ruling family of Totomixtlahuaca and the former -ruler of Tlachinollan- is depicted in folio 21 of Codex Azoyú 1 sitting over this place.

13 This place is an interesting one. Referred as “In the House of the Woven Straw Boxes” (Gutierrez 2002: 174) or “Place of the Mat Houses” (Oettinger & Horcasitas 1982:7) the physical location of this place as an archaeological site it has not been found although there are evidence of some remains below the modern town of Petlacala. What is interesting is that according to some sources, Petlacala could refer to “a house where the tribute is stored” (Thelma Sullivan personal communication with Oettinger & Horcasitas 1982:21) and according to Berdan (1992:Vol. I 64) and Berdan & Anawalt (1992: Vol. II 229) petlacalco may refer to a building to store the food or certainly a place related to the calpixque and the petlacalcatl or head overseer of the storehouse. Since the archaeological evidence of a place called Petlacala lead us to a small town probably what it was attacked during this period was an Aztec storehouse settled in the north frontier of Tlachinollan's altepetl.

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Calandra Lark-Arrow died and his son, Rain (Quiahuitl), succeeded him the day 14 Deer and

apparently was negotiated an agreement that on the one hand stopped the advance of Nahuatl

settlements but on the other hand generated a tense frontier between both polities (Nahua and

Tlapaneca [Yopes]14) along the Zizintla river. In ca. 1461 was celebrated a meeting between the

Aztec embassador Bee and Lord Rain where the later was given the title of huitznahuatl, a position

that converted Tlachinollan in a client state of Tenochtitlan and Rain into an official of the whole

region that in a sense ended with the tension though.

Treason against his own polity or not, this event was considered as such by powerful polities of

Cuitlapan and Yoallan. It is possible that these altepeme tried to kill Lord Rain since Codex Azoyu 2

recorded an event where he was attacked in Huilotepec, a town attached to Tlachinollan almost 50

years before by a marriage alliance in times of Lord Lizard. After the attack some polities formed a

coalition against Tlachinollan and allied to Yoallan whereas some others support Tlachinollan's

cause. Interestingly, Gutierrez (2002: 202-204) noticed that while Yoallan-Cuitlapan's band were

constituted mainly by Mixtec-Tlapanec polities, Tlachinollan's coallition was formed by Nahuatl-

Tlapanec, possibly indicating the transformation of this altepetl into an Aztec province (indicating

subjugation) not only a client.

14 See Gutierrez (2002: 98-105) and Nigel (1967: 135-151) about the Yopitzinco province and the relation with Tlapanecs.

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Figure 3: 1447-1453 expansion

As a result of this confrontation during the years AD 1462-1482, Lord Chalchihuitl (Jewel Bead) of

Yoallan was killed along with 12 Eagle and “Cradle” -possibly his son and daughter-15 after the

warrior Bird captured him. The battle, that took place near to Atlamajalcingo del Monte, led the

destiny of the region at least until the Spanish conquest (Gutierrez 2002: 21, 198-203).

With this victory in his hands Rain was able to perform diplomatic agreements with Cuitlapan

through his wife Coacuey (Skirt of Serpents) who agreed the peace with Lord Fish-Feathers, from

the Tlahuiscalera lineage, which was linked to Tlachinollan since 1412 when Lady 4 House,

probably the daughter of the Lord of Tlahuiscalera, married Lord Lizard. With this “agreement”

Lady Coacuey made Cuitlapan, Huitzapula, Acatepec and Texmelincan to surrender to Tlachinollan.

After Lord Rain's death in 1477 (11 Ehecatl) a violent succession took place in Tlachinollan. During

the process Lord Monkey (Rain's brother?) was killed, perhaps by Rain's son, Xihuacoatl

(Turquoise Serpent), who spent most of the time trying to maintain his position as leader of

Tlachinollan while losing it as huitznahuatl, a position that almost costed the life of his father.

During this period Atlamaxac and Ichcateopan were conquered, although, Atlamaxac, according to

Gutierrez, had a position similar to Texcoco to Tenochtitlan, where due to the distance between

Tlachinollan and Atlamaxac16 and the way the spatial social organization of these polities used to

work as well as their historical relation, instead of getting more control over the area caused internal

problems (2002: 207).

Certainly, Xihuacoatl is not going to be remembered as a great governor, instead, as a ruler that put

in danger the region so much that finally under the leadership of Ahuizotl in 1486, ruler of Mexico-

Tenochtitlan17, the Aztecs decided to finish the relative independence of this polity that finally

ended up paying formal tribute (Gutierrez, Konig & Brito 2009; Gutierrez 2002:207-209). After

Xihuacoatl's death, in 1498, Lord Green Corn, the new tlatoani of the newly created province and

altepetl of Tlapa (Tlapa-Tlachinollan)18 took the power of the polity until its last days as a native

state. Along with the Aztecs, Green Corn conquered Alcozauca and the fortress of Tenanco

(Hueycatenango) (Figure 4).

15 12 Eagle, according to Codex Azoyú 2, and Cradle, a children younger than 3 years according to a similar glyph in Codex Mendoza (Gutierrez 2002: 203)

16 Less than 2 hours walking according to the Network and the Cost Surface map.17 The main altepetl of the Triple Alliance, the core and political power of the Aztec empire (Hodge 1984: Chapter 2).18 See Gutierrez & Medina (2008:23-25) about Tlapa or Tlappan toponym as depicted in the Codex Mendoza.

19

3. Altepetl: Spatial Social Organization

In order to understand the landscape, that is, the modified environment, I consider certain variables

that together construct what Manuel Castells called the spatial social organization (1980). In

general, the landscape according to this is determined by: 1) economic, political-juridical and

ideological instances; 2) by the combination of the three of them; 3) by the persistence of spatial

ecological forms, raised by previous social structures and 4) by the differential action of the

individuals and the social groups over their framework.

Therefore, Castells (1971) suggests to establish the difference among the spatial forms in

accordance to their diversity and taking in consideration the different ways a urban society can

constitute itself, defined as a system of values, norms and social relations with a historical

specificity and an organization and transformation logic of their own. In this sense, when I use the

word altepetl I will talk about a specific spatial form of a particular type of social formation with an

specific cultural system, where exists something that we can call urban culture, defined as a matrix,

conscious and unconscious, that gives meaning to the social behaviour and beliefs, articulated in a

particular form of space occupied by a definite population (Hinojosa Baliño 2009; Castells 1971

and 1980; Varela 2005).

The altepetl, sometimes called the native state, literally means "the waters, the mountains" (from

Nahuatl “in atl, in tepetl”) and is considered the main political and administrative unit in central and

southern Mexico. Although firstly refers to a territory its meaning refers to an “organization of

people holding sway over a given territory” (Lockhart, 1992: 14). In general terms it was

constituted by a royal household or (calpolli) and the corresponding land or territory (altepetlalli,

communal lands of the entire city-state) and people (altepeua, inhabitant of a city, of a country)

recognizing a particular ruler (tlatoani) that lived in altepeyolotl, in the heart of the altepetl; once

established, an altepetl would have had a main temple which is considered a symbol of sovereignty,

as well as a market. (Lockhart, 1992; Hirth, 2003; Gutierrez, 2002; 2003; Smith 2008; Hinojosa

Baliño 2009).

Due to its nature, when one of these polities spread its size and influence over others, the altepetl

could be considered a big conglomerate of smaller and autonomous units, that under the influence

and power of the main one, shared political duties and benefits.

20

“The Nahua manner of creating larger constructs, whether in politics, society, economy,

or art, tended to place emphasis on a series of relatively equal, relatively separate and

self-contained constituent parts of the whole, the unity of which consisted in the

symmetrical numerical arrangement of the parts, their identical relationship to a

common reference point, and their orderly, cyclical rotation.” (Lockhart 1992: 15)

The expansion of Tlapa-Tlachinollan, as explained by Gutierrez, consisted of annexation of other

altepeme within its sphere of command, nevertheless, instead of control the whole territory, the

leaders of Tlapa-Tlachinollan were more interested in controlling the labour and specific resources

of the region (2002:13). By the end of the 15th historical century and after Tlapa-Tlachinollan

altepetl fell to Aztec military the region became an important tributary province where around 20

villages were linked to Tlapa-Tlachinollan without intermediaries and at least eight other

independent polities with their own independent villages were also subjugated to Tlapa-

Tlachinollan (Gutierrez 2004: 96, 106; Berdan & Rieff Anawalt 1997: 85).

21

22

Figure 4: Depiction of province at the end of the 15th century.

Chapter Three. Viewshed analysis, cumulative viewsheds and Monte Carlo simulations.

“returning from the mountains, 'no matter who his companion might be,' stated Giuliano Stefanut, 'he usually turn the conversation to matters concerning God, and always introduces some sort of heresy. And then he argues and shouts in defense of

his opinion.'” (Ginzburg 1992: 2-3)

Most of us have grown so blase about computer developments and capabilities […] that it is difficult to believe or imagine there was a time when we suffered the noisy,

painstakingly slow, electromechanical devices that chomped away on punched cards. Their saving grace was that they continued working around the clock, except for

maintenance and occasional repair […]. But these machines helped enormously with the routine, relatively simple calculations that led to Hiroshima (Metropolis 1987).

Several critiques related to visibility analyses have marked the story of its development (Mark &

Woodman 2003). Unfortunately and fortunately, the past is an entity hard to understand and

certainly all the critiques must be welcomed due to their potential impact on research. However, one

of the most famous phrases in the world, “let him that is without sin among you first cast the stone

at her” (1890 Darby Bible, John 7:53), rumble in our days strongly. Nobody can call him/her self a

sinner, neither bad nor good, when we talk about science, so these words should be rephrased in

academic terms: “let him that is able to explain the past in its full complexity first cast the

critiques”. Analyse the tools that we use and test them in order to see their potential utility is good,

not least because the researchers tend to be constructive in their critiques but also because one can

see the wobbly legs of the Leviathan19 that we are trying to build.

One part of the critique goes directly to the methodological problems that come along to the use of

some techniques used to perform analysis. As referred by Lake & Woodman (2003) following to

Wheatley and Gillings, these problems are procedural -GIS specific- and pragmatic - GIS and non-

GIS visibility studies-. The other part put in doubt its application due to a postpositivist growth in

the archaeological thought (Lake & Woodman 2003).

In general, the issues that are related to visibility analysis are summarized by Conolly & Lake as 1)

computational: the ability of the software to perform certain tasks in order to calculate the

intervisibility; 2) experimental: where not only the ability of the user but also the mixture of

dependant variables used as well as computational process play an important role; 3) substantive:

19 See Vazquez de Leon (2003) to have a brief review of this Leviathan in Mexico.

23

determined by those parameters that most of the time are independent of the computational

processes parameters, for instance the acuity of vision of the observer or even the size of it, leading

us to the experimental problems and; 4) theoretical: including ontological, epistemological,

methodological, and ethical aspects (Conolly & Lake 2006: 228-233; Lake & Woodman 2003:693-

694).

Regardless these issues, the fact is that visibility analysis are somehow popular as we can noticed in

the extensive list of references over the journals, where we can find works like Matthew Fitzjohn's

one, who tried to see the way people construct images of the space using the photo elicitation

approach (see Harper 2002) and the GIS, which basically is used to show polygons representing the

panorama in the photographs (Fitzjohn 2007), but also complicated models using Open Source

Software like GRASS GIS to literally “tailor” a program to the needs of archaeologists that

produces Cumulative Viewsheds (Lake et al 1998).

Nevertheless, I think the main issue could be related to the fact that even in this age of information

most of the archaeologist tend to use the tools in a fashionable way instead of actually comprehend

what a map is and what a map is for, or even the use of a map or more precisely a geographical

information system.

