Reliability Modeling Development at Ek Xux

Marc A. Abramiuk

A thesis submitted to the Faculty of Graduate Studies in partial fulnllment of the requirements

for the degree of

Master of Arts

Graduate Programme in Social Anthropology York University Toronto, Ontario

January 1999

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Reliability Modeling Development at Ek Xux

by MARC A. ABRAMIUK

a thesis submitted to the Faculty of Graduate Studies of York University in partial fulfillment of the requirements for the degree of

MASTER OF ARTS

Permrsston has been granted to the LIBRARY OF YORK UNIVERSITY to lend or sel1 copies of this thesis, to the NATIONAL LIBRARY OF CANADA to microfilm this thesis and to lend or sel1 copies of the film.

The author resewes other publication rights, and neittier the thesis nor extensive extracts from it may be printed or otherwrse reproduced without the author's written permission.

Abstract

The purpose of my thesis is to investigate when and why the ancient Maya of the cornmunity of Ek XUX abandoned settlement in the ninth century A.D. It is my contention that the Maya left their homes in the Maya Mountains of southem Belize as the resuit of insufficient arable land with which to sustain the expanding population. Since the communities of these mountains are believed to have been self-sufficient, although economically interconnected, I propose to treat Ek Xux as if it was one of several components in a system. By utilizing the mathematical concept of reliability. 1 will constnict a mode1 that describes the development of Ek Xux and in so doing illuminate the role that subsistence fluctuation played in its demise as well as estimate a time for its collapse. By using reliability to generate theoretical dates for the collapse it will be possible to test the theoretical dates with actual dates that are obtained by future excavations and epigraphic stuciy.

Acknowledgments

1 would like to thank my thesis supervisor Dr. Elizabeth Graham for her time and patience in looking over my previous clrafts and for her input on several aspects of Maya archaeology .

1 would also like to thank Dr. Malcolm Blincow for his cornrnents on the previous draft of this thesis.

I cannot emphasize enough the important d e that Dr. Peter Dunharn played in introducing me to the Maya Mountains. 1 thank him for the several years of encouragement and the several fieldwork opportunities 1 was given as a member of the Maya Mountains Archaeological Projec t (MMAP).

The hardships which were overcome while conducting fieldwork deep in the tropical raini'orests of the Maya Mountains are memones that ody a handful of people experience. Because of the type of fieldwork I conducted, which was mainly surveying, 1 operated on my own very far fiom base camp, often with only two Kekchi or Mopan guides. I especially thank Greg, Margarito, Enrique, Pedro, and Benino with whom 1 worked most closely. As much as I would like others to appreciate the events that transpireci in the field, these individuals will be the only ones that t d y understand.

Lastly, 1 would lïke to thank my mother, father, sister, and the rest of my family for their constant and enduring support. 1 also thank Anita Gombos for her encouragement over the past three years.

Finally, 1 would never have been able to accumulate as much data as 1 had without the hancial assistance fiom the Sigma Xi, the Scientific Research Society and the Explorer's Club.

Table of Contents

Absîract Acknowledgements Chapter l - introduction Chapter 2 - Background of Study Area

- The Maya Mountains - The Bladen River Drainage - Ek XU - Ek Xux Settlement - Chronology at Ek Xux

Chapter 3 - Background of Domestic and Househoid Archaeological Trends in the Maya Area

- Identification of the Household - The Developmental Cycle

Chapter 4 - Carrying Capacity - Introduction to Canying Capacity - Previous S tudies of Camying Capaci ty - Factors Which Influence Canying Capacity - Sustaining Area and Site Size: Variables that Describe C-g Capacity at Ek X w

- Archaeodemography Chapter 5 - Reliability

- Introduction to Reliability - Systems - Systems Reliability - A Systems Approach to Reliability dong the Bladen Branch - Component Reliability

Chapter 6 - Methods - Constmcting the Reliability Mode1

Chapter 7 - Analysis and Interpretation - Results - Ek Xux Valley Settlement - AC Valley Settlement - The Ek X w Realrn - De fining Intermunicipal Boundaries - Interpreting the Relationship between the Ek Xux Valley and

the AC Valley Seîtlement - The Collapse Phenornenon

Chapter 8 - Conclusion - Further Directions and Conclusions

Appendix A

Appendix B Re ferences

vii

List of Figures

Fig. 1 - Map of Belize with Major Sites and the Maya Mountains Fig. 2 - Map of Upper Bladen Branch Fig. 3 - Survey Map of the Ek Xux Site Core Fig. 4 - S w e y Map of Ek X w Settlement amund the Ek Xux Site Core

Fig. 5 - Settlement Area Data Fig. 7 - Reliability Data for Ek Xux Valley Settlement Fig. 8 - Reliability Data for AC Valley Settlement Fig. 9 - Reliability Data for Al1 Ek X w Fig. 13 - Failure Data for Ek Xux Valley Settlement Fig. 14 - Failure Data for AC Valley Settlement Fig. 15 - Failure Data for Al1 Ek Xux

Fig. 6 - Settlement as a Function of Time (Cycles). From Top to Bottom: 127 Ek Xux Realm, Ek Xux Valley, AC Valley.

Fig. 10 - Reliability as a Function of Time (Cycles) for Ek Xwc Valley 128 Fig. 1 1 - Reliability as a Function of Time (Cycles) for AC Valley 129 Fig. 12 - Reliability as a Function of Time (Cycles) for Entire Ek X w Realm 130 Fig. 16 - Failure as a Function of Time (Cycles) for Ek Xux Valley 131 Fig. 17 - Failure as a Function of Time (Cycles) for AC Valley 132 Fig. 18 - Failure as a Function of Time (Cycles) for Entire Ek Xux Realm 133

viii

ter 1 - IntroducIipn

for Mv R e s e a

My interest in the collapse phenornenon began as a desire to predict

mathematically the collapse of a community. Given that 1 knew possible causes of the

collapse, and given that I knew how the community operated with respect to the causes,

in theory I could constnict a systemic representation of the community through time. The

operational inmr workings of the community would Wear as tirne went on, sirnilar to the

Wear to which the gears of a mechanical device are subject. The deteriorating process

would kevitably continue until the seizing of functioning parts in the community would

cause a system-wide shutdown.

Unfortunately, mathematically modeling the detenoration of social systems, such

as ancient communities, is not as easy a s modeling the detenoration of a device. For one,

ancient communities do not always make explicit the causes of their demise. Second, it is

not always kncwn how the community fhctioned; even if this is known, the levels at

which the comrnunity operated are often too numerous to include in a concise model.

Therefore, over the course of my research, the model that I had previously in mind was

simplifieci. First, it was decided that the most obvious cause for the collapse of Ek Xux

was that it reached its maximum carrying capacity. This cause would be the instigating

factor in the collapse until more information codd be gathered on other likely causes.

Second, only one ievei of operation was chosen to act as the operating force behind Ek

Xux, because this was the most fundamental level, and the level upon which the cause for

the collapse was contingent: household growth. One advantage of such a mode1 is that it

is flexible and can be improved upon in future work. Another advantage lies in the fact

that the mode1 can be tested and the assumptions that were utilized to conscnict it

similarly tested.

. . . . se of CI-

For centuries, and no doubt millennia, people have wondered why communities

disappeared, O ftentimes leaving behind ma@ ficent monuments and temples - the 1s t

remnants of a once great civilization. The reasons that people leave their communities

are difficult to understand. This is because eiiher there are too many faciors to account

for, or the factors for decline are so enmeshed in a cause-effect web that they are difficult

to distinguish. Rarely can we narrow down one factor as the predominant cause (Ellen

1982). The ancient Maya are a perfect case in point.

a=mawmc The ancient Maya were long thought to have disappeared as the result of some

mysterious cause (Stephens 1843). It was not until the middle of this century that

hypotheses were being generated to explain the collapse phenornenon (Thompson 1966).

Many romanticized the collapse of the ancient Maya (Morley 1920) while others

fomulated more realistic hypotheses (Culbert 1973). One theory held that Maya

civilization in the southem lowlands collapsed as the result of invading peoples fkom the

Gulf Coast (Sabloff 1973). Another proposed that the Maya were involved in a new type

of warfare that arrived in the southem lowlands fkom the north, and slowly pulled apart

the fabric of the traditional ways (Schele and Freidel 1990). This new, aggressive,

imperialist form of warfare dictated that sites be conquered and their political and

econornic infrastructures taken over. Another hypothesis held that the Maya were so

economically linked that a disturbance caused al1 the sites in the southem iowlands to

fdl, one after another (Culbert 1973). Disease and drought were also popular themes

(Willey and Shimkin 1973).

Whether these were the reascns for collapse are, to this day, hotly debated, but as

more data are collected, many scholars believe that a query into the instability of Maya

civilization is a question more capable of being answered. Some ancient Maya cities had

been flourishing for nearly three thousand years. Why at this point in their history should

they be abandonecl?

The question of this hstability in recent years has been closer than ever to being

answered. What we see in the Maya Iowlands is one of the most populated regions in the

pre-industrial world. Even the study area to be discussed, the Maya Mountains, was a

highiy populated region according to the archaeological evidence that has been

accumulateci in recent years @unham 1990; Graham 1994). With such a large

population, the question arises whether ancient Maya society had enough food to support

it. In fact, the evidence indicating subsistence fluctuation as the cause of instability for

the Maya is impossible to ignore. Some have hypothesized that the problem of

insufficient food yields became so pressing that it led to the necessity of food exchange

among sites (Culbert 1995). Whether fiuctuating subsistence was the cause of instability

in Maya infrastructure, which led to the collapse, or whether it was the direct cause of the

collapse is a question that deserves a rigorous analysis.

t of-

The area that 1 will be discussing is the Maya Mountains of southem Belize

(Figure 1). High up in this rnountain range several previously unrecorded sites have

been discovered over the past decade by the Maya Mountains Archaeological Project

(MMAP) (Dunharn1998). 1 will discuss one of these ancient comrnunities in particular,

Ek Xux. Ek Xwc was chosen to study because thus far we have more archaeological data

on Ek Xwc than any other site in the area.

In the following chapters 1 hope to shed light on the hinction that Ek Xux served

with respect to its peer polities, and to ascertain a demographic chronology for Ek Xux

with which we may constnict a mode1 for its collapse. This latter goal will be

accomplished by using a mathematical construct called reliability, which will be based on

the fusion of two fwidamental concepts, namely the developmental cycle and carrying

capacity .

The work done here on Ek Xux will also set the foundation for a much larger

future project, one which will encompass Ek Xux and four of its neighboring sites in a

network. For the purposes of this paper, however, 1 will analyze Ek Xux and estirnate its

probability of success as a fùnctioning community throughout the Late Classic. In so

doing it will be possible to calculate the date of collapse for Ek Xux. Though Lowe

(1985) and many others believe that multiple factors eventually caused the demise of

Maya civilization, I will study the effect of one cause on a single community. 1 will show

that it is possible to calculate how long the cultivable land available could support the

exploding population at Ek Xux.

tv"* A L

1 hypothesize that there were two counteracting yet complementary pressures,

namely increasing settlement due to the increasing population, and decreasing

agriculhiral land. In other words, Ek Xux had reached a saturation point. Unable to

sustain itself with the diminishing agriculnual area, Ek Xux was eventually abandoned.

1 propose that during Ek Xw's waning years that Ek Xux's carrying capacity

coefficient or ratio between settlement area and total agricultural area was nearing that of

the cntical canying capacity coefficient for ancient Maya sites. The camying capacity is

not only important for telling us the critical state Ek Xw< was in at the tirne of collapse,

but 1 believe that the coefficients make ideal measurements for reliability. The concept

of reliabîlity can be used to generate a mathematical model, one that can generate

themetical dates for the collapse of Ek Xux as well as the site's probability for

hctioning at different points in t h e .

For example, a site's reliabifîty at the tirne of abandonment can be calculated

simply by subtracting the sites CCC from the critical CCC for the Maya areê The result

will be a very srna11 nurnber because, according to our hypothesis, the Maya abandoned

Ek Xux because they were approaching a critical CCC. Here, Ek Xwr's CCC is simply

the basal area of settlement divided by the total agriculhual area. The critical CCC for

this region can be estimated by using Raoul Naroll's (1962) formula relating basal area

and population in conjunction with the standard support capacity for the Maya area

(Culbert 1 995).

The purpose of Chapter 2 is to provide a detailed description of the environment

and the settlement that surround Ek Xux, especially since the rise in settlement in

conjunction with the delimiting environment contributed to the collapse at Ek Xux.

In Chapter 3, I will briefly review the previous literature on domestic archaeology

in the Maya area in the hope that it rnay illuminate the social dynamics of ancient Maya

society at Ek Xux. An important concept called the developmental cycle will be

introduced later in the chapter, which will allow me to reconstruct settlement growth with

respect to time, and provide the operational framework for constmcting a reliability

model for Ek Xux.

Chapter 4 will discuss the other important concept in constructing a reliability

model, carrying capacity. Canying capacity will allow me to detemine the settlement to

sustaining area ratio at a point in time, also known as the carrying capacity coefficient

(CCC). Using the same reasoning a maximum or critical canying capacity coefficient

(CCCC) can be calculated for the Maya area. The CCCC minus the CCC for Ek Xux is

the probability that Ek X w will continue to function properly and will be taken to be the

measurement of reIiabiIity.

In Chapter 5, the probability that a comrnunity will Function properly, or its

retiability, can be extended to many points in time assuming that the developmental cycle

of Chapter 3 is operating. Reconstmcting the probabilities of success and failure of any

system is the material that is covered in this chapter and the matenal that will permit me

to constnict a reliability model for Ek Xux.

In Chapter 6, the methods used in measuring settlement area and sustaining area

in the field and in the laboratory will be presented. Derivations of the basic formulas

presented in the earlier chapters will be applied in this chapter and allow for a

mathematical model of the reliability of Ek Xux to be constnicted.

In Chapter 7, the results are presented for the Ek Xux valley, AC valley, and the

entire Ek Xux realm. The relationships between the Ek Xux valley settlement and the AC

valley settlement is interpreted fiom the results and a collapse date is predicted for Ek

Xux, which can be tested through future excavations.

Chapter 8 will be the conclusion. 1 will discuss what has been achieved with my

application of reliability modeling and conclude with future directions that will be taken

as the result of this research.

The Maya Mountains

The Maya Mountains of souhem Belize were home to thousands of Maya

inhabitants for hundreds of years (Dunharn 1998). Therefore, the purpose of this chapter

is to intmduce the study area and provide some background on the environment and on

any archaeological evidence of settlement in the vicinity of Ek Xu. This information

will help us to understand how the environrnent and the ancient Maya interacted through

time, allowing us to situate Ek Xux spatially and chronologically.

a Mo-

The Maya Mountains nui dong a southwest-northeast axis in the intenor of

Belize. The northeast end of the range is located in the present day Cayo District of

Belize while the southwest end of the chah extends into neighboring Guatemala. Along

this axis the Maya Mountain chah is approximateb 150 kilometers long and about 75

kilometers wide. The highest point, Doyle's Delight, is approximately 1,200 meters

above sea level. This is the only mouritain range in the entire Maya lowlands, in fact, the

only main relief feature on the Yucatan Peninsula (Wright et al. 1959; West 1964). The

Maya Mountains are not imposing in the sense of height; however, they do constitute a

formidable area to penetrate. It is for this reason, as well as the fact that the Maya

Mountains exhibit no value in tems of mineral resources (Dixon 1956; Graham 1994) or

extensive cultivable land (Wright et al. 1959), that the mountains are uninhabited and

commercially unexploited today. It is not until we shed Our contemporary views that we

see that the Maya Mountains zone comprises a wide range of mineral and biotic resources

that provided attractive opportunities for resource exploitation in the past (Le., in the

context of a non-globally oriented market).

The Maya Mountains have a high annual rainfall, which approaches five meters.

It also retains cool temperatures, which can get as Iow as 4 degrees Centigrade. For this

reason, the Maya Mountains of southem Belize support a wide range of flora and fauna.

Also, as one of the two 1s t Pleistocene refuges on Earth (the other being the Amazon

Basin) (Dunham 1998), the Maya Mountains harbor several biological species that have

become extinct elsewhere.

Due to the high relief and extremely rugged tenain, the mountain range is

geographically isolated nom the rest of the Maya Lowlands and is, therefore, difficult to

traverse. Hemando Cortez discovered this fact when he lost over two-thirds of his horses

crossing the western Banks of the mountains in 1 525 A.D. (Sharer 1994; p. 736).

The nvers and streams draining the rnountains cut steep courses, and deposition of

alluvium is limited to relatively small pockets, at least until the rivers reach the coastal

plain, where more extensive alluvial deposition is possible (Wright et al. 1959). The sites

on which 1 focus are located in these pockets.

The Maya Mountains, since Cortez' journey, have rernained little explored with

the exception of hunters, miners, chicleros, and loggers (Graham 1994). The reason

behind the lack of exploration by archaeologists was the prevailing view that the region

was a hunting and gathering area for the ancient Maya and not an area that could sustain

permanent settlement (Hammond 1975). Preliminary archaeological survey and

excavations, however, have been conducted in the eastem foothills of the Maya

Mountains and coastal plain, as well as in the Cockscomb Basin by Graham (1994).

Graham traced the sources of stone used in several ancimt Maya grinding stones fiom

two major lowland sites, Uaxactun and Seibd, to the Maya Mountains and in so doing

provided evidence for inter-regional exchange (Graham 1987; Shipley and Graham

1987). From that point on, the Maya Mountains were the subject of renewed interest.

In 1 992, the Maya Mountains Archaeological Project (MMAP) began discovering

sites near the divide of the mountains. What was found over the course of five years were

sixteen sites, thirteen of which were previously unrecorded. Several caves with artifacts

were also discovered. The Maya Mountains, previously thought to have been a

backwater, are now seen as a region with once bustling populations.

In light of the work conducted thus far it is inconceivable that the ancient Maya

would have overlooked the Maya Mountains as a place to exploit minerd and biotic

resources, or as a place to settle. The Maya Mountains lie within the Maya lowlands,

much closer to the major lowland sites than the highlands of Guatemala, the next closest

mineral source. It seems much more Iikely that minerals assumed in the past to have

corne &om the Maya highlands (e-g. Rathje 1973), such as granite for grinding stones and

pyrite for mirrors, ùistead came kom the Maya Mountains (Dunham 1998; Graham

The Bladen River Drainage

The Bladen Branch is a river system located in the southwestern part of the Maya

Mountains. The Bladen drains the mountains fkom West to east, eventually joining the

Monkey River. There are five sites that are nestled deep within the tributary valleys of

the Bladen, and among these sites is Ek Xux, the object of this study.

e B u - Trade Route

It is most likely that the sites dong the Bladen utilized the Bladen drainage as a

long-distance trade route to the foothills and fkom there to the cayes. Evidence for this

lies in the fact that sea shells that could ody be obtained fiom the Caribbean were found

in tombs at a site known as Muklebal in the Muklebal valley. Similarly there is evidence

that the sites of the Bladen engaged in regional trade. A grinding Stone found at Ek Xux

can be traced to Quebrada de Oro Ruin in the Ramos Quebrada, a few valleys to the east

of Ek Xux.

ce of the Riad-

The precise role that the sites of the Maya Mocntains piayed in the Maya world is

difficult to assess until M e r excavation is carried out. However, there are two principal

hypotheses conceming the purpose of these sites high in the mountains (Dunham 1990).

The &t is that the sites were settled as a response to the Maya collapse that was

beginning to take shape a Little after 700 A.D. By response, 1 irnply that the larger

lowland communities were beginning to break up and therefore that the Maya Mouritains

settlements were essentially peripheral sites that were last attempts to hold on to the old

ways. If this is the case, then the Maya Mountains sites have a very short life span, from

the end of the Late Classic to the end of the Terminal Classic. The second hypothesis is

that the Maya Mountains sites were inhabiteci much earlier and acted as small centers,

independently exploiting mineral and biotic resources and exporting them to the larger

Iowland sites. If this is the case, the sites were occupied throughout the florescence of

Maya civilization and played a key role in the ancient econorny.

Regardless of which mode1 is correct, these settlements were exploiting local

mineral and biotic resources @unharn 1998). Al1 five sites appear strategically located;

al1 are nearly quidistant ftom each other along the Bladen, and al1 five sites occupy

valleys with distinct mineral resources. It is reasoned that since regional ûade existed,

and each site was associated with its own distinctive mineral resource, that each site

exported its mineral resource for goods in exchange. If this is tme, then each of the sites

was acting as a component in a system of exchange involving larger Maya centers

throughout the lowlands.

Ek Xux

The ancient Maya site of Ek Xux, or black Fer de Lance in Kekchi, was narned

&er hding such a viper at the site. Ek Xux was discovered by the MMAP in 1993

along with four other sites that same year. Ek Xux lies on the western Bank of the Ek

Xux tributary, which flows into the Bladen Branch. The Ek Xux tributary flows roughly

north to south through the western half of the valley, crossing midway down to the

eastem half of the Ek XLUC valley. It continues to flow the rest of the way down to the

Bladen Branch on the eastern side of the Ek Xux valley. The Ek Xux valley, tapered at

the headwaters near the divide to the north, gradually widens farther south as it meets up

with the Bladen valley drainage. The Ek Xux valley, therefore, is an alluvial pocket

circumscribed by high sheer limestone cliffs, its area approximately 2.6 squared

kilometers. On the West of the valley is a small pass, which allows easy access to the

next valley to the west (Figure 2). The valley to the west has been dubbed AC pocket

because of the mouth of a cave system that points at Our campsite. The cool air rushes

out of the mouth and cools the camp area several degrees thus acting as a natural air-

conjitioning, or AC. The AC tributary, running parallel to the Ek X w tributary, also

flows into the Bladen river system. The AC valley is considerabl y narrower than the Ek

Xux valley and covers about a fifth of the area of the Ek Xux pocket, approximately 0.7

squared kilometers in ares The AC vailey, like the Ek Xux valley, is circumscnbed by

hi& sheer cliffs.

The Ek Xux valley offers a wonderfil opportwiity to study the natually isolated

site of Ek Xux. The valley or alluvial pocket contains water throughout the year, and

because high cliffs surround the pocket, the site's temtory is well dehed. The cliffs act

to contain Ek Xux and make it difficdt to cultivate land anywhere beyond the confines of

the alluvial pocket. Conditions are thereby created that act as a laboratory in which the

area utilized for agriculture can be accurately measured and the realm of Ek X w easily

detennined.

v Ek Xux is a modest site when compared to the large lowiand Maya centers;

however, when factoring in its surroundings one is awestruck that such extensive

settlement could be packed into a valley of this size. Ek X w is a Late Classic center

(Figure 3). Its main features consid of a large civic plaza, a maller stela plaza, and an

elite satellite group or east group. The stela plaza and the elite group are comected to the

civic plaza by parapetted and raised (sacbe) causeways on the north and east,

respectively. The east causeway acts as a dam separating Reservoir 1 on the north frorn

Reservoir 2 on the south. These reservoin are slightly lower in elevation than the rest of

the site and collect the runoff fiom the rainy season. The buildings of Ek Xux consist

mostly of earth core, which was most likely obtained fiom these reservoirs and fiom a

bluff just north of the site. The buildings' next most abundant constituent is river cobble,

likely coming fkom the very same bluff. There is a small amount of cut limestone that

makes up the southem façade of Structure 3 and the upper edge of the northwesteni face

of Structure 2.

By studying the layout of Ek Xw, major phases in the sequence of its

construction and the sources of its materials can be deduced. The stela plaza and northern

causeway are accommodateci by the chic plaza; this suggests that they were both the

result of planning and built at approximately the same time. However, there is little if any

accommodation in the civic plaza for the eastem causeway from the dite groups, which

indicates that the east group was likely added after the civic plaza. Neither did the

reservoirs accommodate this causeway, forcing the causeway to weave between them.

The reservoirs and chic plaza predate the causeway and perhaps the associated elite

cornplex. Separate from the civic plaza is Reservoir 2, which is closely associated with

Structure 24 and Terrace 12. Reservoir 2, Structure 24, and Terrace 12 may date apart

fkom the causeway and east group. It is likely, therefore, that Reservoir 2 acted as the

borrow pit for Structure 24 and Terrace 12, whereas Reservoir 1, being conternporary

with the civic plaza, acted as the plaza's designated borrow pit. The bluff was the

probable source of cobbles for al1 the structures of the site as well as the source of earth

cote for the stela and east groups.

. . ttes in Versus That at

To the ancient Maya, the most important cardinal directions were east and north.

East, however, represented the direction that the Maya held most sacred, for it was the

direction in which the sun god retumed victoriously from battle in the underworld. It is

for this reason that many believe that the Maya oriented their cities using the sumise as

their marker (Ashmore 1986). In fact, this is the reason that many antient Maya centers

also adopted a rnistake; that is, since the sun actually rises slightly south of tme east, so

do we h d that the ancient Maya centers are almost al1 oriented slightly south of east.

However, the sites of the Maya Mountains, arnong them Ek Xux, are unique in that they

are orienîed north of east, which makes little sense if they were building their sites with

respect to sunrise'. Peter Dunham notes that the reason for the odd orientation rnay be

that the Maya in this region were orienting their sites according to alternative criteria,

perhaps to the west. An explmation for the westward orientation is that the Maya

Mountains are littered with caves - in fact, some of the most extensive cavern systerns in

the world. The Maya regarded caves as the entrances to the underworld and so it would

seem possible that west, the direction to the underworld, would be part of this region's

ideology, forcing the orientation of the sites to follow suit.

Ek Xux Settlement

The settlement of Ek Xux spans two d e y s , narnely the Ek Xux valley and the

AC valley. The Ek Xux settlement, like the structures of the site core, consists of

platforms, what we will often refer to as mounds or structures. Platfoxms are the

foundations upon which were placed the actual dwellings; afler abandonment, collapse,

decay, and vegetational regrowth combined to transfomi abandoned platforms into

='moundS".

Dwellings of the p s t , like the Maya houses today, were wattle-and-daub

structures with thatch roofs. A typical wattle-and-daub structure was constructed by fmt

erecting the corner and subsidiary posts that would support the roof. The roof was made

out of huano leaves (Sabal mexicana). The walls were then built with thimer posts (ca

Quirigua in southeastem Guatemaia ais0 displays such an orientation, which may or may not suggest a comection between it and the Maya Mountain sites.

2-5 cm. in diameter). To this wail of "wattle," a clay-like mud was daubed onto the sticks

until a thick coating resulted. Lime was often then applied to create a white surface.

Evidence of daub is not uncornmon on some of the rnounds ancl iii archaeological

deposi ts in general.

The mounds as they appear today are formed of river cobbles, clayey soil, and

sometimes cut limestone. The cut limestone was used in the construction of platform

faces; it is primaril y a feature of the site core and seen li ttle at the surrounding settlement.

Platfonns consisted originally of a core of clayey soil and were faced, depending on the

sophistication of the structure, with river cobbles or cut stone. Based on what we know

about the architecture in the Maya Mountains drainage in Stann Creek, a core of clayey

soil is retained by an unfinished face of river cobbles, which in tum is faced by cut stone

(Graham 1994, pp. 79-80). In the Ek Xux zone, evidence suggests that cut stone was

used for platfonn faces only within the site core.

What we cd1 now mounds were actually well defined platform structures in the

past. However, with the trees growing in and around the structures as well as the Iayer of

mulch and dirt that has accurnulated on and around the structures, al1 that rernains of the

platforms in some instances are great indefinable rock piles. Collapse is comaon, and

stones from the upperrnost features on the top of the structure ofien roll off and reside at

the base of the structure. Rather than having straight sides, mounds are characteristically

sloped. The structures in the site core can be as high as 4 to 5 meters. The structures in

the settlement usually are anywhere nom about 20 centimeters to about 3 meters in

height. Al1 structures are roughly rectangular in ground plan. The structures that make

up the surrounding settlement number about 280 and span two valleys, the Ek Xux valley

and the AC valley.

of Ek Vallev Settl-

The settlement around the Ek Xux site core continues the southwest-northeast

pattern (Figure 4). To the north it extends in a line p s t the stela plaza, where it would

continue farther if it had not been for a bluff, which forces the line of settlement to veer

slightly to the west. The setîlement continues to the west, stopping just before the Ek

Xux streambed, then continues on the other side of the Stream until it hits the east cliff

face of the valley. The rest of the settlernent surrounds the core in a fairly uniform

pattern of distinct patio groups. We can see this clearly on the map, which contains al1 the

settlement within a radius of about 300 meters of the site core. The rest of the Ek Xux

settlement beyond 300 meters of the site core has not yet been mapped, only sketched.

A unique trend that should also be noted, as was pointed out by Andy Kindon, a

graduate student at UCLA, is that the settlement as a whole tends to be oriented toward

the site core. In other words, open plaza groups such as those that consist of three

structures often have the open side of their patio group facing the Ek Xux site core. This

is only seen at Copan and at 0 t h sites on the southem fillige of the Maya realm

implying a possible connection between the Maya of the Maya Mountains and the

southern Maya

Other distinguishing features that constitute the cultural material in die Ek Xux

valley are terraces. Though the Ek Xux pocket is relatively flat, there is still a gradua1

declining slope fiom the north to the south, which is the direction in which the river runs.

A half kilometer north of the site core, terrace faces nui along an est-west line,

presumably to retain the topsoil m o f f from the north to the south. One such tenace is

about 107 meters long, hHelve meten wide, and stands over a meter high on its south

side.

The topsoil runoff was most likely caused by extensive cleming for agriculture.

Here the vegetation is drastically different h m rest of the valley. The bush is low, thick,

and dry. The incline intensifies the farther north one gets, and in fact the number of

mounds decreases in this direction as well. This could have to do with the fact that it is

increashgly harder to prevent erosion From occurring in this northem section. This north

end of the valley must have been the least agriculturally viable area. The northeast

portion of the valley, on the other hand, contains the highest density of mounds. The

north central portion and the northwestem portion of the valley, on both sides of the Ek

Xux tributary appear to be very unlikely areas for agriculture, because these areas are

much too steep. The lack of terracing and lack of mounds add support to this assumption.

Below and on either side of the site core, senlement intensifies but tapers off the

farther south one moves, except along the Ek Xux tributary, which is lined with mounds

nearly al1 the way down to the Bladen Branch. The slope in this southem part of the

valley is not so apparent, and the lack of terracing supports the conclusion that this area

had Iess of a problem with erosion. The vegetation is lush and high and it appears that

this region was highly suitable for cultivation. Close to the Bladen the drop off increases

and evidence of erosion once again is apparent. The fact that this part of the valley was

not cultivated is confirmed by the absence of settlement altogether.

The AC pocket to the West is a narrow valley, which also sustained a relatively

hi& population. The AC pocket's most rnarked feature is the river terrace, which

parallels the modem river on the eastem side of the valley. It is a very narrow tenace,

perhaps 200 meters at its widest. The valley floor is flooded most of the year. Upon this

temice sits almost al1 of the settlement that was observed in the valley. Sorne very

extensive patio groups were found here, one consisting of six structures in a tightly

organized formation. Some structures are as high as three meters. The most promising

cultural feature, though, is what appears to be an administrative center. It consists of two

range structures aligned dong a northwest-southeast a i s . Two long structures extend to

the northeast on either side of the northemmost range stnicture, and a smaller structure

extends northeast fkom the southernmost range structure. The shape of this

organizational center takes the form of a giant "E . Interestingly enough, the double

plaza group's open ends face the direction of Ek X w in the very next vailey. Iust to the

north of this small center is a large, extensive and well-organized five-structure plaza

group, which may have served a residential purpose. The fact that this E-group lies close

to the mal1 pass leading to the Ek Xux valley and is onented toward Ek Xux suggests to

me that it is part of a subordinate site - a hamlet under the domination of Ek Xw. It rnay

have served the function of adrninistenng the settiement in this valley for Ek Xux. In

most cases, satellite sites of a dominating site have ail the features of a large center

(Dunham 1990). The E-group, however, has nothing more than two range structures with

no other feature of a typical satellite center. Such characteristics demonsirate that the

settlement in both valleys likely developed contemporaneously, and that the settlement in

the two vdleys probably acted under one central authority, Ek Xux. The two valleys

most likely operated side by side: those living in the Ek X w valley cultivated crops in the

Ek Xux valley, those living in the AC valley sustained themselves through the available

agricu1tura.i land in the AC valley.

Four Types of Housernound alEmugs

The settlement surrounding Ek Xux is of four types: clusters, patio (plaza) groups,

aligned mounds, and lone mounds.

The clusters are roughly circula-shaped groups consisting of anywhere fkom five

to nine structures in close proximity. Seven structures in a group, however, did not occur.

More often than not these clusters were not in any patio group formation, which is

unusud. The higher the number of structures per group, the more likely it was to find an

agglomerated rather than patiosriented pattern. In other words, domestic u ~ t s have the

tendency to agglomerate rather than form organized patio groups as nurnbers of structures

increase.

This c m be shown by creating an 8 x 2 contingency table where the two columns

are classified as less organized and more organized, respectively, and the rows from top

to bottom are the decreasing number of structures in the domestic unit. The data are in

the form of frequency of structures that were mapped within 300 meters of the Ek Xux

site core. The way agglomerated groups and organized patio groups were differentiated

by me was the orientation of the structures. Structures organized in patio groups are

oriented either parallel or perpendicular to each other. Agglomerated groups have one or

more structures that are skewed f?om the majority of structures in the unit. Using the

Fisher test on the contingency table, the p-value was show to be 0.0069. This implies

that we may reject the nul1 hypothesis, which suggests independence between the number

of structures in the domestic unit and the manner in which they were built. In essence,

we may accept the alternative hypothesis that there exists an association between the

building of stnictures in organized or disorganized groupings, and the number of

structures in the domestic unit. Interestingly, the units that were classified as

disorganized had only one or two structures that were skewed. The rest of the structures

of the larger domestic units were aligned regularly.