As was pointed out by Lake, Woodman & Mithen, archaeologists and, I would say, social

researchers in general, what are actually doing is to let the program dictate the questions they ask

and how they answer them, software that most of the time -if not always- was designed with non

archaeological purposes (1998:27), moreover, researchers tends to use programs only to

superimpose layers of information and “analyse” them intuitively since new programs allow you to

perform certain analysis without the necessity of actually understand the principles in which the

technology or the analysis relies (Conolly & Lake 2006: 1; Schuurman 2004: 7), and certainly by

osmosis is not the way, even under our actual circumstances :

“What characterizes the current technological revolution is not the centrality of

knowledge and information, but the application of such knowledge and information to

knowledge generation and information processing/communication devices, in a

cumulative feedback loop between innovation and the uses of innovation. […] As a

result, diffusion of technology endlessly amplifies the power of technology, as it becomes

appropriated and redefined by its users” (Castells 2010: 31)

24

1. Viewsheds. Did the visual affordances of this mountainous region affect the character of the polities?

A viewshed or view area, is defined as the total number of cells in a raster map that can be seen

from a particular location that is, the terrain visible from a single point (viewpoint) or from multiple

observer viewpoints (Figure 7; Conolly & Lake 2006:226-228; Lake & Woodman 2000; Lake,

Woodman & Mithen 1998; Travis et al, 1975; Amidon & Elsner 1968). In this study, were

calculated the viewshed sizes of several sites in two relatively small areas within the total extent of

the study area, using the GRASS module r.cva20, in order to perform a non-parametric test to

evaluate whether the sites are in a privileged visibility position or not. The module was run without

the -f flag where each viewpoint are transformed into raster cells marked with the number of cells in

its viewshed, where “the only cells that contain genuine data in the output map are the viewpoints”

(r.cva 2001).

To analyse the values of the archaeological sites and test their specificity in comparison with the

average viewshed size of the background environment, we need to compare them with another

population of sites. To this purpose were created 20 random samples per area analysed, each

composed with the same number of random points as the total amount of sites involved within the

boundaries of each area.

The method was proposed by Lake & Wooden to reduce the uncertainty generated due to the fact

that intuitively low probability of a relatively small number of sampled viewpoints would provide

representative information about a big background population. Hence, a possible solution would be

"to draw more than on sample in order to build up an envelope" that describe the background

population more appropriate (Lake & Woodman 2000: 498). Since conceptually, the method falls

under the general principles of 'Monte Carlo method' (Metropolis & Ulam 1949)21, instead of

generating "n" number of random samples to test their significance, they are referred as simulations

"in terms of simulating the range of site viewshed distributions which are possible under the null

hypothesis" (Lake & Woodman 2000: 499).

20 See Appendix 1 to learn the basics about how to compile r.cva in a Linux based environment and having a full version of GRASS GIS 6.3 or more along with the source code. r.cva was developed by Mark Lake from the Institute of Archaeology, University College London, as part of the MAGICAL software. It needs to be installed separately as an add-on.

21 "the process is a combination of stochastic and deterministic flows. In more technical terms, it consists of repeated application of matrices -like in Markoff chains- and completely specified transformations" (Metropolis & Ulam 1949)

25

The basic idea of this test resides in the fact that we can estimate the correspondence between a

random sample of individuals with real population parameters, examining the distribution of values

across the samples (random and real) using an statistical measure. This non-parametric test

considers a spatial variable (viewsheds) that, nontheless, does not rely on the spatial distribution of

the variables or an understanding of the shape of the population (Conolly & Lake 2006).

The underlying power of Monte Carlo simulation resides in reducing the uncertainty related to this

basic question: How can we know if a specific random sample is representative of the background

population? To tackle this problem, what we can do is precisely compare one real population of

sites with “n” number of random populations (Lake & Woodman 2000):

“If the site viewshed distribution falls outside the envelope then this provides

string qualitative evidense that the sites wer not randomly located with respect

to viewshed size. If the site viewshed distribution falls partially or completely

within the envelope then a quantitative assessment will be required.” (Lake &

Woodman 2000: 498)

26

Figure 5: A viewshed generated with VIEWIT on a UNIVAC 1108 computer in 1968 (Amidon & Elsner 1968)

In the case of this study, I am trying to characterise the altepetl of Tlapa-Tlachinollan in

geographical terms according to 1) the distances between the sites using the least-cost of travelling

from one place to another, 2) generating hypothetical territories considering the relative influence of

the archaeological sites based on their area as recorded in the field, an anisotropic cost surface and

the employment of the XTENT formula22 and 4) considering that the sites are located, in general, in

areas with good visibility due to the political problems shown in Chapter 2. In the following lines I

will describe how a non-parametric analysis was applied to explore whether the viewshed sizes

played an important role in the location of the ancient sites or not, using the Monte Carlo approach.

2. The simulations

The Area 1 shown in Figure 6 was chosen trying to group the sites that are closer to the valleys

where the majority of the sites fall. The sites that are far from this area where excluded mainly

because the topography is not mountainous and the core area is in La Montaña whereas the

excluded sites are mainly in the Costa Chica region or according to the Network Analysis (Chapter

3) are not well connected, so the viewshed sizes may vary significantly. This area consists in 217

archaeological sites and as we can see in the map most of them fall in the valleys.

22 In order to compare the relation between the network paths and the territories and as an alternative approach for future research.

27

28

Figure 6: Area 1

The Area 2 shown in Figure 5 was chosen to test the significance of the results in Area 1. This area

is based on the land form “Canyon” that shape the river valleys around Tlapa-Tlachinollan and

consists in 137 archaeological sites that fall within the boundaries of the canyon. Is expected to find

larger viewshed sizes in he samples since the viewsheds fall in the valleys and should have similar

characteristics as the actual archaeological sites. Also, is expected to find larger viewshed values in

the valleys due to its flatness. In general, several number of sites within them have large viewshed

sizes; from 134 sites, 73 are above the mean (29502.01). If we consider the lower hinge of the Box

Plot shown in Figure 9, whose box represent 50% of the sites, then 108 sites fall within this

boundaries and all of them have values of more than 16 000 cells. Now, if 160 sites in Area 1 have a

viewshed size above 16 000 and 67.5% of these sites are in the Canyon, we should constrain the

area of analysis in order to have a better representation of our background population in this area

(that concentrating this quantity of sites, could bias our results), due to the shared characteristics in

geographical terms.

29

Figure 7: Box plot (ESRI 2009)

30

Figure 8: Exploratory analysis

31

Figure 9. Area 2

2.1. How to perform viewsheds of more than 5000 viewpoints!

In order to generate the simulations was created a script in Python that guides the user through a

series of steps to automate the process (Appendix 2). The script will work automatically using the

following parameters in r.cva, although, eventually these values can be changed:

r.cva

option Default value Description

'o' Overwrite the output raster map if it already exists.

Input USER INPUT, string

output USER INPUT, string

sites USER INPUT, string

obs_elev '1.7' Height of the observer (in metres) above the elevation of the

viewpoint

target_elev '0.0' Height of the object of interest (in metres) above the elevation

of the target cell

max_dist USER INPUT, numeric Maximum distance (in metres) from the viewing point within

which the line-of-sight analysis will be performed. Options: 0-

99999 (stated in map units). Default: 100

seed '1' # not used The seed for the random number generator used during random

sampling. This option allows exact reproduction of a previous

result. Options: 0-32767. Default: 1

sample '10.0', The sampling frequency as a percentage of the number of map

cells in the current region. Options: 0.0-100.0. Default: 10.0

type 'sites' The type of sampling regime used to select viewpoints for

analysis. Options: `all', `systematic', `random', `sites'.

curvc '0.0' Earth curvature factor

It has to be considered four things. For the USER INPUT options:

1) Raster to calculate random points: The script use a raster map to calculate the random points

with r.random. This way we can assign NULL values to the raster where we do not want

random points (e.g. constrained areas, islands). Ideally, the extent of the raster used to

produce the random points should consider the radius of the maximum viewing distance to

avoid the edge effect. “When the distance between a given viewpoint and the edge of the

map region is less than that radius it follows that the viewshed may be artificially truncated,

thus invalidating comparison with the viewsheds of other viewpoints that were further from

the edge of the map" (Conolly & Lake, 229).

32

2) Raster used to perform the Viewshed: In this case we need to specify a Digital Elevation

Model so r.cva can calculate the values. The extent of this raster should consider a buffer

zone of the same width as the maximum viewing distance (Conolly & Lake, 229)

3) While the number of samples depend on the degree of confidence that we want to have,

there is no way to calculate how many samples we need to obtain a specific degree of

confidence due to the stochastic nature of random samples, however,. Lake & Woodman

suggest an average of 25 samples to generate “reasonable accurate information about the

background population” (2000: 499).

The p-value (p) or degree of confidence is the probability of an observed result in a

statistical test, the significance of this result will determine “whether the Null Hypothesis is

accepted or rejected” (Fletcher & Lock 1991: 61; Illian et al 2008: 481; Drennan 1996: 154).

According to some archaeologists there are conventions to take this decision. The

significance level is the “probability level at which a null hypothesis is rejected in favour of

the alternate hypothesis in a statistical test, and denoted either by α or p” (Conolly and Lake

2006). The convention says that if p < 0.05 (5%) we have to reject H0, otherwise H1 is

accepted, and, if we decide to accept or reject whichever of both hypothesis, against the

results, probably in favour of our thoughts, is often said that is produced an error I, when H0

is accepted, or error II when H1 is accepted (Conolly and Lake 2006).

4) The number of random points to be generated has to be the same as the real population.

5) The maximum viewing distance has to be chosen carafully according to the research

questions and taking into account the acuity of vision, the contrast, the curvature of the

Earth and sensitivity related to the subtle and massive changes, changing the observer height

(Conolly & Lake 2006:230 233).

After the creation of the Random Samples we can analyse the data with R Statistical Package

following the procedures described in Appendix 3.

33

3. Analysis

3.1. First test

To analyse the analysis is useful to explore the data generating a histogram (Figure 10) of densities

and frequencies (Figure 11). This way we can see the general behaviour of our sites. We start with

the distribution of sites shown in Figure 6, Area 1. In general terms it can be considered as a

Symmetric, Non-Normal, Short-Tailed like distribution according to the definition found in

NIST/SEMATECH (2010: Histogram). From left to right, it is possible to distinguish that most of

the sites fall between 0 and 50000 cells. Nonetheless, between 25000 and 35000 approximately we

can see a reduction of sites within this range and then suddenly there is an increment of values

around 40000 that finally starts to decrease steadily until 60000 where finally the distribution

finished and beyond this point there are only isolated values, called outliers, that are far from the

distribution and have larger values than the rest. We can see that the non-straight line of the

Quantile-Quantile (QQ) plot (Figure 12) confirms that our distribution is not normal since the QQ

plot works with a normal distribution (imaginary or drawn as reference) from the left bottom to the

right top corner of the graph, where “the greater the departure from this reference line, the greater

the evidence for the conclusion that the two data sets have come from populations with different

distributions” (NIST/SEMATECH 2010: QQ plot). In this case, one of these distributions is the

normal distribution (straight line) and the other is our data.

34

Figure 10: Densities. Theoretical normal distribution in red.

35

Figure 12: QQ plot

Figure 11: Frequencies

We expected to find non-normal distribution since at least from a science/engineering point of view,

that distribution occurs most often in nature (NIST/SEMATECH 2010: Histogram). In terms of

probability, if our sites where located randomly is expected to find a normal distribution of data.

In the case of the samples of Area 1, we compared 20 samples of 217 sites using an accumulated

poison distribution created in R with the function ecdf (empirical cumulative distribution function;

Figure 13; NIST/SEMATECH 2010: Poisson Distribution; Bevan & Conolly 2009: 957) and a

series of Box-plots (Figure 14), generated after calculating the mean values of both, the samples and

the viesheds of the archaeological sites. In general, we can see –from left to right– that the red line

representing our sites goes in another direction from the beginning until 5e+04=50000 cells, that

can be interpreted as follows: While the majority of random points that are contained in the

envelope go from 0 to ca. 30000 cells with lower values in general, our sites go from 0 to an

average of around 5e+04 showing a tendency to remain stable around 4e+04=40000.