The patio groups norrnally consist of four to wo structures, however, some patio

groups were observed with six sûuctures. A patio or plaza group is defined by structures

organized around a cornmon patio or plaza space, much like the way the site cores of

ancient Maya centers are organized. In four structure plaza groups, the east or north

structures often contain a household shrine where the memben of the household placed

offerings to the ancestors (Ashmore 1986). This, however, is not always the case. Four-

structure and three-structure plaza groups cm be easily identified; two-structure plaza

groups, less so. Two-structure patio groups are identified by the L-shape that is formed

when the two structures are perpendicular to each other. When the structures lie parallel

to one another on opposite sides of the plaza, the group is harder to detect, especially

when the m o u d density is high. Aligned mounds, or structures aligned end-to-end, are a

unique settlement pattern at Ek Xux. O h the chah of structures numbee anywhere

kom two to four. These alignrnents can also be hard to detect when moud densities are

high. Lone mounds are those with no particular affiliation to any other patio groups.

Lone mounds are relatively distant fiom al1 other groups and comprise most of the mound

formations at Ek Xux.

Chronology at Ek Xux

A rough chronology for Ek Xux can be established based on two main sources:

artifacts fkom caves within a few kilometers of Ek Xux, and through excavations carried

out at Ek Xux.

Caves in Vicmty of Ek X u S . .

The main massif of the Maya Mountains is composed of igneous material;

however, most of the surface fatures, especially dong the Banks, are karstic (Wright et

al., 1959). Because of the abundance of limestone in the Maya Mountains, some of the

largest underground caverns in the world are found here. Caves were special places to

the Maya because they were regarded as the entrances to the underworld or Xibalba

(Sharer 1994, p. 524). For this reason, the ancient Maya deposited offenngs in caves and

rock shelters, while other Maya buried their dead in them.

Because the MMAP for the first four years concentrated on surface

recomaissance (locating and mapping sites and caves), much of what we know about the

ancient Maya in the Ek Xux area cornes from caves. The artifacts discovered in caves

date from the Late Classic (650 - 850 A.D.) to the Post Classic (900 - c. 1500 A.D.)

Period,

I was in charge of the cave reconnaissance in 1996, and 1 was involved in

sweying for caves the previous two seasons. This allowed me the opportunity to

observe first-hand what a tmly important place the Maya Mountains were to the ancient

Maya. In 1994 1 encountered a cave that contained a globular olla, an um, and a censer.

The globular olla, shaped in the f m of a turkey, was of Mixtec ongin. Whether it was a

vesse1 fkom Oaxaca nearly 500 kilometers to the west or whether it was made in Mixtec

style by a local, tells us that perhaps long-distance trade or at les t communication with

the Mktec zone characterized Maya Mountains communities well into the Post Classic.

This same part of the mountains may have acted as a major pilgrimage stop, for in

1996 I located Tusbil Pek, a large cave that is connected with an extensive underground

river systern. About 50 meters past the entrante, a 3 meter high and 30 meter long

artificially built stone wall obstmcts the main passage. In fiont of the wall was a large

stone-built altar littered with broken and intact vessels. Scattered about the floor were

broken ceramics both in fiont of and behind this great wall. Behind the wall is a hard

clayey slope, made to look like a pyramid. Cut into the dope are tenaces and a staircase.

Past this is a doorway into the next chamber containing severai other small rock walls.

Tusbil Pek was no doubt an important pilgrimage center attracting hundreds of people

and is so far the only one of its kind southeast of the Maya Mountain divide.

Several other cave finds add to this data pool and to what we know of the Maya in

this region. What they do not tell us, though, is whether the people that were depositing

their relics in these caves were actually inhabitants of the Maya Mountains or whether

they were pilgrims fkom distant lowland centers. What these finds do tell us, however, is

that evidnice of occupation in the Ek Xux area before the Late Classic has not been

encountered. This fact will help us in formulating a chronological sequence for Ek Xwr.

Through excavations at Ek Xux we recovered evidence that some structures went

through a few construction phases. In 1996, ritual Structure 15, located in the northern

end of the stela plaza, was excavated. The core was primarily composed of river cobbles,

and evidence indicated it was built in a single phase, which may indicate that it was a

recent addition to the Ek Xux site core. In 1998 four structures were excavated. Ody

Structure 23 was of multi-phase coostruction. Structure 23 is an elite residential structure

located in the east group. Approxhnatety 1 meter into the core of Structure 23 we

encountered evidence for a termination cache or ritual. Mixed with a burned layer of soil,

many vessels were discovered at this depth, fomiing a ceramic concentration of

approximately 2.5 x 3.5 squared meters. Termination ntuals are associated with new

construction phases. Structure 1 14, in a residential patio group northwest of Structure 23,

revealed no more than one construction phase. Nor did Structures 22 and 13 1, in a plaza

southwest of the stela plaza, reveal more than one constmction phase. Commonly, most

sites have several of these construction phases because they normally occur every few

decades. We have evidence of only a few construction phases at one structure, thus fa,

which suggests a very short occupation. Similarly, none of the ceramics recovered are of

the Early Classic or for that matter the Post Classic. From this information we gather that

Ek Xw: was in active occupation sometime between 650 A.D. and 850 A.D., the time

interval for the Late Classic.

Identification of the Household

Ikkh&Qu

Ethnographie and ethnohistoric data show that the fundamental building block of

ancient Maya society was considerd to be the household (Ashmore and Wilk 1988). The

ancient Maya were known to have lived in both nuclear and extended family settings.

Descent in these family groups was primarily patrilineal, though at Palenque there is

epigraphic evidence to suggest that rnatrilineality in conjunction with patrilineality was

known to have existed in the ruling fmly 's lineage (Schele and Freidel 1990). Farnily

groups, elite or non-elite, were the building blocks of society and were essential to the

swivai of the community or state. If these family groups struggled then the cornmunity

as a whole struggled.

Ashmore and Wilk (1 988) define the household as a small group of people that

share in activities, which contribute to the group's social growth within the cornrnunity.

The household may or may not consist of people sharing the sarne residence or dwelling -

- the members may be spatially separateci. The coresidential group is a group of people

who live in the same residence or dwelling but who may not share in those activities that

d e h e a household. The dweiling is the structure or area where residential activities took

place.

Ashrnore suggests that the group of people defined as a household must share in

one or more of the following activities: production, consumption, pooling of resources,

reproduction, coresidence, and shared ownership.

Although al1 members of a household may not be directiy involved in food

production, 1 assume that al1 members of the household are supported by food production

cmied out within the community, and in which one or more household members are

involved. There must be enough food to feed the members of the household in order to

maintain the socio-cultural system that serves to integrate the community. Therefore,

whoever in the household is involved directly with food production m u t make sure that

enough food is available to feed everyone in the household. Occasionally, the household

is scattered spatially throughout a site (Wiik 1988). 1 have often seen ihis among the

Kekchi villages of southern Belize. Though in most instances extended households live

close together, in some instances extended household members are far apart, though in

most cases still within the same village. Whether living under the same roof'or not, often

these members get together and share in the twice-a-year corn harvests. If they do get

together, the tracts of land used in cultivahg corn are proportionately larger because

there are more people to support. If they do not get together, the tracts of land are

considerably smailer, orj*xst exugh to feed a single household, though in recent years a

surplus is often grown so that some cm be sold on the market.

If we were studying the household on the individual level and how it produces

food, we would have to concern ourselves with being able to locate the members of a

household in a given vinage. However, if we look at the village or community in its

entirety, we need only assume that the household is the basic production unit. We do not

need to distinguish the role of rnembers of the household. In the case of Ek Xux we are

looking at the site as a whole and the members of the community as a single cooperative

unit. We are interested in the net effect of the al1 the people that lived and worked the

land at a given time. The hinctioning of individual domestic units is di fflcult to how

until more data are available. For the purposes of this paper 1 define the ancient

community of Ek Xux as a single component of a much Iarger socio-cultural system that

includes several other sites, and not as its own systern in which the individual domestic

households are the components.

b

Since we are dealing with al1 of the people of Ek Xux at particular times

throughout the cornmunity's history, we must look at several implications of the

sealement patterns. The organization of structures as interpreted fkom their layout could

represent four phenornena: 1) The greater the number of dwellings in a group, the iarger

the household. 2) The greater the number of dwellings, the wealthier the household or

the higher status the household. 3) The greater the number of dwellings, the greater the

number of fhctions represented by them. 4) The greater the number of dwellings, the

more t h e the household had to evolve into a well organized domestic unit.

For our purposes the fourth implication is the most satisfying of the implications

for it naturally includes implications 1 ) and 3).

The more time a household has been around the more tirne it had to reproduce.

Thus, the more structures would be needed to accommodate the new members of the

howhold. Similarly, the more time a household has been around, the more

nonresidential structures were probably needed to account for the increasing rnemben

(Le. more kitchens, more bathrooms). Kitchens are known to be small subsidiary

structures of penshable materials, and are rarely even identified. They are not

represented in the structures 1 have mapped. Shrines and non-residential buildings are

alrnost certainly represented and ultimately 1 will be able to identiS them when M e r

excavations are carrieci out,

Grcater number of dwellings could reflect status rather than tirne. Until I know

more about domestic unit functioning at Ek Xux, however, particularly elite residential

units, 1 cannot adequately account for this factor.

Immigrants to Ek Xux are assumed to have an extended household whether they

constnict one large or several smaller structures to accommodate the household. Their

dwellings are interpreted in the same way as households who have evolved in situ. M e r

the immigration, the number of residents in a domestic unit will grow steadily according

to natural birth and death rates.

The Developmental Cycle

e Develo

The concept of the developmental cycle has been applied in social anthropology

since the late 1950s (Fortes 1969 [1958]). It nas been utilized more recently in

archaeology in the work of Tourtellot (1988), Weeks (1988), and Haviland (1988). The

developmental cycle is a pattern of farnily growth, which repeats itself every generation

in a given society.

The first to utilize the developmental cycle model was Jack Goody (1969 [1958]).

Goody uses the model to explain the dynamics of domestic groups of the peoples of the

Gold Coast. Goody concentrates on two agricultural peoples in particular, the LoDagaba

and the LoWiilli. He notices that the units of production between these two peoples are

significantly different. The sizes of the fanning groups (the average count of males that

can work the fields in a &en household), or what he defines as the strengths of the

groups, are markedly different. Goody maintains that strength of the Lo Wiili famllng

group is greater that that of the LoDagaba because fission occun earlier in the

developmental cycle of the LoDagaba than it does with the LoWiili. Here, fission is the

process by which the eldest sons leave the household of their parents to begin a new

household. The fact that fission occurs earlier in the LoDagaba household would result in

the lower strengths of LoDagaba households. The main reason for this earlier fission is

the difference between the LoDagaba and the LoWiili kin structure and thus the

differences in systems of property relations. Among the LoDagaba, the eldest sons are

encouraged to move out of the house earlier, because when the father dies, the eldest sons

inhent nothing. This is because inheritance is matrilineal and oniy a rnember of the

father' s matriclan can inherit his property . Among the Lo W iili inheritance is patrilineal

and thus the sons are not as rnotivated to leave the household. This clearly explains the

numerical differences in households between the LoDagaba, and the Lo Wiili. These

differences will continue for they are closely linked with a cultural pattern, which repeats

itself every generation in a cyclical manner.

A similar situation occurs with the ban of Bomeo as J. D. Freeman (1 969 [1958])

attests. There are two ways that fission occurs with the ban domestic unit. The first is

partition, whereby a new domestic unit is created and residence lies neither in the

husband's nor the wife's natal houschold. The second way fission occurs is to leave

one's own farnily or bilek to start one's own family by out-marriage. This is

accomplished by taking up residence with one's spouse's family. In partition one can

still inherit goods fkom the natal bilek when the head of the family estate dies. When one

out-manies, however, one loses filiation with one's natal bilek, and does not inherit.

What Freeman notices is that large families tend to marry out into other families more

fkquently than they undergo partition. The reason behind this is that inhentance is

divided equally among al1 of the siblings in an Iban bilek. Therefore, it is more

worthwhile for one with many siblings to choose out-rnanying rather than partitioning

because through out-marrying to a small bilek it is possible to inherit the estate of the

spouse's natal bilek. For the one who has only one or two other siblings it remains

worthwhile to remain affiliateci with one's natal bilek, thereby staying entitled to a large

portion of the inhentance.

in Goody's and Freeman's ethnographies, a cultural phenornenon was explained

using the concept of the developmental cycle. Meyer Fortes notes that the developmental

cycle among the han has three main phases. The first is the phase that lasts fiom the

marriage of two individuals until the completion of their family. The second phase

begins with the marriage of the eldest child and continues until al1 the children are

marrieci. The final phase begins when the youngest child remains on the family estate

and ends with the death of the parents. Thcse cycles often overlap. The phases are no

doubt different among diffeient peoples; however, the concept of the developmental cycle

is applicable to any culture, including that of the ancient Maya. Fortes (1 969 [ 195 81) also

suggests that, '%esidence patterns are the crystallization, at any aven time, of the

developrnental process." It is this corollary that allows archaeologists to draw certain

inferences fkom the settlement patterns of ancient civilizations. Coupled with

ethnographie and ethnohistoric data, the developmental cycle can be utilized to infer

temporal trends in settlement.

. . e Develu- Prewous A r c w c a l -

Weeks (1 988) describes a historical rnissionary document fkom the eariy S panish

seventeenth century. It consists of a census nom 16 15 of five Maya comrnunities in

present day Campeche, Mexico. Weeks is able to estimate the composition of the census

and in so doing notices five different residence groups. Solitary groups most commonly

refer to single individuals or widowers, and nonfarnily residence groups refer to

coresidents with no identifiable nuclear family stnicture. The single family residence

group refers to couples, couples with children, or widowed persons with children. The

extended family residence group refers to a single family with one or more relatives other

than children (i.e. grandparents). A multiple farnily residence group refen to two or more

family groups that are connected by consanguinal or affina1 relationships. In al1 five

villages, single-farnily residence groups make up approximately 40% of the a11 groups,

extended family groups, only 5.8%, and multiple- family residence groups, 5 1 .1%. The

rest of the composition is ma& up of s o l i t q and nonfamily residential groups. The

trend then is large clusters of multiple family residence groups. The low percentage of

extended family groups suggests thzt many were ernbedded in the multiple-family

residence groups.

There are two ways to view multi-family residence groups arnong the Maya.

They could represent the typical patrifocal view of the family clusters in and around the

patriarch of the household, who is usually the eldest member in the family. Or they may

represent a simple case of lateral extension of family gmupings around each other with no

specific focal point in muid. Either way the tendency in this ethnohistoric example of

seventeenth century Maya is that we see families that are related living in close

proximity. However, conditions of the seventeenth century were obviously suspect

because the Maya had been missionized. Therefore, the most usehl data conceming

settlement patterns of Precolumbian Maya would be the census data, which were

collected by the very first missionaries. Evidence of this exists in the recordings of early

Spanish missionaries. When the missionaries fint came into Campeche in 1604, they

obsemed Indians living in what the Spaniards called rancherias or what we cal1

residential groups, clusten or plaza groups.

Weeks believes that each residential group had its own specific growth cycle, and

1 believe this is the case, especially in this instance, because the Maya were going through

a drarnatic transition phase under missionaq influence. 1 would argue, however, that

there are limited ways that the family growth cycle manifests itself and that a completely

different cycle does not exist for each household. The number of different ways a

household develops is limited, and becomes more limited the farther back in time we go,

especially in the Classic period. Evidence of a hi& level of uniforrnity in ancient Maya

settiement patterns is visible in the work of Gair Tourtellot (1 988) and William A.

Haviland (1988) on the developmental cycle of households in the Classic penod. We will

use Tourtellot's and Haviland's diachronie studies and supplement them with Weekys

data (essentially synchronie) on Maya households so that we obtain a clearer picture of

the dynamics of family growth during the Late Classic Period.

Haviland (1 988) has noticed strong evidence for the developmental cycle at Tikal.

He studîed one domestic group in particular, called Group 2G-1. He suggests that the

five structures of this patio group were constnicted at an average of about a generation

apart after the initial construction. The initial structure is larger than the rest of the

structures, which implies that it was the residence for the founding member of the

household. This is also evidenced by the age of the structure in cornpaison with other

younger structures. He also hypothesizes that the residents were a patrilocal extended

family. According to this hypothesis, Haviland then genealogically traces the burials

within the household. Though he believes, along with Wilk (1 988), that there is no

normative household focal pattern for the entire Maya area, he sees ample evidence for a

patrilocal household at Group 2G-1.

Tourtellot (1988) distinguished a trend among the domestic units at Seibal that

may be a trend at other sites as well, which is that the nurnber of structures in a given

patio group are related to tirne. As the nurnber of structures increases, so does the

crystallization of the family developmental process. He notes that if this is mie then the

settlement at Seibal should pass nine tests, which demonstrate whether the developmental

cycle is at work. The first test is to see if the number of dwellings within domestic units

increase with tirne. The second is that domestic uûts occupied for longer times should

have more dwellings than uni& occupied for shorter times. The third is that those new

domestic nits with few dwellings should be in the minority, whereas those with many

dwellings, in the majonty. The fourth is that al1 other dwelluigs of a residential group

should be approximately the sarne size (not including the largest structure). The f i f i test

is that the largea dwelling in a domestic unit belongs to the founder of the domestic unit.