After ordering the mean values as Lake and Woodman suggest (2000) our sites' mean was ranked

first, which mean that 1/20=0.05, indicating that we have 95% of confidence to reject Ho (The sites

are distributed randomly), and in terms of the convention we are just fine. With this test, “the

distribution of values of some statistic (such as the sample mean [like in our case]) can then be

examined in order to obtain a better estimate of the population mean” (Conolly and Lake 2006:

303). As we can see, with this samples and this site population, we can say that people around

Tlapa-Tlachinollan's altepetl were choosing good visibility locations to settle down their polities.

36

37

Figure 13: Poisson distribution

38

Figure 14: Box plots. As we can see the sites population is clearly above the mean values of the rest of our samples.

3.2. Second test

As we explained before, we needed to constrain the area of analysis since there is not way to think

that our data is not biased due to the fact that most of the sites in the analysis of Area 1.

Surprisingly, the results of Figure 9 Area 2 are quite similar, although the distributions of our data

are different (Figure 15; Figure 16).

39

Figure 15: Densities of viewshed sizes of archaeological sites in the constrained area. Theoretical normal distribution in red.

The distribution looks a little bit normal. In general there are no outliers and most of the viewshed

values are distributed normally since there is no abrupt variations in our distribution. Based on the

fact that there is no evident variation, we can actually expect that our values be random (see QQ

plot Figure 18). However, we maintain the idea that the sites are distributed accordingly to the

environment to have the best view possible to prevent an attack, or face it in the best way possible,

or even communicate from one place to another using methods that we do not know.

40

Figure 16: Frequencies of sites

41

Figure 18: QQ plot of sites in Area 2

Figure 17: QQ plot Area 2

After Monte Carlo test we could see that the line representing the sites in Area 2 are closer to the

envelope compared with Figure 13 but still we can see a tendency of the sites to get farther from the

envelope around 4e+04=40000 cells. Since the red line goes almost in opposite direction to the

envelope, we have a strong evidence that even in this constrained Area the sites present a particular

distribution in accordance to the environment in order to have the best visibility.

42

Figure 19: Poison distribution Area 2

The graph is a good way to show that even under similar circumstances of visibility between the

random viewsheds and the archaeological sites, the later present larger viewsheds. Apparently, the

sites are located in specific areas where they can have a good view of the valleys in general. Taking

into account that the region was experimenting great distress due to the expansion of capital polities

this could be related to the fact that, indeed, they are trying to have a visual control along the

valleys. Also, to have visual access to the river flows to the Balsas, and certainly to the natural route

of passage between the north areas (mostly related to Nahuatl people coming into this area) and

iyolloco in altepetl of Tlapa-Tlachinollan, that is, the hearth of the polity, which according to the

network used to connect and still connects the Basin of Mexico and the Valley of Tlapa.

43

Figure 20: Box plot Area 2

Chapter Four: Network: Depicting Tlapa-Tlachinollan through nodes and edges.

Nihuinti, nichoca, nicnotlamatinicmati niquitoa nic elnamiqui:

Maca ic nimiqui,maca ic nipolihui.

¿In can on micohua?¿In can on tepetihua?

Inma ca niauh...Maca ic nimiqui,

maca ic nipolohui.(Cantares Mexicanos, F14 v, 17-20)23

How can we test, know or explore if the roads (routes) that used to communicate the archaeological

sites affected the character of the polities related to Tlapa-Tlachinollan, after all, as far as we know,

there is no evidence of roads in the region. Now, let us suppose that we can actually propose

hypothetical routes using a computational model, in such a case, what do we want to test, to know

or to explore and how can we analyse it? Indeed, we can appeal to formal analysis in order “to

produce falsifiable, repeatable results” (Bevan 2008: 3).

Movement is an intrinsic part of our lives and has been with us from the very beginning of human

history and certainly is one of those things that, regardless the theoretical issues involved in these

words, help and have helped to build the landscape and in a different level, help to order it, to

construct what it was called in Chapter 1, spatial social organization (Trombold 1991; Ortiz 2006;

Gutierrez & Van Rossum 2006; Garcia 2006; Fournier 2006; Conolly & Lake 2006; Llobera,

Fabrega-Alvarez & Parcero-Oubina 2011).

In Mesoamerica, the movement itself is considered a fundamental part of life and part of it relies in

the roads that people used to use to go from one place to another; these roads (otli in Nahuatl) were

made with perishable materials, most of them were thin lines along narrow passages through the

mountains and dense forest. Some roads that must have existed, nowadays is practically impossible

to find them, whether they have been covered by natural processes or human activity (Ortiz 2006;

Gutierrez & Van Rossum 2006; Garcia 2006; Fournier 2006; Hirth 1991).

23 I feel drunk, I cry and suffer / when I know, say and remember: / Hopefully I will never die, / hopefully never perish! / Where there is no death? / Where is the victory? / I'd go there ... / Hopefully, I will never die, / hopefully never perish (Translated from spanish by me)

44

According to Ross Hassig “the nature and significance of roads are not given in any analysis”

(1991:17) since these issues are related to the specific approach the researchers take. However, and

besides the fact that there are roads that have been discovered and studied, researchers tend to

analyse them with a historical approach, descriptive or functional (Hassig 1991:17).

Roads add complexity to human relations but roads were not constructed before humans. Although,

as archaeologists we are not interested in the architectural properties of a road or how a road can

improved human mobility, in order to explore the relation between the social phenomena and the

roads -both as an abstract and a physical entity that belongs to the social system- it is worth to

examine this relationship in a wider context.

Considering all this, what we should do to try to understand to what degree did routes of

communication affect the character of the polities related to Tlapa-Tlachinollan's altepetl? In the

next pages I will try to explain a possibility.

1. Network

Based on the topography as well as in the least cost path that connect the sites it was possible to

create a network representing the amount of time in seconds that theoretically is required to travel

from one site to another. I think that, since there is no physical evidence of roads in the area, one

way to hypothetically reconstruct them is by calculating the least cost path between two sites in

order to reconstruct a possible route they could have used, assuming that they were only following

the routes that presented the least cost in terms of energy due to changes in the topography, even

when eventually could have existed several factors that were involved apart from energy costs.

In this specific case, was built an anisotropic model of routes among the sites (network) based on

the least cost path to and from each site in a vector point dataset and then analysed it. This model

was analysed to see how the sites (nodes) are interconnected using the amount of time (cost) that is

required per route (edge or tie) to go from one site to another and then try to understand how the

organised their space based on the archaeological data available for this region that comprehend

sites near to the coast.

45

46

Figure 21: Full Weighted Network and areas mentioned in Chapter 2 for the non-parametric analysis to show them in comparison with the whole universe of data.

In the case of the network that I am using for this analysis the weight of each of the ties is based on

travel times to and from each site recorded using anisotropic cost surfaces. With this information is

possible to develop an analysis of centrality. To understand how this network works it is necessary

to explain some characteristics of it.

Although it is necessary to build the network in a robust geographical framework mainly based in

Euclidean distances, the power of the network relies in its topological aspects. Topology is a branch

of the geometry concerned with those properties of an object that are not related to its spatial

specificity reducing “empirical reality to its bare essentials” (Santley 1991:203; Conolly & Lake

2006; 299). A network is a specific type of graph that is composed by points called vertices or

nodes and connections, called arcs or edges that, integrated in topological relations, can be studied

using graph theory (Conolly & Lake 2006:234-252; Isaksen 2008; Gorenflo & Bell 1991; Santley

1991)..

The analysed network is called weighted, since “the strength of a tie is generally operationalised

into a weight that is attached to the tie, thereby creating a weighted network” (Opsahl 2009: 14). In

this work the weight is going to be used to measure the value of each node according to the weight

of each tie, which results in the identification of the centrality of the nodes. The measure that has

been used is called closeness centrality, defined as the inverse sum of shortest distances (least cost

paths) to all other nodes (to sites) from a focal node (from site)24 where the main limitation is that

all the sites must be connected (Opsahl, Agneessens & Skvoretz 2010; Isaksen 2008) although it

could be very useful identifying the archaeological sites which could reach others quickly.25 To

calculate the closeness centrality as well as other values a series of commands were run in R

Statistical Package using tnet a program developed by Tore Opsahl. Refer to Appendix 4 to see step

by step the procedures.

The strength (weight) of the ties between the nodes could indicate practically any value, due to this

fact is relatively easy generate a subjectively biased network analysis that might invalidate it. In

order to use a precise weight value is worth to retain elements from the research question and

setting since it affects the outcomes of weighted network measures. In this case, an anisotropic

least-cost path between to and from each site recorded based on topography, considers the distances

among them as a dynamic phenomenon related to human mobility across a determinate landscape,

in this case the rough and steep mountain of Guerrero.

24 To and from each site recorded25 The cost surface map created contain cell values representing the minimum accumulation cost in seconds from one

location. It is expected that the higher the values the higher the cost of travelling, therefore, higher closeness values will represent archaeological sites that do not reach other quickly, instead, the lesser the values the better connected the sites.

47

Using the GRASS module r.walk it is possible to measure the lowest cumulative cost of moving

between the user-specified start point(s) through an specific area using a Digital Elevation Model

(DEM) where each cell category values represent elevation. The minimum cumulative costs are

computed using Dijkstra's algorithm (Dijkstra 1954), considering an anisotropic travel time due to

the different walking speed associated with downhill and uphill movements.

Generally speaking, moving downhill is favourable up to a specific slope value and then becomes

adverse. For humans the default slope value threshold (slope factor) is -0.2125, corresponding to

tan(-12), where >5 and <12 degrees corresponds to a moderate downhill and >12 degrees to a steep

downhill.. The default values for a) underfoot condition (a=1/walking_speed), b) underfoot

condition and cost associated to movement uphill, c) underfoot condition and cost associated to

movement moderate downhill and d) underfoot condition and cost associated to movement steep

downhill, are those proposed by Langmuir (0.72, 6.0, 1.9998, -1.9998) based on man walking effort

in standard conditions (Fontanari 2002).

Using the script v.travelnet6426, we can create the network of least-cost paths since is possible to

compute automatically each of the points in our dataset. In general, the script use r.walk cyclically

to perform the action over and over while is tracing the “flow” (the path) with r.drain through the

cumulative cost map and then generates a vector map of the resultant path that is patched to another

vector file containing all the paths that have been generated. Each path has a different cost (weight)

associated and in total, were generated 55932 paths from 237 different points, which means that 237

different ranks were also associated to each path (Figure 22). The rank could be considered as an

ordered and grouped list of values that correspond to the nearest neighbouring links out from each

node.

While we can use the rank to represent the network to generate a visual representation of it,

“filtering” it (See Figure 22),

"archaeologically and historically, we have no reason to assume that three paths

[first 3 nearest neighbouring links] is a valid level of connection in any given

time and place, and a less judgemental approach might be simply to work with

a complete set of connections among sites" (Bevan 2011?)

26 This script was developed by Andrew Bevan from the Institute of Archaeology, University College London who kindly gave me a copy and help me to understand its basic operation.

48

For an uncertain reason, during the data process -that took 8 days-, it was not added the information

of costs in 1416 paths, associated with 6 sites, presenting a value of 0. While for some analysis this

could not be a problem, due the nature of closeness centrality this means that some nodes are not

connected, hence, the analysis cannot be done. Fortunately, there is a workaround developed by

Opsahl, Agneessens & Skvoretz (2010). The problem is that the distance between nodes in

disconnected components of a network is infinite following the original formula:

closeness i=∑ j[d i j]

−1

Where i is the focal node, j is another node in the network, and dij is the shortest distance between

these two nodes. Here, the distances are inversed after they have been summed, and eventually any

49

Figure 22: How the values are calculated and the ranks are assigned. Note that depending on the rank, we can “filter” the network to represent it in terms of the accumulated costs, therefore, the lower the rank the lower the accumulated costs and then a better representation of the best hypothetical network according to the nearest neighbouring links.