The sixth test is that these largest structures should then be the eariiest structures in the

domestic mit. The seventh test is that there should not be more than one large structure

per domestic unit. The eighth test is that the later units should have fewer burials in

them. And the ninth test is that the larger domestic units should incorporate the features

of the smaller units, because the larger ones grew nom units sirnilar to the remaining

smaller ones.

d C w Seibal With

The developmental cycle is a key process at work at Ek X w and is supported by

the similarity of settlement patterns between Ek Xux and Seibal.

The first test is the framework for the developmental cycle. The fact that the

number of structures in a dornestic unit increases with time is an elementary observation

noted archaeologically at many sites and one which, 1 hypothesize, is taking place at Ek

Xux. If Ek Xux is an example of the developmental cycle, we would expect that larger

nine-stmcture clusters are older than eight-structure clusters, and which in tum are older

than seven-structure clusters, al1 the way d o m to the single youngest lone mouds. The

time interval between the consûuction of each succeeding structure in a domestic unit is

called a cycle. Often this cycle represents a generation or a twenty-year increment.

The second test, which is that older domestic units have more structures than

younger domestic units, goes hand in hand with the first test and needs no M e r

explanation.

The third test is that new domestic units with fewer structures should be in the

rninority, whereas domestic units with several structures should be in the majonty.

Tourtellot reasons that this would be an adequate test with only Seibal in mind. Seibal's

Late Classic Period, the period that he is focusing on, spans 280 years, surely enough

time for family Iife at Seibal to develop hlly. Therefore it is reasonable to assume that

more patio groups and fewer lone structures are what should be seen at Seibal, and, in

fact, this is what i s observed. It should also be noted that Seibal had a strong Early

Classic cornponent and that surely many of the family lineages established in Early

Classic times continued through to the Late Clwic. In other words, the entire Late

Classic population at Seibal did not consist of only new mivals - this was not the

beginning of Seibal's history but rather a stage in its development. However, at Ek Xux

we achially do have the formation of a community sometime early in the Late Classic.

An increasing influx of people fiom that point on began moving into the Ek Xux valley.

In fact, the most people are miving when the collapse occurs. Therefore, what we would

expect, based on the evidence so tàr, is that lone mounds would be the most abundant

form of domestic unit, because most of the domestic units in the valley had not yet

reached the "crystallization" of family growth. This is precisely what we see at Ek Xux,

the complete opposite of what occurred at Seibal. At Ek Xux, the majority of a11

domestic units have fewer structures and are newer, whereas the minority are well

developed ana are older.

The fourth test is that al1 dwellings should be approximately the same size

excluding the founding structure. Dwelhgs at Ek Xwc have not been extensively

excavated, so that dwelhg size is difficuit to ascertain at this time. However, in accord

with Rice's and Culbert's figures (1990), 1 believe we may be able to weed out most of

the residential structures from structures serving other purposes by selecting seventy

percent as the best approximation for structures seMng residential purposes. hdeed if

we sarnple, in order of basal area, the 132 structures within 300 meters of the site core we

obtain the seventy percent of the structures to be over approximately 37 squared meters,

with thirty percent, under. Using Naroll's (1962) relation, 37 squared meters is

approximately equal to a structure that harbors close to four individuals, the minimum

number of individuals in a nuclear farnily (Santley 1990). Since larger structures are

more conducive to residence than to mcillary purposes, the majority of the structures in

the seventieth percentile no doubt served residential purposes, whereas the majority of the

structures in the thirtieth percentile no doubt functioned as household shrines, kitchens, or

as other ancillary units. The maximum in this data set is 135 squared meters, or

equivalent to about 13.5 individuals, very reasonable for an upper lirnit on the number of

individuals per dwelling, according to ethnographie data Therefore, though the

difference berneen 37 squared meters and 135 squared meters seems to vary greatly, it is

only equivalent to the difference of the living space occupied by 10 individuals, still well

within ethnographic specifications for family sizes.

For the fifth and sixth tests, the larger structure should represent residence of the

founder of the domestic unit and thus the eariiest structure in the unit. We definitely see

this at Ek Xux. Within most plam groups there is a structure that is drastically larger in

basal area than the other stniciures in the dornestic unit. In fact, when we remove the

larger structures of the domestic units fkom our data pool we see that the range for

residential structures drastically decreases. The maximum basal area in the sample, which

excludes the largest structure of each domestic unit, is lowered to 86 meten squared (with

the exception of an outlier at 108 squared meters) or about 8.5 individuals per dwelling.

This makes our residential structures range between family sizes of 4 to 8.5 individuals,

excluding the founding structure of the domestic units. Nearly al1 of the largest structures

of the domestic units are above 37 rneters squared (-4 individuals), which is what we

would expect of large extended family migrations into the Ek Xux valley.

The exceptions could have been caused by various factors, among them social

standing. This agrees well with what was said earlier about social standing being related

to the time elapsed in one place. Lone mouds represent domestic units that had not had

tirne to crystallize. This is most likely why the largest structures of the larger domestic

units (3 and up) are in many cases larger than the [one structures. By the time lone

structures were built, many people had already settied the valley and had established

themselves in the community. The more people there are, the more difficult it is to

compete for social standing. So by the time the lone units were built, society was less

flexible with less upward mobility than in the original settlement penod. Exceptions

might include those immigrating to the valley with widely known Iineages. An example

may be Structures E and F. These would be good prospects for a test of this exception to

the nile in this hypothesis. Whether the largest structure represents the founding or oldest

structure remains to be seen in m e r excavations. However, since we see evidence for

this phenomenon at other sites, among them Seîbal and Tikal, we should expect it at Ek

Xux, especially since there appears to be one considerably larger structure in most

domestic wiits at Ek XKX.

Since the seventh test intuitively follows from what was discussed, no m e r

explmation is needed. The eighth test suggests that there would be relatively fewer

buriaIs in the newer domestic units with fewer structures than there would be in the older

domestic units with more structures. This stands to reason; however, since a thorough

excavation has not yet been conducted on many of the stnictures, we cannot hypoihesize

on this point. The ninth test states that if older domestic units began much as did the

newer domestic units, then we should expeci that the older domestic units should have

many of the sarne f e u e s that the newer domestic units have. At Ek Xw, the only

features that were noticed among the domestic units mapped were stairs, bridges between

structures, evidence of paved plazas, and lines of stones defining raised plaza floors.

Only a few of these features that were visible were shared among domestic units of

different sizes and thus stages of development. Another exarnple of a feature that

Tourtellot expects to be common amongst most domestic units is that the largest structure

is rarely located in the east, because this is usually the place for the household shrine.

This is not applicable at Ek Xux because the orientation of Ek Xux is far kom the nom.

Ek Xux is not onented according to the cardinal directions but rather along a northeast-

southwest axis as mentioned earlier. Excavations revealed that the shrine is not always in

the east. And the largest feature of a domestic unit is sometimes on the east. Structure

108 for instance, the largest structure of its patio gmup and the one most likely to be the

founding structure, is in the northwest corner of the group. This is highly unlikely for a

residential dwelling, even if it was built for the head of the family, because the northem

side of the plaza group is not comrnonly used for raidences. Therefore, the steadfast

rules that have to do with orientation of settlement at most lowland centers do not apply

as strictly here in the Maya Mountains. If we look at the largest structure of the lined-

structure residential groups, which are unique at Ek Xux, and compare it with the other

structures in the group, we see no particular order. Sometimes the largest structure is in

the middle; sometimes it is at the end. Not only does the configuration change but the

orientation of the line similarly changes. Sometimes the Iined group follows a northwest-

southeast orientation; sometimes it follows a northeast-southwest orientation. Because of

this unique feature involving orientation, 1 do not believe that Ek Xux can be entirely

tested using the ninth test.

It is obvious that Ek Xux and the other sites in the Maya Mountains have an

orientation of their own. Whether this is due to their own unique cosmological view, or

due to a Lack of attention to rigid urban plaxing, is unknown at this time. However,

what is known is that Ek Xux followed many of the trends that the larger lowland centers

followed, among thm, the developmental cycle. This is supported by what is obtained

through the survey of the Ek Xux settlement as well as through what we know of the

settlement patterns of the ancient Maya and what we know fiom ethnographie sources

and the archaeological work done at other sites. From the information that we cm infer

about Ek Xux, 1 believe that there is enough observed to support a hypothesis. That is,

that the developmental cycle at Ek Xux was a process that govemed the way people built

the structures of their domestic units.

In my desire to constnict a demographic mode1 at Ek Xux, 1 adopt an assumption

that is not a characteristic of the developmental cycle used by Tourtellot but rather a

qualification that 1 use solely for the purposes of being systematic. This assumption is

that [urger structures are older than smaller structum. In other words, not only is the

largest structure of a domestic unit the oldest, but the second largest structure is the

second oldest, etc. Though this is not necessarily hue7 this method is used to create a

rough model of the developrnent of Ek Xux. By doing tlus it should also be known that

the enor produced by doing this is quite insignificant, because structure areas do not

differ drastically fiom each other once the first structure of the unit is built. Similarly,

this has no effect on the final count at the time of collapse, which is the most critical point

in the model.

ter 4 - C a r r y w a c i t v

Introduction to Carrying Capacity

For decades specialists in the sciences have used the concept of carrying capacity

to descnbe relationships between phenomena and the arnount of support needed to sustain

them (Ellen 1982). Over the years anthropologists have begun adapting the notion of

canying capacity to describe human behavior (Rappaport 1984). In archaeology,

carrying capacity, or support capacity, is the measurement of an environment's potential

for ssutaining a hurnan population (Culbert 1995).

. . . Limitations have Prev-ed Accwate

Given the limitations of the archaeological record, the utilization of carrying

capacity has long fiusûated archaeologists because of its methodological complications.

Often we cannot accurately measure the energetic potential of a paleoenvironment to

sustain an ancient community. In the face of this difficulty, simply ascertaining the

relationship between community size and the supporting agricultural area will allow us to

gain valuab!e insights into how communities operate at the subsistence level and whether

or not there are general trends that can be defined. Understanding this relationship will

allow us to estimate agricultural area if site size is known or site size if agricultural area is

known.

Previous attempts at determining carrying capacity in the Maya area and

elsewhere have fallen short because of the difficulty in defining the boundaries of

sustaining areas in the archaeological record. The Maya lowlands have few topographie

barriers that would facilitate delimiting sustaining areas. Fomuiately, in the Maya

Mountains of southem Belize, Late Classic Maya sites oscur within alluvial pockets that

are clearly dcfïned by topographk barriers, and that lend themselves to agriculture. In this

study, the Maya Mountains site of Ek Xux will be measured and compared with its

ideally ckcumscnbed subsistence area, the Ek Xux valley. A proportionality constant

relating these two variables - site size and sustaining a r a - will result. Eventually, this

hial ratio or carrying capacity coefficient (CCC) may then be compared with the CCCs of

other sites in the Maya Mountains to generate a common coefficient that will

approxirnate the energy required to have sustained the associated populations. The

concept of CCC wili be used to illuminate the dynamic nature of Maya subsistence.

Previous Studies of Carrying Capacity

to Previous.shidies

The previous studies pertaining to carrying capacity sought a way in which the

archaeologist could put into perspective the amount of sutenance or land needed to

support a population. Though they may differ slightly in their methods, they al1 have a

comrnon objective in aîtempting to reconstnict the past in order to arrive at their

variables. Two variables in particdar are essential in determinhg my version of carrying

capacity, and they are site size and sustaining area. It is these variables and the methods

used to approximate them that the reader should keep in rnind when assessing the

previous studies, reviewed below.

Dickson

Dickson (1980) was one of the first Maya archaeologists to begin utilking the

term canying capacity to refer to a measmement of the productivity of a place and a

people. He defhed productivity in terms of nutritional mergy. There are three steps to his

approach. First, one must deduce the yield o f a given crop through a subsistence strategy.

Seconci, one must know how much of this crop was consumed by the average person.

And third, one must calculate the energy content of that which was metabolized by the

average person. In theory one can then deduce the nuiritional energy present for human

wnsumption on a given agricultural plot of land. Unfortunately, to obtain a figure for

step one would be difficult Not only did the Maya grow more than a single crop, but they

also cultivated their crops using a variety of agrïculhiral techniques: slash and bu.,

raiseci fields, temcing, and irrigation. The second and third steps assume that we know

the quantity consumed and rnetabolized by a prehistoric human being. For an archaeo

population, these are not observable numbers. Without solid figures, the estimable error

codd be quite high if Dickson's method was used. The only observable figures that

would be o f any value to archaeologists are the structures left by the ancient

population.

Mkl

A study of the relationship between surface area and population size was

conducted by Yellen (1977) on !Kmg Bushmen. Though not using the term canying

capacity, he is in essence attempting to establish a correlation between the !Kungls living

area and the !Kung's social unit size. This is pertinent to CCC since sustaining area and

site core size will be related. Yellen uses the limit of nuclear scatter, or the main

concentration of artifacts associated within a living space, to estimate the boundaries of

the area in which the nuclear family lived. A major factor, unfominateiy, affects the

application of Yellen's study to the ancient Maya in the Maya Mountains. We have no

observational data on the population sizes of ancient Maya comrnunities as we do with

the !&mg Bushmen. Of previous studies of wrying capacity, Yellen's methods best

approximate mine with one exception. Yellen deals with a mobile band level society,

whereas 1 deal with a stationary state level society. Still, limit of nuclear scatter rnight be

appropriate if we had conducted large-scale excavation at Ek Xux. As it stands, we must

use a difEerent concrete variable for site size that withstands the decaying effects of time

and one which is applicable to state level sites.

te Cat-

Site catchment theory is another technique that is relevant when discussing

carrying capacity. In fact, it has fiequently been applied in archaealogy. It estimates

exploitation tenitory using one variable, the approximate distance prehistaric humans can

travel at standard pedestrian speed, in a standard amount of time (usually a half day), in

order to sustain themselves. Sustaining area is therefore expressed by an encapsulating

concentric circle with the center being the site core and the radius being the distance its

inhabitants are willing or able to travel for daily sustenance (Hodder and Orton 1978).

Site catchment theory has certain drawbacks that discourage its utilization within

the Maya Mountains of southem Belize. Since site catchment is based on the premise that

the area of exploitation of a settlement is a hc t ion of the distance a human can walk in a

half day (the other half of the day is used for rehiming), it neglects the size of the

settlement. It assumes that al1 communities of peoples in a culture have the sarne

exploitation area. It would appear to be more usefil for hunter-gatherer societies than

state level societies, which depend on agxicultural ara being in close proximity to the

settlement. Nevertheless, it still may be a useful technique to estimate exploitation

territory for centers like Lubaantun. The centers deep within the Maya Mountains,

however, are different.

Site catchment analysis ignores ciifferences in the geography. Theoretically, site

catchent would be most useful on flat lands, but deep in the Maya Mountains the

landscape is too mgged for this method to be applied to accurately describe sustaining

area. In a direction where there are more hills and strearns to cross, the distance traveled

will be less than in a direction where there are fewer hiils and strearns to cross, but the

mode1 does not accommodate this. Thus, the exploitation temtory would have a different

radial distance waiked by humans in each direction. A concentric circle for exploitation

temtory is, therefore, a much too simplistic way at amving at an estimate of sustaining

area of settlements, especially in such rugged terrain as the Maya Mountains.

In the Maya Mountains however, we have the ideal situation for approximating

sustainhg areas. Sites like Ek Xux are situated in alluvial pockets that are circumscnbed

by high ctiffs. These delimiting nahual boundaries act far more accurately as limits for

sustainhg area then does site catchment theory .

Factors Which Influence Carrying Capacity

Chisholm (1 968) considered how resource distribution conditions settlement

potential at a location. It does so by shaphg carrying capacity. We can think of carrying

capacity as a dependent variable and 1) natural circumstances, 2) technological

improvements, and 3) area as independent factors. To provide a fuller picture, some

background surroundirig these factors will be discussed.

N a W circumsfances include soils, water, weather, and agricultural techniques.

Technological improvements con& mainly of Maya water storage technology or land

preparation techniques. Agricultural area is the factor that will be related to site size in

order to estimate carrying capacity.

Snil

Soi1 is the b t important factor that influences the carryhg capacity of a

settlement. We know settlements are situated near cultivable soils and are, therefore,

dependent on them because the yields received from the land must be greater than the

work put into the entire harvesting process. This process includes, most importantly, the

transportation to the agriculturai plot of land, and if this distance is too lengthy, then the

sustaining benefits are not worth the work put into cultivation and harvesting. The effort

put into the harvesting process is also variable according to the richness of the soil, for

the energy invested in cultivating poorer soils is more than that invested for richer soils.

Thus, the amount of time spent commuting to cultivate crops and the quality of soil

dictate settlement productivity or canying capacity.