From To Value Rank █ Origin █ End

1 2 2 2 Case 1 Case 21 3 1 1 1 1 2 2 1 2 1 21 4 3 3 1 1 1 12 1 2 1 3 2 3 2 22 3 2 2 3 32 4 3 3 4 43 1 1 13 2 2 2

3 4 2 3 Case 3 Case 44 1 3 3 1 2 2 1 24 2 3 2 1 1 3 34 3 2 1 3 1 3 2 2 2

2 1 14 4

From To Value Rank2 1 2 13 1 1 14 3 2 11 3 1 1Accumulated cost 6

1 2 2 23 2 2 22 3 2 24 2 3 2Accumulated cost 9

2 4 3 31 4 3 33 4 2 34 1 3 3Accumulated cost 11

1 2

3

4

1 2

3

4

1 2

3

4

number summed by infinite equals infinite. Nonetheless, since the formula was designed to measure

the sum of inversed distances, according to the authors of tnet, can be rewritten as the inversed of

sum of distances. To exemplify the new formula, the authors says that, for instance, if you try to do

the next operation 1/Inf in R Statistical Package the returned value is zero. In this sense, instead of

having a disconnected network, what we got is closeness values of 0 of those nodes that are

disconnected. The new formula is as follows.

closeness i=∑ j

1

d i j

And, in order to run the new new formula in R, instead of the original one, we need to set to TRUE

the value gconly while running t.net (See Appendix 4).

To sum up, we are trying to calculate the hypothetical least-cost distance between the sites

according to human mobility, specifically in La Montaña during AD 1300-1500 where basically the

people movement was by foot. We are dealing with archaeological sites within a place where two

sites can coexist relatively close each other but due to the orography the linear distances are most of

the time irrelevant. In some sense we are trying to measure the actual distance of travelling by foot

between sites using the least cost path so we can also provide some information related to further

research on trade or communication routes among them.

2. Towards the exploration of significance in network analysis.

According to Andrew Bevan a key issue related to network analysis is the possibility to test the

significance of the results or to test if the network is susceptible to uncertainty (2011?). Statistical

methods to compare two or more populations could be applied to this purpose (Merril & Read 2010;

Conolly & Lake 2006: Chapter 8; Lake & Woodman 2000). Andy Bevan propose some

workarounds in order to modify the original network changing the initial parameters used to create

it or considering the exploration at different scales (Bevan 2011?). He also propose the use of not

observed nodes but hypothetical candidates, something like the generation of simulations alike to

our network (Bevan 2011?).

The basic idea of Bevan's proposal is to generate random hypothetical settlements over a specific

area trying to simulate their location on the basis of a previous study of the actual sites, considering

the position in terms of slope, altitude, and separation between them. The problem with this

50

approach viewed with a Monte Carlo perspective is the amount of time required to perform a

determinate number of simulations to have a good representation of the background population as

described in Chapter 2. For example, if following Lake and Woodman, we generated 25 samples

for a population of 24 individuals, –i.e a total 600 simulations and approximately 360000 paths –,

we would require 52 days to process them27, as well as a huge amount of computational resources.

To tackle this problem we can instead use the random network generator included with tnet and

perform a script to do the process several times. The process takes less than 10 seconds to generate

1 random network based on the actual network. This network can be used to create a benchmark

value to gauge whether the outcome is “high” or “low” (Opsahl et al 2008).

Tnet can generate random networks from a weighted network like the one used here in a function

called Weight Reshuffling:

“The weight reshuffling procedure consists simply in reshuffling the weights

globally in the network. This null model maintains the topology of the observed

network. Therefore, the number of ties originating from a node (degree) does

not change” (Opsahl et al 2008).

The problem now is that the values generated will be related to the same network structure, i.e, will

bear no relation to reality, thus making it impossible to undertake any spatial calculations, such as

modelling or simulating a topology based on slope, altitude, or geographical location.

27 Based on my personal experience, it takes an hour to generate 291.34375 on average.

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Figure 23: Threshold 10000 meters

Now, recently developed, the focal mobility network considers an accumulated cost surface as a

landscape formed by valleys and ridges, where changes in “elevation” represent variations in the

cost surface from a specific origin (Llobera et al 2011). In this model “valleys” are areas that

converge at the origin naturally, since they are the lowest values in our DEM or accumulative cost

surface. The origin is the cell from which the cumulative cost of moving starts incrementing. In a

sense, the system can be compared to an endorheic basin, where the water converges to a single

point inside the basin, known as a sink (Wikipedia contributors 2011). Consequently, all the “river”

basins that feed this drainage basin eventually flow into the sink, which ironically is the flow's

origin in terms of costs (Llobera et al 2011).

3. The “Total Network”, Focal mobility Network and Monte Carlo Approach.

Following this model, a test was generated to see how the network works (Figure 23). To generate

the anisotropic accumulative cost surface were used the GRASS modules r.walk and then it was

used r.watershed to generate the focal mobility network. At first glance the correspondence of this

model with a filtered version of the weighted network is certainly impressive, but what is more

important is that it does not rely on the location of one or more sites but only on the different natural

least-cost paths that are generated from the origin. Several sites are close to these routes or the

routes go directly to them. Its power as a prospection tool to identify possible routes to unknown

sites from a certain origin, where it is possible to define “archaeological basin areas”, is evident.

However, considering that the flow of the network goes directly to one origin, we are assuming that

the network is hierarchical with a dendritic pattern (see Hassig 1991: 19-20) as if we were seeing a

tree from below.

Testing by its authors with simple algorithms within the ArcGIS 9.3 suite, concluded that is a

reliable alternative mechanism to construct a network in order to explore movement, regardless of

the issues that they themselves pointed out. So, following this model, I produced a similar model

where not only one but several origins were used to generate an anisotropic cost surface with

r.walk, in order to explore the resultant network taking into account all the polities in La Montaña

mentioned in codices. I called the model Total Network (Figure 26) since the number of paths is

“infinite” depending on the threshold size of the exterior watershed basin specified in r.watershed

and represent the flow interaction of “n” number of sites. Consequently, we do not want to specify a

very small threshold or build a model with lots of origins, otherwise the paths will be, if not useless,

at least hard to analyse, and the computer may also run out of memory.

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Compared with the network created with v.travelnet64 (Figure 24), there are differences. First of all,

the network built with v.travelnet64 considers the whole universe of sites, and the paths have a

directionality (since the algorithm tries to find the least cost path from one site to another)28 whereas

the focal mobility network depends on the size of the watershed threshold following the natural

flow from one site to the whole universe of cells. Secondly, using v.travelnet64 we generate edges

that are repeated “n” times and overlap each other due to the fact that the network was created using

237 nodes connected by directional edges. On the other hand, the network created using the focal

mobility approach only has 16 nodes or origins from which the flows of the watershed spread all

over the basins. Finally, the Weighted Network is a vector file that has information about the time

spent from one point to the other, whereas the Total Network is a bunch of pixels that need to be

converted into a vector format so we can store information related to the cost of travelling from one

node to another.

At present, further research needs to be done in order to better understand the possibilities of these

three approaches. The ultimate goal of this exercise is to compare the networks visually and in

terms of how much time is required –once the problem of transforming the Total Network into an

actual topological weighted network– to study the significance of our network-based archaeological

data with a Monte Carlo approach and the closeness centrality values.

28 This network can emulate the focal mobility network if we query it displaying only low ranks, so we can have a depiction of a network that uses only the nearest neighbouring links (Figure 25).

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Figure 24: Weighted network and edges to circled sites

Figure 25: Comparison between networks

Whether the problems can be solved in the near future or not, we can spend around 30 minutes to

produce a Total Network of random points, where the process that is going to take more time and

will vary according to the number of nodes is the creation of the accumulated cost surface. After

that the creation of the “streams” it does not take more than 1 minute and in general. Once we find a

proper way to convert the “streams” into a vector format while adding the costs of travelling to each

edge, the time will not take more than 5 minutes with an automatized process. The creation of the

final dataset to perform the network analysis and get the closeness of centrality index it should not

take more than 1 minute. Finally, the significance of our network can be tested in different ways,

but with a non-parametric test as applied to the viewsheds in Chapter 2 which, in this case, does not

take more than 1 minute. Supposing that the whole process can be done in 1 or 2 hours per each

random network, we can generate the same 25 samples mentioned above in only 2 days

approximately. It falls out of the limits of this dissertation to test this method, but can be considered

for other researchers interested in Network Analysis.

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Figure 26: Watershed threshold 10000. If we reduce this value when creating the stream lines we can explore the data at a lower scale.

Analysis

Following the model of expansion proposed by Gutierrez (2002) and adding routes according to the

expansion, choosing the first 8 Nearest Neighbouring links, we can see that the routes that appear

linked to the new attached polity are related with the polities that were attached in a subsequent

phase.

Stage Site 1 Site 2 Site 3

Stage 1 Tototepec (164) Figure 27

Query: ("nrank" <9 AND ("tosite"=24 OR "tosite" = 164) AND NOT "seconds" =0)

Stage 2 Teteltipa (13) Figure 27

Query: ("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13) AND NOT "seconds" =0)

Stage 3 Huilotepec () Tlazallan Ocoapa (38) Figure 27

Query: ("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38) AND NOT "seconds" =0)

Stage 4 Yoso None (163) Atliztac (169) Tlaxco Figure 27

Query: ("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163) AND NOT "seconds" =0)

Stage 5 Totomixtlahuaca (150) Field of Cacao Figure 27

Query: ("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR “tosite”=150) AND NOT "seconds" =0)

Stage 6 Oztotzinco (173) Petlacala (189) Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173) AND NOT "seconds" =0)

Stage 7 Yoallan(165) Cuitlapan (158) Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173) AND NOT "seconds" =0)

Stage 8 Atlamaxac (36) Ixcateopan (30) Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173 OR "tosite" = 178 OR "tosite" = 165 OR "tosite"=36 OR "tosite" = 30 OR "tosite" = 193) AND NOT "seconds" =0)

Stage 9 Atlamajalcingo de Monte (193) Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173 OR "tosite" = 178 OR "tosite" = 165 OR "tosite"=36 OR "tosite" = 30 OR "tosite" = 193) AND NOT "seconds" =0)

Stage 10 Chiepetepec Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173 OR "tosite" = 178 OR "tosite" = 165 OR "tosite"=36 OR "tosite" = 30 OR "tosite" = 193 OR "tosite"=43) AND NOT "seconds" =0)

Stage 11 Alcozauca (43) Figure 28

("nrank" <9 AND ("tosite"=24 OR "tosite" = 164 OR "tosite"=13 OR "tosite" = 38 OR "tosite"=169 OR "tosite"=163 OR "tosite"=150 OR "tosite"=189 OR "tosite"=173 OR "tosite" = 178 OR "tosite" = 165 OR "tosite"=36 OR "tosite" = 30 OR "tosite" = 193 OR "tosite"=43) AND NOT "seconds" =0)

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Figure 27: Stages 1 - 5

61

Figure 28: Stages 6 - 11

Accordign to this we can see that the annexation of Teteltipa was crucial in conquering

Totomixtlahuaca and years later Petlacala. In the same way, Yoso None and Yoallan, were important

to conquest Ocoapa and Atlamajalcingo, which at the same time possibly were important to

conquest the far Totomixtlahuaca and open the route to the coast.

This analysis is mainly visual but even though, we can see a tendency to expand to the south and

related to the proximity of the sites in terms of travelling costs. There are one possibility, though, to

explain this with the fact that to the north of Tlapa the Nahuatl presence constitute itself a definite

factor to stop the expansion to the north. Nevertheless, we can explore another possibility related to

the cost of passage from one place to another where Tlapa is the focal node where two different

areas are divided. We said that closeness centrality is a way to explore which nodes are the best well

connected. After the analysis the results were quite impressive. Needless to say that confirm the

directionality of the expansion shown in the preliminary visual results but indeed, for some reason,

the network have places better connected to the south rather to the north.

The divisions between the classes shown in the histogram accompanying the map with the closeness

centrality values, were chose trying to group the values Figure 30. Interestingly, the lowest values

(best connectivity) are in the Valley of Tlapa, and then then next group of values –before the

dramatic change in the distribution does around “0.52x10-3”– correspond to the the sites to south of

the Valley of Tlapa. To the north of Tlapa we have the next group which basically concentrate the

majority of the population. After 0.57x10-3 the values represent outliers in the distribution and

cannot be considered well connected. If, in fact, the network based on the least cost path is able to

represent the actual expansion of Tlapa, what makes the Valley of Tlapa the border?

In order to answer this question, and only as a mere curiosity, we create an alternate exercise

depicting an aleatory route from the coast to the end of Tlapaneco River trying to draw the

topographical profile of this area. The test was made using the proper API of Google Maps to do

that as implemented in AntropoSIG29 calculating the distances as if we were walking. Despite the

fact the process of generating the least cost path is almost instantaneous, the interesting thing about

it is not the path itself, but the profile the it is generated. It is often say that Tlapa-Tlachinollan is the

hearth of the Mountain, but possibly a better term should be the Gate to the Mountain, and certainly

its location in the beginning of the steep slopes, is proof of that. Possibly, the expansion can be

explained in terms of cost of passage but also in the several social interactions in the Mountain

which apparently, once you there, is quite easy to go everywhere. Also, we normally think about the

29 http://antroposig.ciesas.edu.mx:8080/joom/mapotecadigital/profileanalysis

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heart as a central place, but possibly iyolloco in altepetl make reference to the beginning of the

system. If, in fact, the heart is not considered only as a nuclear place but something related to

something alive, what is flowing through the mountains, irremediably finishes and originates in

Tlapa-Tlachinollan.

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Figure 30: Closeness centrality

Figure 29: Closeness centrality

Figure 31: Visualizador de perfiles topograficos. AntropoSIG.

Chapter Five. Territoriality: Tlapa-Tlachinollan's dependencies and its territories

“To be indigenous in Guerrero is like being African-American in Mississippi 50 years ago. People barely subsist in abject poverty, and

starvation is rampant. Racism has a long, wicked history and a stronghold on the present. Those who dare speak truth to power are threatened, imprisoned, tortured, disappeared, raped, and murdered

with absolute impunity.

[…] When I asked Abel what sustains him, he spoke about the spirit of community that he and his colleagues have learned from the

indigenous people of the mountain who share all they have and live for the benefit of their communities, their rivers, their forests, and

their mountains. The words on the wall of Tlachinollan’s office ring true: “The Mountain will flourish when justice inhabits among the

Me’Phaa, Na Savi, Nauas, Nn’anncue, and Mestizo peoples.” (Kennedy 2011)

In Chapter 1, we talked about the altepetl as a particular form of spatial social organization. In this

chapter I tried to reconstruct the territory of each polity considered “important”, based on its

inclusion in the codices mentioned in the Chapter 1 and accordingly to the area recorded on the

field. The main goal of this is to visually represent the limits of each polity associated to Tlapa-

Tlachinollan as well as to represent how could they compete each other for resources in the border

of each territory. The territories are polygons that represent boundaries in scales of time.

According to Gerardo Gutierrez, the nature of the Mesoamerican political organization could

provide a framework to comprehend how these polities interacted and competed in Guerrero. In this

sense in a period of agitation (AD 1300-1521) where small polities fought each other in order to

control all over the waters and the mountains, the complexity of the human actions can be

simplified using GIS so we can understand some of these processes according to our individual

simplicity.

Native American people did the same thing when they drew the maps that represent their territory,

their political organization (the altepetl), the history or the conflicts among the polities where they

use to live (Hinojosa Balino 2009). Also, at least in Nahuatl and Mixteco, there are references to

something that we can call “city” in modern times but indeed, a different and particular form in

which society organise its space. Terms like ñuu cánu (big place?, could be translated as big

altepetl; Wired Humanities Projects: 2011b) in Mixtec or iyolloco in altepetl in nahuatl (Lockhart

1992; 480 note 22), refer to a place where a palace, a temple and market were built. Lockhart and

66

others (Hirth 2003; Gutierrez 2003) are against the idea of the term city since even when we can

find “a formidable degree of urban nucleation”, there is no names referring to an actual city but only

in a few documents that bear the political life and, the concept itself, “was not really compatible

with the principles of altepetl organization” (1992: 19). Therefore, we cannot talk about Tlapa-

Tlachinollan's altepetl as a city that ruled over the other settlements but as a “high-ranked” –in

Lockhart's words– polity that constituted the larger state, called altepetl itself which in this system

the highest-ranked one was Tenochtitlan or the Triple Alliance (Tenochtitlan-Texcoco-Tlacopan)

and its provinces the next rank (Figure 32).

What is interesting about this model is that according to Lockhart:

“in a complex ethnic state whole altepetl played the same role that calpolli

played in the simple state; in other words, a set altepetl, numerically and if

possible symmetrically arranged, equal and separate, yet ranked in order of

precedence and rotation, constituted the larger state” (1992: 21)

In other words, we can use this model to reconstruct the territories of each unit in the altepetl of

Tlapa-Tlachinollan according to the influence that each tlayacatl and another exercised to each

other. To start, we defined the sites that could have constituted a tlayacatl altepetl. Unfortunately

not all the places that appear in the codices have been found and those that have been found on the

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Figure 32: Hypothetical Organization of the Triple Alliance altepetl in a upward flow of tribute (redrawn after Lockhart 1992 and Hassig 1985)

field have not been dug, but only a few. In this sense, to develop this task I chose those sites that

have been recorded by Gutierrez (2002; 2007; 2008) and whose location and urban characteristics

seem to be correspond to the pre-Hispanic settlement mentioned in codices Mendoza, Azoyu 1 and

2 (Table 1).

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Table 1: Archaeological sites selected

Site Name Ancient Name ID Aarea (m) vsize Area Fixed Rank by CodexHuamuxtitlan-Tecoapa Huamuxtitlan 93 299193.25 40229 0.28 3Xocotla Xocotlan 18 1061221.68 38624 1 4Cualac-Apetlanca Cualac 171 44875.2 38148 0.04 3Ocuapa Ocuapa 38 87976.32 30477 0.08 3Contlalco Tlapa-Tlachinollan 24 849741.55 29094 0.8 3Ollinala Ollinala 170 191699.65 28396 0.18 4Igualita-Yoallan Yoallan 165 308483.47 26254 0.29 3Ixcateopan Ixcateopan 30 272699.66 23909 0.26 2Tenango Tepexi Coxcatenango 155 98505.08 18567 0.09 2Manila Atlamaxac 202 167594.98 15962 0.16 3Texmelincan Cuitlapan 154 568002.01 15066 0.54 3Mexquititlan-Organal (Ahuacatitlan) Ahuacatitla 180 129523.45 14305 0.12 2Huitzapula Huitzapula 160 236591.08 8794 0.22 3Alcozauca Alcozauca 43 214485.88 6550 0.2 3Chiepetlan Oeste Chiepetlan 226 469080.21 6432 0.44 3Petlacala Pueblo Petlacala 189 1198.46 5465 0.0011 3

1. Territories and the XTENT model

The territories of each polity that appears in Codex Mendoza or Codex Azoyu 1 and 2 that used to

pay tribute to Mexico-Tenochtitlan and subordinated to Tlapa-Tlachinollan, were reconstructed in

order to explore the resources that could have fallen within its “boundaries” as well as to reconstruct

the area of influence. This was made according to their sizes in square meters (normalised using the

highest value -Xocotla 1061221.67549m2) as recorded by Gerardo Gutierrez and also using a cost

surface or friction surface generated by GRASS64 module r.walk per site. The area was calculated

using the XTENT formula as proposed by Renfrew and Level in 1979 (alpha α 0.5) where it is

assumed that the influence of a centre is proportional to a function of its size, and declines linearly

with distance,

I = f C – k×d I 0

where I is the strength of influence, C is the centre weight, d is referred as the distance between the

maximum area of influence (x) from an specific centre according to k, which is a constant defined

as “the rapidity with which influence decays with increasing distance” (Bevan 2008:15). On the

other hand the function f(C) is defined as a function of the relative size of a site Cα where α is

another constant used to re-weight site size (Bevan 2008:15; Renfrew & Level 1979: 151). The

coefficients α and k determine the balance between the size and distance, therefore, if k equals 1 and

each centre has a constant weight of 1, the territories are going to compete under the same

circumstances giving as a result a diagram similar to a Voronoi tessellation unless we use a cost

surface map (Ducke 2009).

GRASS add-on “r.xtent”, developed by Benjamin Ducke, making use of the XTENT formula and

cost surfaces maps were used to calculate these territories and/or areas of influence of each site. A

value of 0.00027 was used as the k value for the first level of influence that, as explained in the next

lines, correspond to an area of influence of one hour relative to the largest site. When we reduced

the value of k, we define the area of influence of each centre according to certain values that we

consider important, in this case, the cost of movement in seconds from each centre to another. I

decided to use increments of 1,2,3,5,8,10 and 12 hours, starting with territories with a k value

equivalent of 1 hour of influence around the centre with the largest size since there are evidence in

modern times that a person can spend an average of 1 hour (3600 seconds) travelling about 5 km

(5000 meters) in a daily basis (Bevan 2008:10; Ausubel & Marchetti 2001: 21-22). Basically, if we

want to generate territories within 1 hour of influence relative to the largest site, we need to obtain

the value of k taking into account that d is not a linear distance but an accumulated cost value given

69

in seconds. Let us put as an example Xocotla, which is the largest site, calculating its territory

within 1 hour: C=1 (1061221.67549/1061221.67549) , d=3600 seconds, k=?

According to Renfrew and Level, “the influence of each centre […] declines linearly with distance

from the centre, reaching zero at the point where f(C) = k*d (1979: 149), in such a case,

k= C/d

k = 1/3600 = 0.00027

I = f C −k×d=10.5−0.00027×3600=0

which is the same as if we were saying that Xocotla lose all its influence after 1 hour of travelling.

Nonetheless, it is necessary to note that a low C value is going to generate an area of influence very

small, that is the case of Petlacala (see note 12), unfortunately with no archaeological evidence of a

big town, being recorded only 1198.46 m2 that is,

1198.461061221.67549

=0.00113

k = 0.00027

I = f C −k×d=0.001130.5−0.00027×3600=0.034−1=0.938 I 0

residual= 0.034*3600 (to transform value to seconds) = 122.4s that is,

50003600

×122.4=170 meters

which is approximately the resultant territory in the W-E axis.

According to this is possible to say that Petlacala lose all its influence after approximately 2

minutes of travelling. Eventually, if the remains of Petlacala show only a small concentration of

ceramic sherds with some evidence of ceramic burials, constituting an area of at least 1198 m2 (0.1

ha) that can be walked completely in seconds, a theoretical territory of approximately 3 hectares can

be considered a good territorial model even if does not fit in the historical evidence. If we consider

Petlacala a store house the assigned territory could be accurate.

When we talk about influence we have to consider that is not in reference to the actual power of the

polity, instead is referred to the area that possibly was consider part of the limits of an specific

spatial entity (e.g. town, hamlet, village, city, altepetl) with delimited boundaries. Since an altepetl

itself does not have boundaries as we consider them nowadays, at least is an approximate of the

limits of the entity useful for practical purposes. Doing this exercise helped us to understand the

dynamic of the polities when compared with the network and viewsheds, but also can help us in

future research to explore the accessibility to certain resources in the area doing some kind of

catchment analysis. For now, the results of this is only presented as an appendix (Appendix 5).

70

Chapter Six. Conclusions

To characterise a spatial entity modified by humans or not, is not as easy as it looks. We have to

consider several variables and have a precise knowledge about them. In fact, nowadays is quite

common to find papers super specialized in one topic about a topic related to another one and most

of the time is because it requires a full comprehension about details that could require an entire life

to know. Evidently, is practically impossible to fully understand human actions but at least we are

now in a very privileged position in history. Keeping apart political and economical postures,

recent technological improvements have changed our lives. No matter if you cannot use them, the

fact that you are living in a world that is connected almost completely through these technological

advancements that have been changing you life.

Now, in which sense this is related to Tlapa-Tlachinollan? According to the viewsheds, inhabitants

of this altepetl built their settlements in specific areas with an advantageous position, so they

probably were able to stay connected in this network of polities walked every day by thousands of

persons. Needless to say that most of the time they were moving from one place to another with

anything but a couple of legs. And yes, this is the whole point about this. While we are living in the

smallest world of all the times, they use to live in this little niche of around 4000 square kilometers

that it self constituted a whole world.