Soils must be nch enough to support the Maya staple crops such as corn, beans, or

squash. Other important crops to the Maya were manioc, ramon (Brosimum alicusîmm),

and cacao (Theobroma cacao). Tropical min forest soils, however, are typically difficult

to cultivate due to pests and weeds (Nye and Greenland 1965). A select area for growing

crops has always been dong rivers and streams where nuirient accumulation is high

(Chisholm 1968). The Maya took full advantage of what the riverine terrain had to offer.

They commonly cultivated flood plains and alluvial pockets. And within the Maya

Mountains of southern Belize, alluvial pockets are the primary regions where agriculture

is possible. Secondary regions are thin hillside slopes, which were sometimes terraced.

ter & Water St- T-

For an agricultural people iike the Maya, good soils are of little use if water is not

plentifid in the area. The availability of water at a given site is a factor that is vital to the

concept of carrying capacity. The amount of water available at any settlement CO-

the number of people. Water is a seasonai resource and is managed in a variety of ways.

Inhabitants of a settlement need water for consumption, technology, and agriculture. As a

result, the shortage of water in a settled area diminishes the carrying capacity. The longer

the time taken to commute kom a site to a water source, the greater effect it will have on

diminishing the carrying capacity of the settiement.

The Maya Mountains of southern Belize receive up to 200 inches of rainfall a

year. Rainwater may have bem collected for use in small-scale cultivation, such as

kitchen gardens, but such collection more likely satisfied drinking, cooking, and cleaning

purposes. It is essential that rain water be stored in some fom of receptacle. Roof runoff

was collected in pottery containers; large-scaie storage was effected by means of

reservoirs and chultuns. Reservoirs are large-scale water storage devices that collected

rainwater for entire communities during the &y season. This was intended to 1s t the

community throughout the dry season and thereby increased the carrying capacity of the

settlement. Clrulfuns were sub-surface storage pits that served a similar purpose as

reservoirs, oniy on a much smaller level, and probably supplied one farnily or a few

families. Like reservoirs, they were lined with a baked clay layer which was

impermeable and which contained water quite well (Sharer 1994).

Seasonality affects the carrying capacity of settlements directly by af5ecting yields

fkom cultivation and harvesting. In the Maya lowlands the rainy season lasts fkom about

the beginning of June to December and the dry season runs h m January to June. The

Maya depended on the regularity of rainy and dry season intervals. Fluctuations in this

regularity could have serious repercussions regarding crop yields and thereby affect

carrying capacity. The fact that there is a five-month dry season limits agricultural

harvats to the rainy season, except where irrigation is used. A long rainy season could

delay the preparation of fields for the next crop. As a result, this could delay the

harvesting date. A long dry season, on the other hand, would affect planting, germination

and ultimately harvesting. Fluctuations either way would affect carrying capacity.

There are four main agricu1hu;il techniques that the Classic Maya used to for

cultivation. These techniques are important factors that influence carryuig capacity. They

are swidden, raisecl fields, irrigation, and tenacing (Sharer 1994). Different methods of

agriculture yield different results which in tum affect the carrying capacity of settlements.

Some methods are more efficient in certain areas and will produce more food for the

settlement. The carrying capacity of this settlement will then be rnuch higher than if a

less productive method was utilized. Each method is advantageous dependhg on the

environment. Humans will often resort to the method that produces the highest yields for

their settlement or to a combination of methods that produces the highest yield.

The swidden method of agriculture, also known as shifting cultivation, is a

method that was thought to have been the most commonly utiiized strategy by the ancient

Maya. Swidden agriculture involves the cutting down of the forest within the selected

plot of land that will be cultivateci. The organic debns that was felled is burned, which

retums plant nutnents to the soii. This cultivation continues for several years on the same

plot before nutrients are depleted and the productivity of the plot diminishes. The next

plot will be located at some distance Grom the first to allow the original plot to recover

(Nye and Greenland 1965).

Since the region that is needed for s!ash and b u m agiculture is quite extensive, it

often but not always necessitates the movement of settlement to accommodate planting.

For instance, in regions of high population densities such as the Maya lowlands, the

cuhivation of rnaize, or milpa cultivation, was one of the principal methods used by the

ancient Maya Many believe, however, that swidden agriculture produces less food per

unit area than other agricultural techniques known to the ancient Maya; thus use of

swidden alone would diminish the carrying capacity of the settlernent (Culbert 1995).

The high population densities for the ancient Maya that have been documented suggest

higher carrying capacities and, thus, more intensive techniques of agriculture were likely

to have supplemented milpa f e g .

A more intensive agricultural strategy utilized by the ancient Maya was the raised

fields method. Raised fields occur near slow-rnoving rivers and Stream upon alluvial

flatlands that are flooded during the miny season. These regions not only contain

sufncient water for intensive agriculture but they also are replenished with nutrients and

rninerals h m seasonal flooding. The rivers usually provide adequate drainage but

sometimes canals must be dug to speed up the drainage process. The seeds are planted

while the land is still moist and the crops are cultivated and then harvested before the next

rainy season. Siemens (1972) was the first to have discovered evidence of this

agricultural technique in Guatemala and along the Rio Hondo in northem Belize (1 972).

Ground and air reconnaissance along rivers revealed more evidence for raised fields.

Puleston (1 977) reconstructed the procedure and experirnentally applied it to the

swarnplands in northem Belize. Combinhg what he knew archaeologically of raised

fields and a sirnilar method that is used today in the lake region south of Mexico City, he

determined it to be a more effective agricultural technique than the swidden method.

Irrigation is the next method that the ancient Maya may have used in intensive

agriculture. Irrigation is a process thai involves the digging of canals fiom a fresh water

source (most commonly a stream or river) to the plot of land that was to be cultivated.

Controlling the water in the canals allowed the fields to be flooded when needed. It just

as quickly allowed water to stop flowing to the fields. Evidence of canals (imgation or a

drainage system) has been uncovered in Cerros, Belize. Bridges and dams that controlled

the flux of water through the canals have also been uncovered. Canals were used in

conjunction with raised fields because raised fields had to be artificially drained using

canals. During the dry season, instead of using canals for drainage, they could have been

used to supply a field with water.

Terracing is the last intensive agicultural method that the Maya utilized.

Terraces retain water, soils, and runoff during the rainy season. Terraced fields were

most cornmon in the Maya highlands of Guatemala and in the W e s t of Mexico (Sharer

1994), but many have also been discovered along smail hillsides in the lowlands

includuig the Maya Mountains near Ek Xux.

The main factor influencing carrying capacity is availabili ty of agricultural land.

The area available for agriculture delimits the population that can be supported. Al1 other

factors being equal a larger sustaining area should support a larger population, a smaller

sustaining area should support a smaller population. If the other conditions and

techniques that affect carrying capacity remain constant, as they would across a single

zone such as the Maya Mountains, then the site size becomes a huiction of the sustaining

area Hence, size and sustainhg area are both variables in a continuously interacting

system defined as canying capacity.

Susteinhg Area and Site Sue: Variables that Describe Carrying Capacity at Ek

Xux

Two variables define the carrying capacity of Ek Xw. They are sustainùig area

and site size, which is indicative of population. Once the carrying capacity was

calculated for Ek Xux, only then was it possible to define a measurement for reliability

and ulthately mode1 the development of Ek Xux through time.

Determining the boundaries for sustaining area is essential for estimating the

carrying capacity of a site. The Maya Mountains are advantageous in this respect because

the sustaining areas of sites are defined by surrounding cliffs. A delimited sustaining area

is necessary for detennining carrying capacity because sustaining area is the independent

variable in the CCC formula. The dependent variable is settlement area, which grows

through tirne u t i l an outside force acts upon it. in order to determine the CCC it is

necessary to have a welldefined sustaining area so that an accurate ratio may be

estimated between it and the settlement area.

Ek Xux, like most sites in the Maya Mountains of southem Belize, is located in

areas of alluviurn. These alluvial pockets are circumscnbed by high cliffs. The area of

agriculhualdluvium available io the ancient inhabitants of Ek Xux is then easily

estimated fiom two prime sources, topographie maps and aerial photographs. The

methods involved in calculating the agricultural area of Ek X w will be more thoroughly

discussed in Chapter 6.

SitmzG

A measurement for site size, the other variable in the carrying capacity

coefficienî, has changed throughout the history of archaeology. Some archaeologists

have used the height of structures, the number of stelae at a site, and some have utilized

severai of these factors together. Previously 1 have used the energy of the site core or the

work involved in transporthg building materials fkom their sources to their eventual

destinations (Abramiuk 1996). The transport work of a site can even be applied to such

cornplex site cores as Copan, where much work is put into detailing architecture. 1 have

found that the transport work of a site core acts as a sort of gauge, which measures the

cooperative effort involved in erecting the buildings of a center.

In this paper, however, we use the basal area of the structures of domestic units at

Ek Xux as the measurement for site size. The reason for using settlement area is to stay

consistent with the unit of our other variable, agricultural area, so that we may produce a

ratio of site size and sustaining area. Another reason for doing this is to stay consistent

with defining the component reliability for Ek Xw, which involves the interaction of

human living Wace with the environment. This will be discussed in the next chapter.

For C-ty C o e m

The carrying capacity coefficient for a site then is the simple ratio:

CCC = L(a)/A Eq. 1

Here, a is the set of basal areas of settlement a = (al, a2, a3, ..., aN) and Z(a) is

simply the sum of these basal areas. A represents the agiicultural atea for the site. At Ek

Xux A is the area of the Ek X w and AC alluvial pockets.

Arc haeodemography

eodempOrapby

To explore the concept of carryîng capacity M e r , it becomes necessary to know

how many people lived at a settlement at a specific point in the. Archaeodemography is

the study of estimahg past populations in a region, site, or associated with a structure at

one or more points in tirne (Santley 1990). The systematic process for estimating ancient

populations consists of three distinct steps. First, through excavation, the phases that are

represented by the recovered ceramics are detemined. Second, the number of platforms,

roorns, or household activity areas are counted. Third, the count is muftipIied by a modal

population per entity in each phase so that a phase specific population cm be deduced

(Santley 1990).

There are several problems, however, in eslimating past populations (Rice and

Culbert 1990). Rice and Culbert (1990) suggest that hidden structures, nonresidential

structures, and issues of contemporaneity, disuse, and household size are factors that must

be accounted for when estirnahg populations.

In certain circumstanca it camot be necessarily assumed that the Maya had

always built a platform as a foundation for their dwellings. In the Preclassic, for instance,

there is evidmce that the Maya built their dwellings on the ground without a substructure

(Cliff 1988). This however, changes in the Classic period when we see dwellings

elevated off the ground. Cliffs work at Cmos (Cliff 1988) shows this developmental

trend in increased use of substnictures through tirne. Nonetheless, we cannot exclude the

possibility, however unlikely, that some structures in the Late Classic did not have

substructures and hence were not detected in the count of structures at Ek Xux during the

reconnaissance of the valley. As is often the case as well, structures through time have a

way of disappearing. Low mounds o f earth core and cobble that were built for the

purpose of acting as foundations are ofien destroyed as tree roots and other disturbances

affect them. O b this results in elevated ground levels, but hawig no other features

such as corners that define them as structures, they may unintentionally be disrnissed as

natural features and not comteci as structures,

Though population figures are not utiiized in this paper directly, any of the

problems that exist in archaeodernography also exist at Ek Xux. For instance, it is always

probable that a structure was missed in the archaeological survey, or a struchae dismissed

because of insufficient grouads for identifjmg it as a structure. I believe, however, that

the probability is small compared to most other sites for one major reason: we know the

realrn of Ek Xux. Most structures are not considered structures because they are not

believed to have been under the domination of the site in question. At Ek Xux we know

the precise boundaries sumu11ding the community. Also, because Ek Xux occupies such

a mal1 area, it is reasonable to expect to fhd nearly dl of the stnictures. It should be

noted, though, that those few structures that may have been overlooked would cause the

actuai count to be an underestimation.

The fact that settlernent structures outside the site core are automatically believed

to be residentiai stn~chnes is another assurnption that could lead to e m r in estirnating

past populations. According to the pnnc@Ie of abundance (Willey and Builard l965),

many archaeologists early in the history of archaeodemography suggested that since the

site core is considered nothing more than a ceremonial center, then the numerous

structures on the periphery of the site core must be residential structures. We h w now

that this is not necessarily bue. As excavations continued, it was discovered that some of

the structures of plaza groups in the peripheral regions served different purposes, such as

kitcheos and shtines. Rice and Culbert (1990) believe that ancillary structures make up

between five and 30% o f the total structures at most sites. This figure can be adjusted to

fit more closely with the evidence.

The fact that nonresidential buildings make up a large portion of the structures

counted should simiiarly not be dismisseci easily. At Ek Xux, we face the same dilemma

as with al1 sites concerning the percentage of structures that were nonresidential. For Ek

Xwr 1 will use the maximum percentage that could have been used for nonresidential

purposes, which is 30% (Rice and Culbert 1990). 1 use this to err on the side of an

underestimation of the actual canying capacity.

Another issue that is pressing in archaeodemography is dating. Often the ceramic

phases at sites are not fine-grained enough to date a life span. Dimitri Shilnkin (1 973)

estimates the average life expectancy at birth to be well under a half o f a century. A

ceramic phase muiimally spans between 100 and 200 years. This is not nearly short

enough to depict populations accurately. As much as four generations may have been

bom and passed away in the span of a phase. Therefore, much of the emr in

reeonstructing population estimates cornes fkom the fact that we often do not have fine-

grained enough dating techniques to use to recreate a reliable demographic profile of the

site through thne. There are exceptions, Copan being one, where obsidian hydration is

used to help in accurately dating populations (Webster and Freter 1990).

We do have an advantage at Ek Xux over most other sites with the issue of

contemporaneity. For one, we are fairly certain that the heyday at Ek Xux was short-

lived and comprised the time interval that dehed the Late Classic period, A.D. 650 to

A.D. 850. This is a maximum time span of approximately 200 years. Many long-lived

sites use ceramic phases that an nearly equivalent to the time of occupation at Ek Xwt.

We can, therefore, conduct a demographic analysis of equivalent standing with many

other sites without the intensive excavations that are necessary at other sites. To segment

t h e M e r at Ek Xw, the developmental cycle will be utilized.

DiS\dSt

Disuse is a topic worth evaluating with the ancient Maya as well. It is a

possibility that structures were not in use for periods of time, thus leading archaeologists

to overestimate the population at a particular site. This is an interesthg phenornenon

observed arnong the ancient Maya, which deserves proper attention. It would seem

logical if a structure were abandonad that new residents or immigrants would take

advantage of the substructures already erected and use them for their own residences.

However, what we see for example at the end of the Tetzninal Classic and Postclassic

periods are instances in which new platrorms are built despite the fact that there are

already extant platforms to utiiize. This observation makes perfect sense, too, when we

consider the developmental cycle of the Maya, where the first structure is the largest and

the succeeding sûuchues in the domestic unit represent the succeeding generations.

Disuse is another issue that cannot be overlooked at Ek Xwc. However, it is

probably not as important an issue as it is with most other sites. The reason is that Ek

Xux has a relatively short occupation span, and abandonment and disuse is not as cntical

a question. in essence, there is very Iittie tirne for disuse to have an effect in a

commun@ that is growing. Rather, disuse is a phenomenon of stabilizing or gradually

disintegrating communities. None of these descriptions characterizes Ek Xux. It may be,

however, that disuse was a common phenomenon in Ek Xux's waning years, so 1 will

again underestimate the Ek Xux settlement and use the maximum figure that Rice and

Culbert (1990) give for structures in disuse, which is 20%.

Lady, the size of the household has always been a question with archaeologists.

In the past, ethnoarchaeologists have ofien put the number of people in a Maya residential

dwelling at between four and ten individualS. It has been observed, however, that Cho1

structures were believed to have housed as many as twenty-five individuals. The

standard number most archaeologists use in the Maya area is 5.6 individuais per dwelling

regardess of the floor area in the dwelling (Santley 1990). It seems, however, that the

number of individu& tends to be greater in dwellings with more roofed floor area than

dwellings with less mofed floor area. In these instances, Raoul Naroll's (1 962) figure of

10 squared meters per individual is a viable estimate. It is Naroll's figure that will be

used throughout this paper.

The household size at Ek Xux, or more appmpriately the number of people in a

single dwelling at Ek Xux, is difficult to assess. Therefore, Ek Xux suffers Erom the same

deficiencies as other sites when we estirnate populations. In those instances at Ek Xux

where population estimates are used, 1 choose to use Naroll's (1962) figure of 10 squared

meters of roofed floor space for a single individual.

It is important to note that for the purposes of this study, I have decided to use

settlement areas to study the development of Ek Xw. Though settlement areas can be

converted into population &mates, and population estimates can be converted into

senlement areas, it is important that we deal strictly with space. Space is the cornmon

"currency" in the interaction between humans and their environment. Space, or more

accurately, two-dimensional space or "ana", provides the environmental context fof

humans. References to numbers of individuals in the system at Ek Xux are avoided.

Utilizing areas rather than population numbers wiil enable us to apply the theory of

reliability to reconstnict the spatial expansion of Ek Xux through tirne.

ter 5-Beliabilitv ..

introduction to Reliability

to . . .

Reliabiliiy is defined as the pmbability that a unit will perfom satisfactorily under

specified conditions for a stated period of tirne. The unit may be a system, a subsystem,

or a wmponent of a subsystem. (Hoyland and Rausand 1994, Hillier and Lieberman

1986). Reliability is a concept that has been fkequently used in operations research

(Hillier and Lieberman 1986), and has made a large impact on the way electrical circuitry

and machinery are built. For this reason reliability is fiequently utilized in physics and

engineering.

Reliability as a human attribute has existed for as long as humans have been

around. However, the study of reliability did not corne into being until about fifty years

ago. It was used in the operationai safety of one-, two-, and four-engine airplanes and

was dehed as the number of accidents per hour of flight t h e (Hoyland and Rausand

1994). It was not until the 1930s that Walter Sewhart, Harold F. Dodge, and Hany G.

Romig established the theoreticai basis of reliability using statistical methods (Hoyland

and Rausand 1994). It was k t applied by a rnathematician named Robert Lusser, who

was called in as a consultant on Weraber von Braun's V-1 missile systern duMg World

War II. It was here that Lusser daived the product probability law of series components,

a law essential to systems applications (Hoyland and Rausand 1994). Reliability analyses

continueci into the post-war years as more complex products were being produced. In the

1970s the h t large-scale, multimillion-dollar project was designed to discover the risk

and safety connecteci to building and operating nuclear power plants in the United States.

The project was named the Rasmussen report (WASH-1400), and though it contained

rnistakes, it represented the fint attempt at malyzing a massive, complex system

(Hoyland and Rausand 1994).

Human lives now depend on accurate reliability estimates and strong

methodologies that are substantiated with tests. An example in which a flawed

methodology had a disastrous result was the failure of the space shuttle Challenger in

1986.

Richard P. Feynman was among those assigneci to investigate the catastrophe.

Thmugh field data obtained prior to the tragic launch, a range safety officer concluded

that the probability of failure was close to 4%. This probability, though small, is

unacceptable where lives are at nsk especially since it could have been reduced to 1%.

However, NASA inspectors before the planned flight claimed that the probability of

failure was 0.001% and they gave no supporthg quantitative estimates. Feynman's

group also discovered conceptual errors; for instance, despite evidence that the O-rings

were eroding, NASA officiais simply interpreted al1 previous manned missions as

successes. This had the same effect a s Russian roulette, and as Feynman noted, " the fact

that the fkst shot got off safely is little cornfort for the next" (Nash 1993).

S y stems

0-t of Cl- << ? 9

A system is a network of interconnected nodes or components that is able to

operate on its own when removed h m its context. Most applications of reliability have

to do with systems in which the cornponents that make up a system have been definecl

and are being tested for reliability and failure. However, before such a large-scale

systemic arialysis can be set into operation, a measure for the reliability of a component

must fïrst be defined, and a scale must be set for analysis. For instance, if one is studying

a molecde and one wants to analyze a molecule systematically, then the system one is

studying is the molecule; the components of this system then would be the atoms. It is at

this scde that one chooses to defhe one's system. in order to do this, clowe of the

systan must be shown. The atoms must be dehed as components because they are the

underlying constihients that operate the molecule. If a specified numbcr of these atorns

fails to operate, then the molecule as a system fails to operate. The components,

thenfore. must be shown to operate on their own, and the probability that the components

operate must be measured However, we know that atoms are made up of subatomic

particles such as protons, electrons, and of'ten neutrons, and that these could very easily

be consïdered the components of a system at the scale of the atom, where the atom is the

system. This redefining of our system could no doubt go on forever with quarks and

gluons, and for as long as a strong enough microscope aliowed. Setting a scale for a

system and an indivisible underlying constituent that behaves as a component is a

difficult task, and one's rationale for deciding to choose a scale and a component must be

clear before an analysis can take place. Nonetheless, in order to proceed with a systems

approach, questions such as closure and what we are defining as component and systern

must be addressed @Ilen 1982).

Evidence for system closure is not cntical for the purposes of this paper, but

ciosure is important when Iarger phenornena are studied. For this paper 1 wiil only

outline the broader system and concentrate on defining the components of the system, and

what wili be used as a meastuement for the reliability of the component.

Systems Reliabüity .

One requirement for applying reiiability to a system is that the system be closed,

as 1 have already discussed. The second reqllernent is that we identiS, a source and a

sink in the system. A source is the generator of the flow in the system whereas the sink is

the absorber of the flow in the system. The other nodes simply connect these points. The

flow between the nodes, however, will eventually end as a mathematical given. The

concept of reliability reflets the systern's ability to continue to function. Reliability can

also be utilized in measuring the iifetimes of systems and the probabilities that these

systems will reach a certain age.

There are a number of situations where reliability can be used in anthropology and

archaeology, especially with macm social phenornena. For instance, nodes can be

thought of as comrnrmities with the branches between these communities as the economic

or politicai interactions between them. Reliability is most applicable to commmities that

are connected in some form but not so enmeshed as to be dependent on one another. It is

also particularly useful if one can isolate the relationship that is connecting the

communities studied. In most large-scale social units such as communities, cities, t o m ,

or moieties, there are a number of interconnecting variables present. However, there are

usuaily distinctiy few signifcant levels at which these variables interact. In order to

compute reliability, the content of the relationship must be common among ail nodes. If

another content exists between nodes, then the latter content comprises its own new

system. Therefore, if one is studying economic interactions between and among

comrnunities, economics must be identified as the primary form of linkage between them.

Analyzing a set of communities as a single system, where the interactions among those

communities are not al1 of one content can be misleading.

In calcdating reliability, the stmcturalfunction of the system m u t be identified.

In other words, the arrangement of the nodes in relation to each other must be

detennined. There are three primary arrangements that nodes of a system can take. The

fbt is a series system, which implies that the flow througb the system will cease if one

node in the system ceases to fùnction? Ifall nodes or components are functioning, then

2 By ctase to flow or cease to firnction, it is lmplied that the flow fiom the source will not be able to reach the sink,

the system will continue to operate. The second arrangement is the parallel system,

which implies that the system will openite properly as long a s at least one component in

the system is still fùnctioning. The parallel system will cease to huiction if al1

cornponents in the system cease to function. The third arrangement that a reliable system

can take is the k out of n system. This system lies between the series and parallel

systems. It will fiuiction properly as long as at least k out of the total n components of

the system function. It wiîi cease to function, though, if less than k out of the n

components of the system operate pmperly. In theory, then, a series system is an n out of

n system and a parallel system, a 1 out of n system (Hillia and Liebernian 1986).

Calculating reliability oAen necessitates that we draw a visual representation of

the system or envision the structural function of the system. The purpose of this is so that

we can id&@ the cntical paths between nodes. According to ou. schematic, we must

then identify the minimal paths and or the minimal cuts in the systern. Minimal paths are

the minimal linkages beîween a source and a sink that ensure proper fûnctioning of the

system. Miaimal cuts are the minimal linkages between source and sink that, if severed,

will bring about the failing of the system.

Reliability, as we have stated earlier, is the probability that a system will fûnction.

Therefore, the knowledge of each of the components' probabilities must be known. It is

these individuai component probabilities that are used in order to calculate the entire

reliability of the system. There are two ways by which we rnay calculate reliability. The

f3st is by using the minimal paths to calculate the reiiability of the system. By using the

minimal paths, we link the systern in a parallel connection. Thus, reliability is calculated

by using the parallel systern of minimal paths and using the individual cornponent

probabilities.3 The second way to calculate the reliability of the system is to use minimal

cuts. By using minimal cuts, we link the system in senes comection. Hence, reliability

is calculated by using the series system of minimal cuts and using the individual

cornponent probabilities. 1 wili not explain the calculation itself for it is a tedious process

and beyond the scope of this papa, but see Hillier and Lieberman (1 986).

The process just described involves the calculation of the exact reliability;

however, it may be more appropriate to compute the upper and lower bounds for

reliability, in so doing, giving reliability a range of values or analogously a confidence

interval. However, this depends on the probabilities that we assign the individual

components and how accurate they really are.

The next feature of reliability is the ability to calculate a lifetime for the system.

The lifetime or t h e to failure can be computed if the failure rate is known, and the failure

rate can be computed if the stnicturai hction of the systern is known. In short, most

failure rates are increasing or constant failure rates. That is, as time goes on, a system

deteriorates more rapidly for every unit of time or deteriorates at the same rate for every

unit of time, respectively. Some unique systems, however, have decreasing failure rates.

That is, as t h e goes on the system has the ability to slow down the deterioration process.

Inevitably, no matter how much the system decreases its failure rate, the system will

3 A "componcnt probability" implies the rcliability of one node in the system of nodes.

eventually corne to an end.

A Systems Approaeh to Reiiabiiity along the BIaden Braoch

Reliability in social systems, theoretically, can be applied if one has dehed a

masure for the probability that a system will fail. Many social systems will have their

own measures for reliability. Needless to say, comm~ties do not al1 have the same

content of linkages and it is, therefore, not expected that they will al1 have the same

measures for reliabiiity. This, however, does not exclude the possibility that they may

behave in similar ways and that the dynamics of different societies may act in a similar

fashion. Reliability's applicability to contemporary anthropological communities is

extensive. If studia in reliability are ever initiateci they could be used to detect

communities that are Ul deche. These studies may also be able to shed more light on our

contemporary circumtances and mggest that perhaps even we are not invincible to

the ' s deteriorating effects. 1 believe that a good place to begin the study of reliability,

and particularly lifetimes, is in communities thaî have long since ceased hctioning.

. . Co-

In applying reliability in archaeology, 1 believe that the fïrst step is to be able to

distinguish the content of the interrelationships one is studying. In the Maya Lowlands

our knowledge of the interrelationships among sites has grown. There is evidence that

ancient Maya sites were independent and self-sufficient city-states. They were, we have

found, involved in a number of political engagements (Schele and Freidel 1990);

however, none were involved in any long-term political alliances until the Texminal

Classic with what we believe to be the beginnings of irnperialist expansion at Dos Pilas.

The primary bond that held Maya communities together was economic. For centuries the

Maya traded with each other. What we see, therefore, is something similar to Colin

Refiew's (1 986) peer polity model.

It must be rancmbered that the Maya region was one of the most densely

populated regions in the world before the industrial age. The Maya were engageci in

intensive agicultural programs to feed a large population on limited area of land. Some

Mayanists believe that overpopulation was the main reason for the collapse of Classic

Maya civilization (Culbert 1995). Subsistence demands may have exceeded the dietary

requirements for the growing population, which ended in a break-up of the social system

(Cuibert 1995). Another way of looking at it is that the carrying capacity reached its

m h u m and the Maya, unable to sustain themselves, began moving out to more

sparsely settled regions, abandoning the cities that they built. Some believe that the

canying capacity reached such a critical point that during the Maya "decline",

comm~ties in the mil regions were exporting food to the core and peripheral regions

of cities before it became too cost inefficient to transport food (Culbert 1995). However,

we see no evidence of food export in the Maya Mountains.

The Maya Mountain sites were no exception to the to the Maya decline. They

were intercornectecl inter- and intra-regionally; econornically we believe they

independently sustaiflecl themselves. The Maya Mountains, during the t h e that these

sites were active, were bustling with activity. This fact is apparent in the extensive

wealth of artifacts that the Maya Mountains communities have accumulated throughout

the Classic Period. Therefore, these highland sites, like their lowland counterparts, faced

a similar situation, narnely a large population and limited cultivable land with which to

sustain it. In the Maya Mountaias, al1 sites are associated with alluvial pockets

circumscribed by hi& cliffs, making agriculture very costly beyond the alluvial pocket

within which the site is located. Therefore, one would expect to find that the settlement

within the alluvial pocket is conditioned by the availability of agricultural area. As the

population grows, available cultivable land decreases. What we should expecf then, is

for cornmunities to reach their saturation point when they camot afford to expand any

farther Ïnto the pocket for fear of reducing the cultivable area to below the level adequate

to sustain the population. When these sites reached a level at which the growing

population or the area of settlement exceeded the area of land available to sustain the

population, the cornmimity ceased functioniag.

Xux

Ek Xux is considered to be the component in a system that includes four other

sites dong the same river system. Since we are studying Ek X w and its component

reliability, for this papa 1 will refhb nom firrther reference to the encompassing system

until more data are collected on the other sites. And though much of the theory behind

reiiability has to do with systems, some of it, such as failure rates and lifetimes, can be

applied directly to the component.

Component Reliabüity

R B W u Be U s 4 . . *

A wmponent's most distirguished features are its reiiability functions. These

consist of the reliability or &val function and the failure fùnction. The probability that

a component will function properly in the time interval (O,t] is the definition for the

reliability fiinction and is writtcn as R(t). The probability that a component will fail in

the t h e interval (O,t] is the definition for the failure function and is written as F(t).

Intuitively. these hctions are related to each other by the relationship,

R(t) = 1 - F(t) Eq. 2

Statistically, F(t) is known as the Cumulative Distribution Function (CDF). We

also h o w that ifwe differentiaîe the CDF we get the Probability Daisity Function

(PDF), Wntten as f(t), so that,

f(t) = dF(t)/dt = -dR(t)/dt Eq. 3

Where F(t) represents the probability of failure at time t, f(t) represents the

probability of failure per unit t h e at time t for al1 identical components at time t. This is

similar to what h a p p a when we differentiate a velocity huiction in order to determine a

projectile's position in space. We call the PDF, Rt), the failure rate. The failure rate is

usehl because we can then find the probability of failure for a component between the

h e s tl and t.2 by integrating the failure rate h m t l to 12, where t 1 < t2.

Another type of failure rate, which we will call the huzard rate, is another useful

equation. Througb some derivation it is found to be:

h(t) lIR(t)*dF(t)/dt = -lIR(t)*dR(t)ldt = -d/dt U ( t ) Eq. 4

This c m also be shown to be:

h(t) = fi(t)/R(t) = fi)/(l -F(t)) Eq. 5

The hazard rate is defïned as the probability of failure per unit rime at time t,

given that the component has d v e d until time t. A very flexible feature that reliability

has is its ability to include other causes for failure. Therefore, reliability is applicable to

those situations where more than one variable is known to cause a component's failure.

For these instances:

~ ( t ) = n ~ ( t ) Eq. 6

Here, Ri@) is the reliability hc t ion for one variable, and the true reliability

fùnction is the product of aii the individual reliability fùnctions for all the variables.

From this we can also get that:

h(t) = r hi(t) ~ q . 7

Here, hi(t) is the hazard rate for one variable, and the true hazard rate is the sum of

al1 the individual hazard rates for al1 the variables.

The mean time to failure is another unique feature that can be oblained by

integrating the reliability function h m zero to infini@ This may also be referred to as

the average lifetime of the cornponent and can be utilized to obtain the expected t h e to

failure.

CIO- a C e v e l

Communities behave in predictable ways just as do domestic units, or for that

matter, individuals. As is the case with most archaeology, since it is so difficult to

identio individuah in the archaeological record, it becomes necessary to look upon the

community as the object of study. The reason for this is clear in the Maya Mountains.

While communities are large and fixed, individuals are mail and mobile. The same is

true for certain phenornena in other sciences, such as physics. For example, the

properties of an electron cloud are easier to observe thaa the propdes of a single

electron.

Applying a systemic analysis at a scale srnaller than an entire community is

misleading. For instance, choosing domestic units as functioning components within the

site of Ek Xux (the systern) requires that we define the components and know their

probability of functioning. Though 1 believe that this can be done with contemporary

communities because we can defîne the household and identify its participants, in our

case with Ek Xux, extensive excavation would be requked to conduct such a systemic

enterprise. Therefore, I define Ek Xux as the indivisible constituent or component.

. .. e w t y o f E n

Extending this reasaning fkher it is possible to predict when a community fails

to operate. It fgils to operate approximately when buildings case being built or

renovated. If we c m hypothesize about the cause for the failure of the community and if

we know how the community functioned or developed, then we may construct a mode1 so

that the initial hypothesis is tested. Through reliability modeling this can be

accomplished. I therefore de fine Ek Xux's reliability, or probability of fùnctioning, as

the probability that Ek Xux's carrying capacity does not exceed the standard cntical

canying capacity for the Maya area. Since 1 h o w precisely the available agricultural

area of Ek X w and 1 know the extent of the settlement at the tirne of collapse 1 can easily

define Eik Xwt's reliability. I define it as such:

Reliability = (CCCC - CCC)/CCCC Eq. 8

Here, CCCC represents the standard critical canying capacity coefficient which

we derive h m Patrick Culbert (1995), and CCC represents the carrying capacity

coefficient at the site of Ek Xux.

ds Se- in the Field & in & Laborata

The objective in obtaining usable data for this paper was to be able to compute the

total settlement area of Ek Xux and the total cultivable area for the entire Ek Xux r e h .