As we noticed in Chapter One, the complexity of Tlapa-Tlachinollan only can be understood in

relation to other polities and variables. The environment plays an important role modelling the

human shape. Is hard to imagine great quantities of resources transported every day from one place

to another in a terrain like the one that we find in the Mountain. Is hard to imagine one Tlapa-

Tlachinollan, in the middle (or the gate to) of the Mountains connected to the coast and to the Basin

of Mexico without wires and tires. Is hard to imagine a network connecting the whole universe of

sites with no more than people. But probably the hardest thing to imagine is that after 5 hundred

years we now have the opportunity to rediscover these dynamic paths of convergence and reproduce

them or try to reconstruct what once was a full network system.

Chapter One wanted to leave that feeling, to go inside the mountain and smell it, feel it, enjoy it and

suffer it. I think that I needed to be a better writer but still it is important to conceptualize the

mountain in these three levels: Historical, Human and Natural. Only considering these three entities

71

as a whole, independent on the approach that anyone wanted to take on. For me, at least, result

important to consider these factor from the beginning so we can be able to understand the

complicated world of the mathematics. Something that underlie the second chapter.

Viewsheds were created in the sixties as a formal method to count the area visible from one point to

another. But that does not mean that the doubt about how to do it was not there before. The results

of the analyses themselves show that visibility analysis has been used before. How can a settler

know which is the best site to start to build a house, for instance, without computers, random

viewshed points, single viewsheds, aerial photographs or digital terrain models? As we can

probably notice, routes and viewsheds are related and certainly, the settler need to know which is

the best place that have good visibility, but how can it make it?

The different kinds of networks explored in Chapter Four depict a weird version of Tlapa but at the

same time let us explore new possibilities of analysis. How can we find a place with good visibility

and a relatively good viewshed size without using automatized processes? I am of the opinion that

answering these underlying issues can make us improve the archaeological thought and possibly

make the archaeology useful for people. The viewshed analysis help us to be confident about our

thoughts but now we should go one step beyond and try to understand how the people we try to

analyse used to chose the right place. After all, the only thing we did was to test a series of samples.

With these preliminary results we know now that they chose the right place and direction to settle

down. Now, we should be capable of understand which mechanisms they use to put them there. One

possible solution could be the use of the network we already built and try to relate it with the

viewsheds of the points with highest values. Possibly, the sites are only in those areas of

convergence where the drainage system starts. Unfortunately, this exercise was one the few things

that has to be postponed for a future research and as a method to evaluate the visibility of the sites

according to the system they used to have to build what they did.

Until now, we have strong evidence about these two related topics –viewshed and network--. On the

one hand, the viewshed analysis showed that even in a constrained area, the values for the sites

present larger values that the samples. On the other hand, and according to the expansionist history

of Tlapa, and based on least cost path values, we can conclude that one possibility of the expansion

to the south not necessarily is because they want access to the coast but to the mountain itself.

72

Taking this into account, what can be done later is to test the reliability of the Total Network and

then, try to analyse if the paths generated keep some relation with archaeological sites so we can

actually contribute with the answer of the question mentioned above.

Finally, the territories of Tlapa Tlachinollan's altepetl, are related directly with the networks and

basically the size of the polity could have incremented in phases, following a natural flow of

communication with the Mountain. That is, when Tlachinollan conquered one site and we added the

nearest neighbouring links of this new site, the edges that start to appear “naturally” following the

least cost path of the 8 first neighbours, tend to go to the next site in the list of Tlachinollan

expansion. This approach is not explored as I would wanted but I think in general is a good way to

build territories and perform some catchment analysis. I tried in Appendix 5 to show the differences

of territories using different K values and then generate some catchment tables with the geology.

However, besides the technique itself and comparing it with the other networks as well as the

viewsheds, no more work was made on this.

Speakers of Nahuatl, Mixteco, Amuzgoor Tlapaneco in the area are very proud of their “country”

but they don't know so much about their history essentially because in general indigenous people

are marginal; I hope this work could be a seed in the granary that someday is going to reach the

light and flourish, contributing a little bit with the development of its history and inhabitants.

73

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Appendices

80

1. Appendix – r.cva installation

Since the GRASS GIS module g.extension does not work properly, the only way to have r.cva up and running is following the directions from this webpage -http://grass.osgeo.org/wiki/Compile_and_Install#Addons- where basically what we need is a full version of GRASS GIS 6.3 or more along with the source code and then compile within this GRASS set up the new add-on. There is another extension developed by Benjamin Ducke called GEM -http://grass.osgeo.org/gdp/html_grass64/gem/index.html- that could do the job, although this extension needs to be installed in a similar way and in any case the line “MODULE_TOPDIR = ../..” needs to be changed.

In this case the purpose of this appendix is to show how can you deal with r.cva installation under a Linux-like environment and a full version of GRASS GIS 6.3 or more along with the source code.

The r.cva module can be downloaded from this web page:http://www.ucl.ac.uk/~tcrnmar/GIS/r.cva.html

First make sure that you have a GRASS folder in /usr/local/src and grab in your mind or in the Clipboard the route to the MODULE_TOPDIR of your GRASS installation, which is basically the folder that contains the whole distribution, normally is referred as

/usr/local/src/grass6x

Then go to the SRC folder of your Add-on package and modify the file Makefile with a program like Emacs. If you are using the package modified by Benjamin Ducke, you have to modify the one contained in /src/raster/r.cva

The lines that you have to modify are:

MODULE_TOPDIR = ../..

Change the directory pointing to your specific GRASS folder

MODULE_TOPDIR = /usr/local/src/grass6x

Then, run as 'root' the following command to compile the module

>make

If you get an error referring to some files in the folder “OBJ.i686-pc-linux-gnu” try to erase all the files finishing in “.o” within this folder that possibly was created in a previous compilation attempt. To do this, is as easy as write

>rm *.o

Now, if after the compilation process there is no errors proceed with the following line to install the add-on:

>INST_NOW=y make

Try to run GRASS and write in the command line r.cva

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2. Appendix 2 – Viewshed Random Samples Generator

#!/usr/bin/env python#cvaSamplesGen#Create random points, calculate viewsheds per random sample and patch the results into a file.#Viewshed sizes in (n) number of points and (n) number of samples Generator ver. 1.3#Useful for statistical analysis#The raster file used to generate random points could be different from the one used by r.cva#Israel Hinojosa Balino (UCL)#This script use r.cva by Mark Lake (UCL)#This script needs GRASS 6.4 and Python to run#Run this script from command line in the GRASS Environment#Reference: Conolly J. and Lake, M. (2006) Geographical Information Systems in Archaeology.#Cambridge University Press: New York

import osimport sysgrass_install_tree=os.getenv('GISBASE')sys.path.append(grass_install_tree+os.sep+'etc'+os.sep+'python')import grass.script as grass

class bcolors: HEADER = '\033[7m' OKBLUE = '\033[94m' OKGREEN = '\033[92m' WARNING = '\033[2m' CONFIRM = '\033[1m' FAIL = '\033[94m' ENDC = '\033[0m'

def disable(self): self.HEADER = '' self.OKBLUE = '' self.OKGREEN = '' self.WARNING = '' self.FAIL = '' self.ENDC = ''

print ("\n" + bcolors.HEADER + bcolors.FAIL + "cvaSamplesGen 1.2" + bcolors.ENDC)print (bcolors.WARNING + "Viewshed sizes in (n) number of points and (n) number of samples generator" + bcolors.ENDC)print (bcolors.WARNING + "Create viewsheds at random points in a definite number of samples" + "\n" "and patch the results into a file" + bcolors.ENDC + "\n" +

"Please write the information required" + "\n")print (bcolors.OKGREEN + "Ideally, the extent of the raster used to produce the random points

should consider" + "\n" "the radius of the maximum viewing distance to avoid the edge effect" +

bcolors.ENDC + "\n")

82

raster=raw_input("Name of initial raster to calculate random points: ")

#check twice if name of DEM or DTM (raster file) exists, otherwise return errorfilex=grass.find_file(raster, element='cell')if not filex['fullname'] != '': raster=raw_input("Raster file with the name"+" "+"<"+ raster +">"+" "+"does not exist. Another try? : ")filex=grass.find_file(raster, element='cell')if not filex['fullname'] != '': raster=raw_input("Seriously"+" "+"<"+ raster +">"+"

"+"does not exist. Please choose another name: ")filex=grass.find_file(raster, element='cell')if not filex['fullname'] != '': grass.fatal(_("You have to check your files before using this script. Bye!!!"))

print (bcolors.OKBLUE + "\n" + "\"When the distance between a given viewpoint and the edge of the map region" + "\n"

"is less than that radius it follows that the viewshed may be artificially" + "\n" "truncated, thus invalidating comparison with the viewsheds of other

viewpoints" + "\n" "that were further from the edge of the map\" (Conolly & Lake, 229)" +

bcolors.ENDC)

rasterCVA=raw_input("\n" + "Name of raster to calculate the viewshed sizes points with r.cva.: ")print (bcolors.OKGREEN +

"The extent of this raster should consider a buffer zone" + "\n" "of the same width as the maximum viewing distance" + bcolors.ENDC)

#check twice if name of DEM or DTM (raster file) exists, otherwise return errorfilecva=grass.find_file(rasterCVA, element='cell')if not filecva['fullname'] != '': rasterCVA=raw_input("Raster file with the name"+" "+"<"+ rasterCVA +">"+"

"+"does not exist. Another try? : ")filecva=grass.find_file(rasterCVA, element='cell')if not filecva['fullname'] != '': rasterCVA=raw_input("Seriously"+" "+"<"+ rasterCVA +">"+"

"+"does not exist. Please choose another name: ")filecva=grass.find_file(rasterCVA, element='cell')if not filecva['fullname'] != '': grass.fatal(_("You have to check your files before using this script. Bye!!!"))

file=raw_input("\n" + "Name of the output vector file containing samples: ")

#check twice if name of previous output file exists, otherwise return errorfiley=grass.find_file(file, element='vector')if filey['fullname'] != '': file=raw_input("A file named"+" "+"<"+ file +">"+" "+"exists. Please choose another name: ")filey=grass.find_file(file, element='vector')if filey['fullname'] != '': file=raw_input("Seriously"+" "+"<"+ file +">"+" "+"exist. Please choose another name: ")filey=grass.find_file(file, element='vector')

83

if filey['fullname'] != '': grass.fatal(_("You have to choose another name. Bye!"))

#customizationmax=int(raw_input("\n" + "Number of samples: ") )maxR=int(raw_input("Number of random points: ") )maxDist=int(raw_input("Maximum distance (in metres) from viewing point (refer to r.cva): ") )

print "\n" + bcolors.HEADER + "Final Check" + bcolors.ENDCprint "Input raster to generate random points: " + bcolors.CONFIRM + raster + bcolors.ENDCprint "Input raster to generate viewsheds: " + bcolors.CONFIRM + rasterCVA + bcolors.ENDCprint "Output file name (vector): " + bcolors.CONFIRM + file + bcolors.ENDCprint "Number of samples: " + bcolors.CONFIRM, max, bcolors.ENDCprint "Number of random points per sample " + bcolors.CONFIRM, maxR, bcolors.ENDCprint "Maximum viewing distance " + bcolors.CONFIRM, maxDist, bcolors.ENDC

yes = raw_input("Continue (yes/no): ")if yes == "yes": print ("Perfect!")else: grass.fatal(_("Sorry. Bye!"))