Settlement area and agricultural area are the variables that are needed to calculate the

canying capacity coefficient (CCC) and only through c a m g capacity can we define a

measunment for reliability. The data were collected in the field and synthesized in the

laboratory .

sahRwAa

Much of the field data presented in this paper are cumulative. Four previous

seasons with the MMAP have allowed me the opportunity to s w e y entire sites, caves,

and surroundhg settlement. This in turn has provided me with well rounded fïrst hand

knowledge of the landscape and the archaeology in the Maya Mountains. My nrst

objective for the 1998 season was to finish mapping all the structures within 300 meters

of the site core. Andy Kindon had already Iocated and mapped many of the structures

within 300 meters; however there were still structura that needed to be mapped. A

complete s w e y of the Ek Xux pocket, however, was still far h m complete, and that

was my next objective - to finish sweying the entire realm of Ek Xux.

Mapping, or îransit sweying, was conducted using a transit and a stadia rod. For

mapping the settlement around Ek Xux, bath Topcon and Nikon Totai Data Stations

(TDS) were used. The batteries for the TDSs were recharged using a generator that we

had flown up to our camp. The stadia rods were extendable and had prism attachments.

All transit measurements beginning in 1998 were recorded in northings, castings, and

zeniths (NEZ), rather than the standard distance and angle measurements in previous

seasons. NEZs were found to be more efficient to graph by hand than the standard

method.

Structures were mapped dong a circuit of station points, which was then looped

back to our ongin point. From these station points the remaining structures were

mapped. We recorded the NEZs for each of the basal and summit corners, as well as

summit elevations on the structures and surrounding elevation shots. Points were also

shot to unique features of stiuctures, such as lhes of stones and stairways, as well as

natural feahues such as cliff faces, and bluff edges. When the corners of structures were

not visible fiom the TDS because of obstructing flora, edges to the structures were shot

in, which enabled the faces of the stnictures to be easily reconstnicted.

My next objective was to swey the rest of the Ek Xux and AC valleys. Here, the

plan was to locate al l or nearly al1 of the mounds in these pockets, then Pace the

structures' basal edges. In this manner, the north, south, est, and West basal edges were

recorded. I chose to use the basal areas of the mounds to represent the floor areas of the

dwellings. Ideally, excavation for post mould stains should be conducted on the

structures to detennine where the dwellings were placed; only then can the tme floor

areas be known. The next best estimate for the floor areas, however, is somewhere

between the basal and summit areas of the structures. This is because as we know through

tirne that structures collapse, making the basal area greater and the summit area

considerably smailer than it was originally. Since the summit areas were not measured

for many of the structures outside of 300 meters of the site core, the basa1 areas for the

mounds were made to represent the maximal floor areas for dwellings. Though the basal

edges of the structures were measured in the field, the basal areas were not calculated

until 1 went into the laboratory.

In surveying for mounds in the Ek Xux valley, the valley was divided into four

quadfaflts, namely the northeast, northwest, southeast, and southwat quadrants. The

corners of these quadrants met at a point just west of the site core. Concentrating on one

quadrant at a t h e , trails were cut in rough north-south transects, with the h t transect cut

along the quadrant's westemmost edge, and with each new transect aiways east of the

previous one. In this way it was possible to survey consistently in one direction sweeping

east along each of the quadrants. The entire quadrant could be accounted for and al1 the

mounds within each of the quadrants documented. To the north, the cliffs of the valley

tapered off at the headwaters and bounded the survey. Settlement at the northernmost

extent of the Ek Xux valley was evideatly not feasible because there was no flat area. On

the south, the heavily eroded region near the Bladen Branch bounded the s w e y . The

e s t and west sides were, siniilarly, bounded by cm faces.

For the AC valley, quadrants were not necessary. The AC valley was not as vast

as the Ek Xwc vaiIey, and was therefore easier to document. The AC valley was similarly

bounded by a constriction at the headwaters in the north, a heavily eroded flood plain in

the south, and cliffs on the east and West sides.

Al1 of the data that were collected in the field were then synthesized in the

laboratory. First, the structures that were transit-mapped using the TDSs were draîted

onto graph paper, which included al1 the structures within 300 meters of the site core. A

d e r was used to masure the sida o f the structures on the map. Where lengths or widths

of opposite sides differecl, a s was o f h the case because we were measuring collapsed

structures, the averaged measwement was used, and L * W = basal area was then

calculated. The rest of the structures that were sweyed were recorded in paces. The

nurnber of paces for each side was converted into meters, and the basal area calculated as

above.

An important factor that allowed me to utilize the developmental cycle, thus

permitting me to mode1 Ek Xux through the, was the identification of domestic groups.

The main types of settlement groupings at Ek Xux have been discussed in Chapter 2;

however, becaw the settlement was so dense, it was sornetimes difficult to distinguish

one domestic unit h m another. In these instances, where it was difficult to distinguish

domestic units, 1 looked for buildings that were closer to one another than to any of the

other surrounding structures. Where it appeared that the structures were more or less

equidistant fkom one another, I looked for signs of separation other than distance. One

example was the case of buildings blocking access to the plaza group. It was in these

instances that one had to look very carefully at domestic senlement patteming. For

exarnple, there were sometimes two plaza groups in close proximity. Because the

structures fonning the plaza groups were in close proximity, it was difficult to

differentiate between plaza groups. In this case 1 would look for access gaps between

plaza groups. Normally, access to plazas was visible only among structures that were

onented around that particular pl- Groupings that were independent of each other

were usually tigbtIy encapsulateci with few openings where access could be gained fkom

outside the group. With Ek Xux it was relatively easy to distinguish domestic units

because it was necessaiy to look for access gaps only between groups near the site core,

because it was here where the highest density of structures was found. Outside 300

meters of the site core, most of the domestic units were well spaced fiom each other and

were easily distinguished from one another.

Determining the boudaries for sustaining area is essential for estirnakg the

canying capacity of a site. In orda to determine the CCC an accumte ratio must be

established between sustaining area and site size.

The area of the Ek Xux valley, which was taken to be the maximum area for

agriculture, was estirnated by ushg two data sources. My first source was topographic

maps, which were based on aenal photographs. The Ek Xux valley was distinguishable

by the contour lines on the topographic maps. By using a cornputer program that traces

enclosed shapes, it was possible to calculate the area of the bottomland of the vailey

depicted on the map.

M y second source of data was land reconnaissance. Ideally, areas that are

recognized as uncultivable at the time the region was settled should be identified, then

subtracted h m the bottomlands. The resuit sbould be the area of alluviutn or the

agricultural area that susbineci the settlement. However, identification of uncultivable

soiis in the valley entails an extensive soi1 sampling s w e y of the valley and a costly

analysis, which was not feasible this season. Therefore, the entire valley floor was taken

to represent the total agricultural area of Ek Xux. Since our estimate for the agricultural

area will consist of the entire valley bottomland, the carrying capacity estirnate will be

modest.

Constrticting the Reliability Mode1

The basis upon which the reliability of Ek Xux has been modeled is largely

influenceci by the developmental cycle. As a time fiame for the model, developmental

cycles are utilized rather than years because it is unclear at this t h e how many years

make up a cycle at Ek Xux. If we use previous work in the Maya area to infer the number

of years representing a developmental cycle, then it is clear that a developmental cycle

should represent a generation (Haviland 1988; Tourtellot 1988). Generations for the

ancient Maya are u s d y calibrated at twenty years. Since this nurnber may change in the

fiiîure as furtfier excavations are conducted, we will initially use the developmental cycle

as our unit of time to construct our model only later substituthg years for the sake of

inteqmtive ease.

on of the DevelopmentPl Cvcle Copc-& the M a

As time progresses, the development of Ek X u is represented by the expansion of

settlement a r a 1 define the settlement area at any given point in time as one half of the

total basal area of the structures. 30% of the structures were deducted h m the total

because they represented aacillary structures, and 20% of the structures were deducted

because they represented structures in disuse (Rice and Culbert 1 990). The result is a

modest figure for the settlement area of Ek Xux that will be used in the model: 50% of

the settlement area. Utiluing what we know about Seibal and Tikal, we conclude that

each structure in a patio group was built once a cycle, or once a generation. Intuitively,

then, we assume that the patio groups or clusters with the most structures represent the

early settlement of the valley, whereas the lone structures represent the latest additions to

the site. Since the largest structure or the structure with the largest basal area within the

cluster or patio group is seen to represmt the fomding structure, it is also considered to

be the fht structure built. Where 1 differ £rom Tourtellot and Haviland in their utilization

of the developmentd cycle is that for the pupose of systematics, each structure built after

the first will decrease in basal area until the last structure of the group is built. The last

structure built would thus be the srnailest of the structures in the dornestic unit or the

structure with the smallest basal area in the cluster or patio group. Therefore,

extrapolating fkom previous work and for the purpose of systematics, size or basal area is

directly proportional to the age of the stnictwe.

This condition, however, makes an assumption about the order of construction.

For instance, perhaps the second Iargest structure in a plaza group was built fourth. In

this instance, our model would not change drastically. This is because al1 structures

constructed after the fust structure are approximately the same size as was show in

Chapter 3. Therefore, a slight difference in orda would have a negligible effect on the

reliability model. However, if most of the structures' sizes were not built as a fiinction of

t h e then we rnight prefer a different o r d e ~ g in our model. For instance, we may prefer

to order structures in a given plaza group according to function. Function, however, is

indeterminable unless detailed excavation of the structures is conducted. Therefore, a

different ordering for our model m u t wait until more data are derived fiorn friture

excavations. For the purposes of this paper, our model m u t be satisfied with the

condition that size or basal area is directly proportional to the age of the structure.

I fwe include t h e in the equation, what we have is a kaleidoscope of settlement.

For example the largest structure in a nine-structure domestic cluster is the first structure

in the valley that is built. The next developmental cycle consists of the first structure

built in the nine-structure domestic cluster pius the building of the second largest

structure in the nine-structure domestic cluster in addition to the building of the largest

structure of an eight-structure domestic cluster. The next cycle consists o f the first

structure, the second structure and the third structure built in the nine-structure domestic

cluster plus the fmt and second sûuctures built in the eight-structure cluster plus the k t

structure in a seven-structure cluster, and so on. The result is a senes of surnmations for

each consecutive generation. When this is completed the amount of settlement per

generation can be plotted. According to the definition of reliability and failure, the

pro babili ty of suMving decreases wi th each generation, while the probability of failure

increases with each generation by a the same amount. Mathematically, this may be

written as Eq. 1, or R(t) = 1 - F(t). Probability of failure increases because as settlement

area increases, the associateci area available for agriculture decreases. Sirnilarly, the

reason that the probability that the settlement will succeed decreases is because the area

available for agriculture diminishes. In order to arrive at a measurement for the reliability

of a settlement, we submct the carrying capacity of the settlement at a given point in the

fiom the criticai carrying capacity figure obtained from Culbert (1995).

tire-

Realm

By combining Culbert's m,uUmum figure for the critical ca-g capacity of 350

people per squared kilometer and Naroll's figure of ten squared meters per individual we

are able to convert Culbert's figure into a Settlement Area/Total Ajgicultural Area ratio

of 0.0035, the critical carrying capacity coefficient. Subtracting our CCC for Ek Xux at a

point in t h e then gives us the reiiability for Ek Xux at that time.

R(t) = CCCC - CCC(t) = 0.0035 - CCC(t) = (9 100 - C(a))/9 100 Eq. 9

Here, v a ) is the sum of the dwelling areas in squareci meters (m**2) at some

point in time in the development of Ek Xux. Time is measured in developmental cycles

and can be approximated using a generation of twenty years. The critical senlement area,

9100 m**2, is supported by 2.60 km**2 of agicultural land (the area of the Ek Xux

pocket).

R(t) = CCCC - CCC(t) = 0.0035 - CCC(t) = (241 5 - Z(a))/2415 Eq. 10

Here, Z(a) is the sum of the dwelling areas (mC*2) at some point in tirne in the

developrnent of Ek Xw. Time is measunxi in developmental cycles and can be

approximated by using a generation or twenty years. The critical settlement area, 241 5

m**2, is supported by 0.69 km**2 of agricultual land (the area of the AC pocket).

Since both valleys are included in the reaim of Ek Xux we use 3.29 krn**2 (2.60

km**2 + 0.69 km**2) for the total agricultural land. Therefore,

R(t) = CCCC - CCC(t) = 0.0035 - CCC(t) = (1 1 5 15 - Z(a))/ 1 15 1 5 Eq. I l

The same terms above apply here for the entire realm of Ek Xux.

The formulas above were derived in order to calculate the reliability of Ek Xux

through t h e for the Ek Xux valley, AC valley, and the entire realm of Ek Xwc for each

developmental cycle, respectively. There were nine cycles for the Ek Xux pocket, six for

the AC pocket, and nine cycles for the entire realm of Ek Xwc.

for the P r o b a u of * .

Knowing the reliability for Ek Xux through time we can easily calculate the

probability of failure for Ek Xux using F(t) = 1 - R(t), or calculate it independently using

the simple formula:

F(t) = CCC(t)/CCCC = Z(a)/a Eq. 12

Here, a is the settlement area of the site at a given point in time and a is the

critical settlernent area.

With R(t) and F(t), we have al1 the data we need to calculate the hazard rate of the

component reliability of Ek Xw, which in tum will enable us to assess the likelihood that

a site like Ek Xux will survive and for how long. The next section presents these results

in a series of tables and graphs, the most efficient way of presenting data of this kmd.

Thc section following this will interprct the results.

SettIement

From our data we find that settlement increases with tirne exponentially. This

would agree with the birth-and-death rate for human populations, which is characterized

by logistic growth. Since we do not have demographic information on what occurs after

the collapse of Ek Xux, the only part of the logistic growth c w e that is visible is that

part before the collapse, which can adequately be expressed by an exponential curve. h

addition to the birth-and-death rate mode1 at Ek X w we have another phenornenon

occurring, and that is immigration into the vailey. Therefore we expect the rate of

settlement development at Ek Xux to be very high. The &ta for the settlernent as a

fûnction of the in the Ek Xux valiey, the AC vailey, and both valleys can be found in

Fig. 5. These three cases are represented visually in Fig. 6. We are mostly concerned

with the settlement of both valleys together, because both valleys make up the entire Ek

Xux realm. However, studying each valley independently c m yield rnuch information on

the relationship between settlement in the two vaiieys.

Reliabilitv

Similarly, the data for the reliability of the Ek Xux settiement, AC settlement, and

the settlanent of both valleys can be found in Figs. 7,8, and 9 respectively. The

reliability data were calcuiated using the senlement data (Fig. 6) in conjunction with

equations earlier. Visually, the reliability data are depicted in Figs. 10, 11, and 12.

Again, as with the settlement data, we are rnostly interested in the Ek Xux valley and the

AC valley together.

Failure

The next set is the failure data for the settlement in the Ek Xux valley, the AC

valley, and both vaiieys together. The failure data were easily calculated using the

reliability data in conjunction with equation D, or F(t) = 1 - R(t). These data are located

in Figs. 13,14, and 15 for the Ek Xux valley, AC valley, and both valleys together.

Again as with the settlement and reliability data, we are most concerned with the entire

realm of Ek Xux. V i d l y , the failure data as a function of time for al1 three cases are

represented in Figs. 16,17 and 18.

The failure data are similar to the settlement data because they follow an identical

hendline. The only difference is that settlement data are represented in units of area,

whereas the failure data are represented in units of probability. The failure rate equations

for the each of the vaIieys are also printed on the diagrams. As can be seen, the

expoaential equation satisfies each of the three cases. The only exception is the AC

valley failure diagram. The AC fdure data exhibit a constantiy increasing tendency.

This mers nom the other two cases in which failure is increasing incrementally at a high

rate.

Ek Xux VaUey Setüement

The Ek Xux valley failure data are most adequately described by an exponential

equafon. This equation is:

F(t) = 0.0073et*(0.5516t), F(t) > O Eq. 13

Frorn this equation we obtain the probability density fùnction for the distribution

by differentiating the failure rate equation. The probability density function then results

in the equation:

r(t)=dF(t)/dt=0.0040e**(0.5516t), f(t)>O Eq. 14

Now that the failure rate equation and the probability density function are known

we can calculate the hazard rate, which wili be the most useh1 in calculating a figure for

the wliapse of Ek Xux:

h(t) = f(t)/R(t) = f(t)/[l-F(t)] =

=O.OO4Oe**(O.55 16t)/[l-O.O073e4*(O.55 16t)], h(t) > O Eq. 15

it must be remembered that the hmard rate as a fbnction of time is the probability

per unit time at time t, given that the components, or the domestic cycles at Ek Xux, have

functioned properly until thne t. It may also be dehed as the fraction of the population

of domestic cycles at Ek Xux ceashg to function per unit time in the interval between t

and t+At, given that the components have sunrived up until tirne, t. The development of a

community and the collapse phenornenon associated with it can, therefore, be uniquely

determined by the hazard rate equation. A direct coroiîary of this is: nie fime tiu

-se for a community facing cn'h'cal subsisteme failure con be defned when

the probability in the hazard rate equation opproaches I , where the maximum-

-Ci of the site is the time at which the hazard rate equation equals 1.