#Create empty file, attach a table and add columns with the proper names and typesgrass.run_command('v.edit',

map=file, type='line', tool='create')

grass.run_command('v.db.addtable', map=file)

grass.run_command('v.db.addcol', map=file, columns="value DOUBLE PRECISION,vsize INT,sample INT")

#generate random points and calculate viewshedsi=1while i <= max: print i namerandom="randomV" +str(i) nameRandomCVA= "randomCVA"+str(i) sampleNo=i print 'Generating'+' '+'random'+' '+'numbers'+' '+'for'+' '+ namerandom i=i+1 grass.run_command('r.random',

overwrite='True', input=raster, vector_output=namerandom, n=maxR)

print 'Calculating'+' '+'viewsheds'+' '+'for'+' '+ nameRandomCVA

84

grass.run_command('r.cva', 'o', input=rasterCVA, output=nameRandomCVA, sites=namerandom,

obs_elev='1.7', target_elev='0.0', max_dist=maxDist, seed='1',

sample='10.0',type='sites',curvc='0.0' )

#Add column to attach Viewshed sizes and perform# a spatial query to extract the values from raster to vector print 'Spatial'+' '+'query'+' '+'for'+' '+ nameRandomCVA grass.run_command('v.db.addcol',

map=namerandom, layer='1', columns='vsize INT')

grass.run_command('v.what.rast', vector=namerandom, raster=nameRandomCVA, layer='1', column='vsize')

#Add another column to attach the sample number print 'Adding'+' '+'column'+' '+'for'+' '+'sample'+' '+'numbers'+' '+'in'+' '+ namerandom grass.run_command('v.db.addcol',

map=namerandom, layer='1', columns='sample INT')

grass.run_command('v.db.update', map=namerandom, layer='1', column='sample', value=sampleNo)

#Append sample to pre-existing samples print 'Patching'+' '+'original'+' '+'vector'+' '+'with'+' '+ namerandom grass.run_command('v.patch', 'ae',

overwrite='True', input=namerandom, output=file)

#Clean dataset from temporal files print 'Deleting'+' '+'supporting'+' '+'files'+' '+':'+'

'+ namerandom +' '+'and'+' '+ nameRandomCVA grass.run_command('g.remove', v

ect=namerandom, rast=nameRandomCVA)

print 'DONE!'

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#export to ascii with coordinates print 'Generating ASCII file with headers and coordinates' grass.run_command('v.out.ascii',

input=file, output='samples.txt', dp=10, columns='vsize,sample')

print 'DONE!' print ("\n" + bcolors.HEADER + "FINISHED!!!" + bcolors.ENDC)

86

3. Appendix – Procedures in R to analyse simulations

#############################################################################

#R code to generate a non-parametric test using Monte Carlo Simulation (example)#The code generates two analysis and the correspondent graphs#Archaeological Sites in La Montana de Guerrero#Israel Hinojosa Balino#Supervisor: Andrew Bevan (UCL)

#############################################################################

#setwd("/folder")

#import data SITES

sites=read.table(file="sites_vsize.txt", header=FALSE, sep="|")names(sites)=c("x","y","z","cat","NUM","vsize")

#import data SAMPLES

sitesR=read.table(file="samples_ascii.txt", header=FALSE, sep="|")names(sitesR)=c("x","y","cat","cat2","z","vsize","sample")

#here we explore the variable using a histogram#to draw a better plot, first we calculate the range of our datag_range=(range(sites$vsize))# Then we create a histogram object so we can #use it later to plot titles, specify number of #columns for the histogram. Turn off axes so we can specify them ourselfsiteHist.vs= hist(sites$vsize,breaks=217)#plot histogramplot(siteHist.vs,

main="Viewshed sizes histogram for core area of sites",sub="Frequency",xlab="Viewshed sizes (cell size 30mx30m)",xlim=g_range,col.lab="black", cex.lab=0.75, axes=FALSE,border=NA,col="grey")

#Specify x axis ranges where 25000*0:g_range[1] equals c(0,25000,50000,75000,100000)axis(1, at=25000*0:g_range[1],cex.axis=0.7,cex=0.70)#Specify y axisaxis(2, las=2,cex.axis=0.7,cex=0.70)#exportdev.print(device=jpeg, file="hist_sites_freq.jpeg", width=800, res=150)

#relative frequency (density)siteHistDen.vs=hist(sites$vsize,

freq=F,

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main="Viewshed sizes histogram for core area of sites",sub="Density and theoretical normal distribution",xlab="Viewshed sizes (cell size 30mx30m)",col.lab="black",cex.lab=0.75,axes=FALSE,border=NA,col="grey",breaks=217)

#to draw a better plot, first we calculate the range of our dataden_range=(range(siteHistDen.vs$density))#Specify x axis ranges where 25000*0:g_range[1] equals c(0,25000,50000,75000,100000)axis(1, at=25000*0:g_range[1],cex.axis=0.7,cex=0.70)#Specify y axisaxis(2,las=2,cex.axis=0.7,cex=0.70)lines(density(sites$vsize))curve(dnorm((x), mean(sites$vsize), sd(sites$vsize)), add=T, col="red")#exportdev.print(device=jpeg, file="hist_sites_den.jpeg", width=800, res=150)#produce a QQ plotqqnorm(sites$vsize)dev.print(device=jpeg, file="QQplot.jpeg", width=800, res=150)

#plot random samples as a background envelope #for the calculating the Empirical Cumulative Distribution Function (ECDF)

i=1plot(ecdf(sites$vsize[sitesR$sample == i]), xlim=c(0,100000), verticals=TRUE, do.points=FALSE, col.hor="grey", col.vert="grey",main="Envelope of 20 random samples")

for (i in 2:20) {plot(ecdf(sitesR$vsize[sitesR$sample == i]), xlim=c(0,100000),verticals=TRUE, do.points=FALSE, col.hor="grey", col.vert="grey", add=T)}

plot(ecdf(sites$vsize), xlim=c(0,100000), verticals=TRUE, do.points=FALSE, col.hor="red", col.vert="red", add=T)

#export plotdev.print(device=jpeg, file="envelope20sites.jpeg", width=800, res=150)

#calculate rank using meanmeans=c()for (i in 1:20) {means=c(means, mean(sitesR$vsize[sitesR$sample == i]))}

means=c(means, mean(sites$vsize))

#labeling meanstype=c()

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type[1:20]="r"type[21]="s"envelope=data.frame(means,type)#ordering valueso=order(envelope$means, decreasing=T)envelope_sorted=envelope[o,]#showing means#we can use this values to calculate degree of confidenceenvelope_sorted

#boxplots to visually represent the mean values of the viewshed sizes#load MASS to order meanslibrary(MASS)

#without order#boxplot(sitesR$vsize~sitesR$sample,data=sitesR, varwidth=TRUE, notch=TRUE, # horizontal=TRUE, at=1:20 - 0.6, boxwex = 0.60, # col="gold", main="Sites vs samples", xlab="Viewshed sizes")

#ordered

boxplot(vsize~sample,data=sitesR, varwidth=TRUE, notch=TRUE,horizontal=FALSE, at=rank(tapply(sitesR$vsize, sitesR$sample, mean)) - 0.6, boxwex = 0.60, col="gold", main="Sites vs samples", xlab="Viewshed sizes", cex.axis=0.8)

#add sites boxplot(sites$vsize,

add = TRUE, at=21 - 0.6, varwidth=TRUE, notch=TRUE, horizontal=FALSE,boxwex = 0.60, col="darkgreen", axes=FALSE)

mean.value=tapply(sitesR$vsize, sitesR$sample, mean)points(1:21-0.6, sort(means), pch = 18, col="red")

#export Box Plotdev.print(device=jpeg, file="boxplot.jpeg", width=1100, res=150)

89

4. Appendix 4 – Closeness centrality

#############################################################################

#tnet procedures used to generate the shapefiles with the values (example)#Archaeological Sites in La Montana de Guerrero#Israel Hinojosa Balino#Supervisor: Andrew Bevan (UCL)

#############################################################################

#load librarieslibrary(maptools) #various utilities for map datalibrary(rgdal) #import/export utilties for various spatial formatslibrary(spatstat) #point process simulationslibrary(grImport) #adding existing pdf features to plotlibrary(classInt) #define class breaks for continuous variableslibrary(sfsmisc) #here to produce small number expressions in a x 10k format

#LOAD tnet#Reference#Opsahl, T., Agneessens, F., Skvoretz, J., 2010.#Node centrality in weighted networks: #Generalizing degree and shortest paths. Social Networks 32 (3), 245-251#Package ‘tnet’#May 4, 2011#Type Package#Version 3.0.5#Date 2011-05-04#Title tnet: Software for Analysis of Weighted, Two-mode, and Longitudinal networks#Author Tore Opsahl#Maintainer Tore Opsahl <tore@opsahl.co.uk>#Depends R (>= 2.10.0), igraph, survival#Description R package to analyse weighted, two-mode, and longitudinal networks.#License CC BY-NC 3.0 + file LICENSE#Repository CRAN#Date/Publication 2011-05-04 15:24:27

library(tnet) #weighted networks

#############################################################################

# LOAD NETWORK AND DEFINE PROJECTION

# we can set the working directory#setwd("/folderNAME/")

# define projection in PROJ.4 format# UTM WGS84 14N

90

proj4string=CRS(as.character("+proj=utm +no_defs +zone=14 +a=6378137 +rf=298.257223563 +towgs84=0.000,0.000,0.000 +to_meter=1"))

#since the vector file is big and R has some problems managing memory, #only a pre-formatted table is used#otherwise we would have extracted the table from the shapefile#### Extract network from SHP file (Example)#edges=readShapeLines(fn="edges.shp", proj4string = proj4string)#net=routes@data[,c(1,2,3)]#names(net)<-c("i","j","w")

network.tnet=read.table(file="shp/network/FINALv.01.csv",header=FALSE,sep=",")names(network.tnet)=c("i","j","w")

############################################################################## (THIS IS ONLY A TEST) we can build a matrix to produce a dendrogram (TEST)# hypotetically this could represent the network by polities#mat=distance_w(network.tnet, directed=NULL, gconly=TRUE, subsample=1, seed=NULL)#calculate distances in the matrix to perform a dendrogram#d=dist(mat, method = "euclidean")#fit=hclust(d, method="ward")#plot(fit, cex=0.2)#dev.print(device=jpeg, file="dendr.jpeg", width=3000, res=300)#############################################################################

#Additional tasks to test the network table

#Calculate the average distance in the binary network#mean(distance_w(bnet),na.rm=T)

#Calculate the average distance in the weighted network#mean(distance_w(network.tnet),na.rm=T)

# Read the directed network#directed.net <- read.table(file="shp/network/fromMainSites.csv",header=FALSE,sep=",")

# Check that it confirms to the tnet standard for weighted one-mode networks#directed.net <- as.tnet(directed.net, type="weighted one-mode tnet")

# Compute the global clustering coefficients#clustering_w(network.tnet, measure=c("bi", "am", "gm", "ma", "mi"))

#############################################################################

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# ANALYSIS AND CREATION OF FILES

# Calculate the out-degree of sites and the generalised measures (alpha=0.5)netDegreeOut=degree_w(net=network.tnet, measure=c("degree","output","alpha"), alpha=0.5)

# Calculate the in-degree of sites and the generalised measures (alpha=0.5)netDegreeIn=degree_w(net=network.tnet, measure=c("degree","output","alpha"), alpha=0.5, type="in")

#Here we calculate the closeness centrality and betweeness#This is to calculate nodes without connection GCONLYclose=data.frame(closeness_w(network.tnet, alpha=1,directed=TRUE,gconly=FALSE))#close=data.frame(closeness_w(network.tnet, alpha=1,directed=TRUE))betw<-data.frame(betweenness_w(network.tnet, alpha=1, directed=TRUE))

#here we import the point file where the attributes are going to be mergedpoints=readShapePoints(fn="shp/sites.shp", proj4string = proj4string)

#here we create a date.frame object so we can merge #the results of the closeness and betweeness with the pointssites=data.frame(coordinates(points),points$NUM)names(sites)=c("x","y","PID")sitesB=data.frame(coordinates(points),points$NUM)names(sitesB)=c("x","y","PID")

#here we create a date.frame object so we can merge the Degree centrality out- and in-sitesDegOut=data.frame(coordinates(points),points$NUM)names(sitesDegOut)=c("x","y","PID")sitesDegIn=data.frame(coordinates(points),points$NUM)names(sitesDegIn)=c("x","y","PID")

#merge closenesssites=merge(sites,close,by.x="PID",by.y="node")names(sites)=c("pid","x","y","close")

#merge BetweenesssitesB=merge(sitesB,betw,by.x="PID",by.y="node")names(sitesB)=c("pid","x","y","betw")

#merge out-degreesitesDegOutM=merge(sitesDegOut,netDegreeOut,by.x="PID",by.y="node")names(sitesDegOutM)=c("pid","x","y","degree","output","alpha")

#merge in-degreesitesDegInM=merge(sitesDegIn,netDegreeIn,by.x="PID",by.y="node")names(sitesDegInM)=c("pid","x","y","degree","output","alpha")

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#Promote back to SpatialPointsDataFrame and export to shapefile

#closenesscoordinates(sites)=sites[,2:3]sitesPoints=SpatialPointsDataFrame(coords=sites,

data=sites@data, proj4string=proj4string)

writeOGR(sitesPoints, dsn = "shp/network", layer = "tnet_nodesClose", driver = "ESRI Shapefile")

#betweenesscoordinates(sitesB)=sitesB[,2:3]sitesPointsB=SpatialPointsDataFrame(coords=sitesB,

data=sitesB@data, proj4string=proj4string)

writeOGR(sitesPointsB, dsn = "shp/network", layer = "tnet_nodesBetw", driver = "ESRI Shapefile")

#out-degreecoordinates(sitesDegOutM)=sitesDegOutM[,2:3]sitesDegOutMP=SpatialPointsDataFrame(coords=sitesDegOutM,

data=sitesDegOutM@data, proj4string=proj4string)

writeOGR(sitesDegOutM, dsn = "shp/network", layer = "tnet_nodesOutDeg", driver = "ESRI Shapefile")

#in-degreecoordinates(sitesDegInM)=sitesDegInM[,2:3]sitesDegInMP=SpatialPointsDataFrame(coords=sitesDegInM,

data=sitesDegInM@data, proj4string=proj4string)

writeOGR(sitesDegInM, dsn = "shp/network", layer = "tnet_nodesInDeg", driver = "ESRI Shapefile")

93

5. Appendix 5 – Territories

Guide to geology keys used in the cross tabulation tables as well as other values

94

Cretaceous InferiorCretaceous Inferior

Limestone Cretaceous InferiorLimestone - Gypsum Cretaceous Inferior

Cretaceous SuperiorPaleozoic Superior

Limestone - Sandstone Paleozoic SuperiorAlluvium QuaternaryGranite Intrusive igneous rockSedimentary Volcano - Gypsum

Intrusive igneous rock

Metamorphic complexGranite

Archaeological sites areas in metersMendoza?

KiCgp Polymictic conglomerateKiCgp-Cz Polymictic conglomerate - LimestoneKiCzKiCz-YKsAr-Lu Sandstone - LutitePcmMV MetavolcanicPcppCz-ArQhoalTGr CenozoicTmplVs-Y Cenozoic NeogeneToGd Granodiorite CenozoicTomR Rhyolite Cenozoic PaleogeneTpaeCgp-Lm Polymictic conglomerate - Siltstone Cenozoic PaleogenepE?PTCM Precambrian PrecambrianpE?PTGr Precambrian PrecambrianpE?PdGt Granitoid Precambrian PrecambrianpE?PdMs Metasedimentary Precambrian PrecambrianDistance to xale Distance in meters from the centroid of each altepetl to the closest xaleArea (m)

Bolean; 1 = site is mentioned in Codex Mendoza; 0 = noAzoyu? Bolean; 1 = site is mentioned in one of both codices Azoyu; 0 = no

Table 2: Geology characteristics of territories after with a k value of 0.0000225

SITE KICZ KICZ_Y QHOAL TMPLVS_Y TPAECGP_LM JMAR_LU TOGD PCMMV KICGP_CZ JMCGO_AR PE_PDMS PCPPCZ_AR TOMR JMTR KICGP Distance to xalle Area (m) Mendoza? Azoyu?

Xocotla 20682500 283717500 63872500 0 193952500 60790000 0 0 80950000 8845000 0 0 12922500 590000 22825000 6633.2 1061221.68 0 0

Contlalco 24487500 110537500 25577500 1895000 685000 66345000 0 0 115770000 0 447500 0 52020000 0 0 2551.7 849741.55 1 1

Ocuapa 0 0 0 0 0 407500 0 0 19050000 0 78267500 0 0 0 0 17916.77 87976.32 0 0

Alcozauca 0 71820000 0 47560000 35050000 21707500 0 0 0 0 1185000 0 0 0 0 13660.9 214485.88 0 0

Huamuxtitlan 15767500 19577500 19612500 0 0 20607500 0 9757500 60102500 1705000 105000 0 0 32500 0 3474.85 299193.25 1 0

Texmelincan 0 0 0 0 0 31595000 0 0 355095000 7845000 292507500 0 108965000 190000 0 23926.03 568002.01 0 0

Igualita-Yoallan 0 46202500 6065000 10627500 0 35715000 0 0 24330000 0 10637500 0 1502500 0 0 2069.49 308483.47 0 0

Ollinala 0 0 0 0 0 14772500 0 82035000 22957500 13097500 48387500 2197500 555000 7972500 3707500 15052.17 191699.65 1 0

Cualac-Apetlanca 0 0 0 0 0 5977500 0 0 2767500 5255000 0 0 0 0 440000 8517.09 44875.2 1 0

Chiepetlan Oeste 2027500 0 0 0 0 5000 542500 6025000 64955000 9265000 126675000 0 17097500 140000 24915000 6643.23 469080.21 1 0

Table 3: Geology characteristics of territories after with a k value of 0.000027

SITE,C,80 KICZ KICZ_Y QHOAL TMPLVS_Y TPAECGP_LM JMAR_LU TOGD PCMMV KICGP_CZ JMCGO_AR PE_PDMS PCPPCZ_AR TOMR JMTR KICGP Distance to xalle Area (m) Mendoza? Azoyu?

Xocotla 16147500 196457500 43197500 0 140430000 39737500 0 0 65332500 7610000 0 0 8825000 577500 19427500 6633.2 1061221.68 0 0

Contlalco 24935000 99152500 25240000 5000 1515000 63375000 0 0 99870000 0 0 0 39180000 0 0 2551.7 849741.55 1 1

Ocuapa 0 0 0 0 0 1035000 0 0 26800000 0 68402500 0 0 0 0 17916.77 87976.32 0 0

Alcozauca 0 67055000 0 33072500 17327500 12892500 0 0 0 0 0 0 0 0 0 13660.9 214485.88 0 0

Huamuxtitlan-Tecoapa 18622500 21472500 23170000 0 0 23462500 0 1965000 42050000 757500 0 0 0 0 0 3474.85 299193.25 1 0

Texmelincan 0 0 0 0 0 14425000 0 0 286150000 5117500 210645000 0 80510000 0 0 23926.03 568002.01 0 0

Huitzapula 0 0 0 0 0 0 0 0 11392500 0 12612500 0 0 0 0 24875.77 236591.08 0 0

Igualita-Yoallan 0 42240000 6385000 1595000 0 32070000 0 0 21927500 0 3875000 0 1560000 0 0 2069.49 308483.47 0 0

Ollinala 0 0 0 0 0 10627500 0 74412500 23907500 10482500 16880000 1877500 545000 6372500 3020000 15052.17 191699.65 1 0

Cualac-Apetlanca 0 0 0 0 0 10540000 0 0 8772500 6090000 0 0 0 0 3022500 8517.09 44875.2 1 0

Chiepetlan Oeste 2027500 0 0 0 0 4015000 257500 1490000 71497500 8975000 92892500 0 19897500 0 26465000 6643.23 469080.21 1 0

Table 4: Geology characteristics of territories after with a k value of 0.00009

SITE,C,80 KICZ KICZ_Y QHOAL TMPLVS_Y TPAECGP_LM JMAR_LU PCMMV KICGP_CZ JMCGO_AR PE_PDMS PCPPCZ_AR TOMR JMTR KICGP Distance to xalle Area (m) Mendoza? Azoyu?

Xocotla 1862500 5555000 22095000 0 5937500 13045000 0 9625000 3495000 0 0 0 0 7912500 6633.2 1061221.68 0 0

Contlalco 13430000 12965000 21977500 0 0 425000 0 4710000 0 0 0 0 0 0 2551.7 849741.55 1 1

Ixcateopan 0 0 0 0 0 397500 0 127500 0 0 0 0 0 0 4945.44 272699.66 0 0

Ocuapa 0 0 0 0 0 0 0 0 0 13667500 0 0 0 0 17916.77 87976.32 0 0

Alcozauca 0 10977500 0 85000 0 0 0 0 0 0 0 0 0 0 13660.9 214485.88 0 0

Huamuxtitlan-Tecoapa 675000 1925000 20825000 0 0 0 0 397500 0 0 0 0 0 0 3474.85 299193.25 1 0

Texmelincan 0 0 0 0 0 0 0 2845000 0 44792500 0 0 0 0 23926.03 568002.01 0 0

Tenango Tepexi 0 0 0 0 0 0 0 13107500 0 0 0 0 0 0 1339.25 98505.08 0 0

Huitzapula 0 0 0 0 0 0 0 15487500 0 0 0 0 0 0 24875.77 236591.08 0 0

Igualita-Yoallan 0 4647500 6402500 0 0 6455000 0 0 0 0 0 0 0 0 2069.49 308483.47 0 0

Ollinala 0 0 0 0 0 0 1345000 12735000 197500 0 175000 542500 2110000 0 15052.17 191699.65 1 0

Cualac-Apetlanca 0 0 0 0 0 882500 0 2665000 1535000 0 0 0 0 125000 8517.09 44875.2 1 0

Ahuacatitlan 0 0 0 0 7130000 0 0 0 0 0 0 0 0 0 11407.72 129523.45 0 0

Petlacala Pueblo 0 0 0 0 0 0 0 220000 0 0 0 0 0 0 4873.43 1198.46 0 0

Chiepetlan Oeste 2030000 0 0 0 0 0 0 25865000 1505000 11297500 0 2557500 0 677500 6643.23 469080.21 1 0

Table 5: Geology characteristics of territories after with a k value of 0.00027

SITE,C,80 KICZ KICZ_Y QHOAL TPAECGP_LM JMAR_LU KICGP_CZ JMCGO_AR PE_PDMS TOMR Distance to xalle Area (m) Mendoza? Azoyu?

Xocotla 0 0 5855000 0 5055000 0 1570000 0 0 6633.2 1061221.68 0 0

Contlalco 560000 142500 5957500 0 0 2217500 0 0 0 2551.7 849741.55 1 1

Ixcateopan 0 0 1272500 102500 962500 0 0 0 0 4945.44 272699.66 0 0

Ocuapa 0 0 0 0 0 0 0 1135000 0 17916.77 87976.32 0 0

Alcozauca 0 1805000 0 0 0 0 0 0 0 13660.9 214485.88 0 0

Huamuxtitlan 0 130000 3955000 0 0 0 0 0 0 3474.85 299193.25 1 0

Texmelincan 0 0 0 0 0 0 0 7857500 0 23926.03 568002.01 0 0

Tenango Tepexi 0 0 0 0 0 1432500 0 0 0 1339.25 98505.08 0 0

Huitzapula 0 0 0 0 0 2732500 0 0 0 24875.77 236591.08 0 0

Igualita-Yoallan 0 5000 2925000 0 525000 0 0 0 0 2069.49 308483.47 0 0

Ollinala 0 0 0 0 0 2490000 0 0 395000 15052.17 191699.65 1 0

Cualac-Apetlanca 0 0 0 0 67500 332500 467500 0 0 8517.09 44875.2 1 0

Ahuacatitlan 0 0 0 1362500 0 0 0 0 0 11407.72 129523.45 0 0

Petlacala Pueblo 0 0 0 0 0 30000 0 0 0 4873.43 1198.46 0 0

Manila 0 295000 1325000 0 0 5000 0 0 0 4628.5 167594.98 1 0

Chiepetlan Oeste 557500 0 0 0 0 4345000 27500 232500 555000 6643.23 469080.21 1 0

97

98

99