Or mathematically:

h(t) = 0.0040e**(0.55 16t)/[1-0.0073e**(0.55 16t)l = 1 Eq. 16

Solving this equation for t gives a maximum time of collapse of approximately

8.1272 developmental cycles. If the developmental cycle is valued at the length of a

generation, or 20 years, then we have a M'îTC of approximately 162.54 years d e r the

first settlement began being built in the valley. This figure does not reflect the length of

occupancy of the settlement; it only describes the tirne it would take for a settlernent to

breakdown, in accordauce with the developmental cycle and under the conditions

d d b e d . The approximate length of occupancy for Ek Xux can be calculateci without

reliability and using only developmental cycle theory. Occupants were still building

structures at developmental cycle nine so that, in theory, the occupancy span can be

stntched to ten cycles or 200 years, respectively. Demographic emigration is ciifficuit to

assess because it is difficult to construct a model of population dispersion d e r the

collapse of a settlement. The growth as depicted by the failure rate and settlement data is

exponential and a very sharply increasing exponential equation at that. This agrees with

the fact that Ek Xux was still in the growth phase of its development and had reached no

population plateau. Ek Xux was expanding and the exponential growth rate of the

settlanent mirrom the birth-anddeath rate model for expauding populations. Whether

the nirmber of lone mounds in the Ek Xux valley represents newly arrived immigrants or

family units breakhg off nom the ancestral patio group is difficult to know at this point

in t h e .

AC Valley SettIemeut

The AC valley settlement data, when plotteci, show initial settlement growth, as

do the Ek Xux valiey data, but the growth takes an overail form quite difXerent h m Ek

Xux. In the early history of occupation in both valleys, the rate of settlement appears

periodically to increase and decrease. The o v d l form that the settlement data take

diffm in that a natural exponential increase is seen with Ek Xw, whereas a linear

relationship is seen at AC. Predictably, a linear equation accurately fits both the AC

vailey settlement data and the AC vaiiey failure data, which suggests that a linear

equation may be more appropriate than an exponential equation. The best fits of both the

linear equation and the exponential equation were calculated for the AC valley. For the

best exponential fit, we receive an r - s q d value of 0.8734. For the best linear fit we

obtain an r-squared value of 0.9865, which is supported by the very low p-value of

0.00000732 and 0.000069 for the intercept and x variable, respectively. It should be

noted that the extrernely good fit rnay be attributed to the small sarnple size. A

polynomial equation of degree two or three greatly improves our fit; however, the

objective in regression is to accommodate the data with the simplest equation and not

necessarily the best-fitthg equation. For the sake of remaining conservative we wiil stay

with the linear equation, for any set of data can have a perfect fit with a polynomial

equation with enough degrees.

Nonetheless, senlement is increasing in the AC pocket, but not as we would

expect. Part of the reason for this may be because only six data points were recorded in

tirne. Therefon a smaller segment of the entire cwilinear relationship is plotted. Take a

circle for example. An arc of two radians would look much more like a straight line than

an arc of 90 radians. Sunilarly, the settlement is low to begin with in the AC pocket,

which makes it more difficult to increase incrementally at a high rate.

However, even taking these points into consideration, there exists something

"unnaturai" about the expanding settlement and increasing failure rate of the settlement in

the AC pocket. We see in the Ek Xux pocket that that there is a much fieer flow of

immigrants and population growth evidenced by the exponential growth rate. Why, then,

should the AC valiey growth rate not share in this ffeer expansion of settlwent? One

explanation is that the AC settlernent growth rate was regulated by an artificiai means.

Looking at the probability density function values between each developmental cycle can

help illustrate this. The Ek X w valley settlement consisis of incremental increases

separated by incremental decteases for the first three developmental cycles. Interestingly,

for the AC valley, the incrernental inmeases and decreases in its first three developmental

cycles follow this exact pattem. For the AC valley, the next, and last, developmental

cycles are consecutively increasing, which is also the case for the Ek Xux vdley

settlement. The difference is that in the AC valley, the interval between cycles four and

five consists of an inchation, foilowed by a declination between cycles five and six,

followed by an inclination between cycles six and seven, followed by two gradua1

successive inclinations between cycles seven and eight, and eight and nine. Because of

this unnaturai p w t h , al1 indications are that either immigration to this valley, or birth

within this vailey, was wntrolled by an administrative body. It seems more reasonable to

believe, however, that immigration into the valley was controlled.

An alternative is that the growth pattmi in the AC valley is simply an indication

of d e y preference by Mmigrants. The difficulty with this notion of preference,

however, is that when we inspect the Ek Xux valley's formative years, valley preference

does not explain the similar pattern of growth at Ek Xux. Nor does it explain how

musual it is that there would be no preference to live in the AC valley before

developmental cycle four. PPeihaps once data are collectecl on all of the sites in the Maya

Mountains, it will become clear that site preference had something to do with the growth

trends witnessed in the Ek Xux and AC valleys. The growth trends witnessed no doubt

stem h m both site preferences of immigrants and administrative control over

immigration, if the sites in the Maya Mountains were contemporanecms. This, however,

involves an intersite examination of the problem, which is well beyond the scope of this

paper. It seems more logical to me, however, for a comrnunity administrative body to

dictate control over an immigrant, rather than for an immigrant to dictate control over a

community administrative body.

Though the linear equation will be utilized over the exponential equation because

of its better fit, 1 wili present both equations to illuminate the ciifferences between a more

naturai exponential equation and an induced linear equation.

For the failure rate of the AC valley we obtain an exponential equation quivalent

to:

F(t) = 0.012 1e**(0.4741 t), F(t) > O Eq. 17

Differentiating the failun rate equation gives us the probability density fiinction

for the failure rate distribution:

Rt) = dF(t)/dt = 0.0057e**(0.4741t), ml s 0 Eq. 18

With the failure rate and the probability density hction, the hazard rate can be

obtained as follows:

h(t) = f(t)/[l-F(t)] = 0.0057e**(O.4741 t)/[l-O.Ol2le**(O.474l t)], h(t) > O Eq. 19

Setting h(t) = 1, we receive a MTTC for the settlement in the AC vdey to be t =

8.4973 developrnental cycles. If we use one generation or twenty years to represent a

cycle we get a time of collapse for the component at approximately 169.95 years after

sealement begins in the valley.

When we use the linear equafion to represent the failure rate data, which presents

a more accurate representation of the data we obtain the equation:

F(t) = O. 1222t - 0.445 1, F(t) > O Eq. 20

We differentiate this fglure rate with respect to t to obtain the probability density

fiinction for the failure rate distribution:

f(t) = dF(t)/dt = 0.1222 fit) ' 0 Eq. 21

With the failure rate and the probability density fiinction for the failure rate

distribution we get the hazard rate equation to be:

h(t) = f(t)/[l-F(t)] = O. 1222/[1 -(O. 1222t-0.445 1 )], h(t) > O Eq. 22

Setting h(t) = 1, we get a 'ITC for the settlement in the AC valley to be 10.8257

developmental cycles, or approximately 2 16.5 1 years if we use one generation to denote a

developmental cycle.

Thmfore, we receive a longer lifetime for the senlement in a linex equation than

we do in an exponential equation. It is difficult to say that had the settlemmt in the AC

valley been allowed to increase naturally, that is exponentially, the AC valley would have

followed a patteni like that of the Ek Xux valley settlement. The fact of the matter is that

the AC valley settlernent followed a very diffment course fkom the Ek X w valley, one

that is substantiated by the linear equation. nie linear equation suggests that the AC

valley would have survived 53.97 years longer than the settlement in the Ek Xux valley.

However, this longer lifetime would have only d t e d had the AC settlement continued

to control the population in the valley and if the AC valley had not been under the

dominion of Ek Xwr. The AC d e y was connecteci with the Ek Xux valley in several

ways, which can be inferreci through the settlement pattern and orientation of the

structures in the AC vaiiey.

The Ek Xux Realm

For the entire Ek Xux realm, settlement inmeases exponentiaiiy just as the

settlement in the Ek Xux valley does. This implies that the failure rate distribution

similarly will be represented by an exponential equation. We denote the failure rate for

the entire Ek Xux reaim as:

F(t) = 0.0056e**(O.S873t) F(t) > O Eq. 23

Diffmtiating the failure rate equation with respect to t gives us the probability

density fiutction for the faifure rate distribution for the entire realrn of Ek Xwc:

fit) =dF(t)/dt = 0.0033e**(O.S873t) f(t) > 0 Eq. 24

Substituthg both the failure rate equation and the probability density hinction for

the entire Ek Xux realm hto the equation for the hazard rate gives u s a hazard rate of:

h(t) = fTt)/[l-F(t)] = 0.0033e**(0.5873t)/[1-0.0056e**(0.5873t)], h(t) > O Eq. 25

Setting the hazard rate qua1 to one and solving for t gives us a time of expiration

for the entire Ek X w realrn of 8.0397 developmental cycles. If we use twenty years to

qresent a developmental cycle we get the t h e of collapse for the entire Ek Xux realrn

to be 160.79 years h m the tirne settlement begins being built at Ek Xux.

It is conceivable that the AC valley was initiaily used as overflow space in

response to increasing settiement strain in the Ek Xux pocket. That may be why there

appears to be no evidence of people living in the AC valley before cycle four, because

there was v n y little settlement stress up to that point. From cycle four until cycle nine

the AC valley had a regulated population influx, or as regulated as possible. However, by

this thne it was already too late, because our hazard rate indicates that the probability of

settlement failure in the interval [t, At] is one at 8.0397 cycles for the entire realrn of Ek

Xw. Therefore, reguiation was administered by Ek Xux as well as could be expected.

However, it was beyond Ek Xwr's capabilities to restrict people fiom settling once they

were ahady there. It does not seem possible that Ek Xux could also regulate whom they

permitteù into the domain of Ek Xw. The large number of single structures suggests that

it was not easy to stop immigrants, and before the ninth generation began, building at Ek

Xux began its dedine. Decline may not have been apparent to the new immigrants and

the new generation. Whether they h e w that Ek Xux was corning to an end is not known;

however, these single stnictures were most likely the 1st structures built at Ek Xux.

Defmhg Intermunicipal Boundaries

To Mer analyze the relationslip between the seâtlement in the Ek Xwc vdley

and the senlanent in the AC valley, the boundary that exists between thern must be

identifid. The section below briefly discusses the different boundaries and how the

archaeologist interprets them.

To delimit an area one must define the boundary. The concept of defming

boundaries is aitical in archaeology. Dunham (1990) identifies t h e means by which

archaeologists can deduce site boudaries. They are tbrough ernpincal means, cognitive

means, and predictive means.

Empirical boundaries are boundanes that rnay not have been recognized by the

peuple of the ancient community at the time. A way in which empirical boundaries can

be dehed by archaeologists is by analyzing the distribution of artifaîts and other

characteristic mains smounding a center. Many Maya centers had ceramic styles

which were unique to the center. Delimiting the center's trend in ceramic style cm allow

us to define the l e t s of this region with an economic boundary. Though ceramic styles

are a means to deduce possible economic boundaries? many times they are politically

insignificant, as will be discussed below. Dunham (1990) discusses previous predictive

methods used to define empirical boundaries.

Empincal induction in defining boundaries benefits fiom a great deal of previous

cultural knowledge of a society. Unfortunately, previous cultural knowledge is not

always available to archaeologists pnor to examination of the community. Denning the

economic boundary based on analyzing artifacts may not be a good indicator of the

center's political or territorial boundary. Especially with the ancient Maya, there is a

general trend for a large center's economic boundary to extend beyond its political

sphm. A Postclassic example is the Mixtec. The Mixtec Iived in what are now the

states of hiebla and Oaxaca in Mexico. Though a non-Maya people, the Mixtec ceramic

style (AD. 1300-1 500) fiourished well beyond the confines of their political control in

Oaxaca and Puebla, well into the Maya Mountains of southern Belize, in fact.

Bo-es C o ~ v e l u . .

Another method by which archaealogists define boundarks is through cognitive

means. Cognitive boundaries are those that locals of an ancient Maya community would

recognize, and which could coîncide with boundaries recognized by an outsider. Many

cognitive boundaries are geographicaily influencecl and refiect naturd boundarïes.

Because they are obvious delimiting markers, rivers or ravines offen form boundanes.

0 t h cognitive boundaries are artificially infiuenced. An example is a fortification

which demarcates territorial extent.

In applying a cognitive approach to delirnit boundaries, archaeologisîs encounter

certain obstacles. In the Maya Mountains of southem Belize, there so far is no evidence

of tension between sites. Therefore walls built for defensive purposa and for delimiting

territorial clairns are not encountered. One must take into consideration, though, that the

terrain itself in the Maya Mountains acts as a defensive b a n h . An ideally defined

boundary would be a geographic boundary, but one which is irnpassable. It must have

more obstructing power than a river or ravine and thus constrain the society within its

confines. We encounter something like this within the Maya Mountains.

. . etec-P&ctiv&

The last method archaeologists utilize to define boundaries is the predictive

approach. Most of the predictive methods are taken h m geography to simulate socio-

eccnornic interactions between centers. Two cornmon techniques that have been utiiized

in Maya archaeology are the Thiessen polygons (Hammond 1974, Garza and Kujack

1980) and the gravity mode1 (Duuham 1990). If little data are available about the

empincal and cognitive boudaries then both predictive methods will allow the

archaeologist to detemine where an intennunicipal boundary should Lie.

Interpreting the Relationship between the Ek Xux Valley and the AC Valley

Settlement

The ridge of karstic terrain that separates the Ek Xux valley nom the AC valley

could be posited as a cognitive boundary. This is supportai by the sheer presence of a

tiny administrative center in the AC valley. If no boundary was apparent to the ancient

Maya between these two valleys it is doubtful whether the ancient Maya would have even

built an administrative center in the AC valley in addition to the Ek Xux site core. nie

difficulty lies in determinhg the strength of this cognitive boundary. If indeed the

boundary had great importance to the inhabitants, how wodd it affect the development of

Ek Xux?

The matural (hear) trend in AC development may be explained by the fact that

Ek Xux was regulating settlement development in the AC vaiiey. When Ek Xux

coilapsed, settirnent in the AC valley also terrninated because it was controlled by Ek

Xux; or, it terminated its linear trend and continueci an exponential trend until what

happened to Ek Xux happened to AC.

One case suggests complete dependence on Ek Xux. This would explain the

lower final probability of failure for the AC vailey in cornparison with the Ek Xux valley.

However, it is likely that AC cooperated with Ek Xux in economy and üade at least. This

scenario would result in what has been described in the preceding section - both valleys

are taken together as a realm or system.

A second case suggests that although the AC valley sealement was under Ek

Xw's mie, as the AC valley fell into decline, the AC valley settlement shed control by

Ek Xux and continued on independently, following in the footpleps of Ek Xux. Once the

connection between the controller, Ek Xwc, and the controlled, AC, was severed, the

result was a r e m to a nahual exponential development for the AC settlement. The fact,

though, is that AC does not continue in Ek Xw's footsteps. Settlement in the valley

abates at a probability of failure of approximately 0.69, far lower than the probability of

failure of the Ek Xux valley, which is 0.89, and AC never r e m to an exponential

growth pattem. This may imply that the AC valley leamed h m Ek Xux's mistakes and

ceased further development in the AC valley. However, if this occurred, it suggests that

fiiture population growth in the AC vailey was abated, and the community cut its own

boat. This case is highly unlikely. which suggests that there was no breaking-fiee of the

dominating Ek Xux vdley, if indeed that was the form of relationship between Ek Xux

and AC.

The only problern with Hypothesis II is that it goes against what we b o w about

the ancient Maya political system. It was rare for the ancient Maya political system to be

so imperialistic as this scenario suggests.

The linear relationship between settlement and tirne may be more appropriately

suggested to be the r d t of internal regdation, that is, the AC settlement administered

its own immigration policies. We know that dominahg polities of the ancient Maya

political system rarely imposed much in the way of control except for the exaction of

tribute from subordinate cities. Though the AC valley is far fiom being a city, it was

more likely than not self-administered. The fact that the AC center was so smail and

without elite structures, and located close to the only easy access between the two valleys,

and onented toward the Ek Xux site core, suggests that it stood in hierarchical

relationship to Ek Xwr. This relationship to Ek Xux could have taken the form of a

lineage that had branched off one of the older farnily limages at Ek Xux.

The idea that the mal1 administrative center and thus the AC valley settlement

might have been regulated by a lineage nom Ek Xux also effectively explains the

unnaturai growth pattern of the AC valley settlement. Because the AC valley may have

been govemed by one lineage, nttministering policy was much a i e r where only one

body governeci. At Ek Xux, like rnost other sites, though there was one elite group

governing, they were no doubt inlauenced by other well-respected family lineages,

perhaps even relatives. In short, we see a more effectively controlled population growth

at AC rather than at Ek Xw because it was much wier to enforce a quota over fewer

people in a smaller area than it was many more people in a larger area.

The CoiIapse Phenornenon

Two models emerge which describe the development of Ek Xux as it approached

collapse. The first is that the two valleys were separate entities, and the AC valley was

dependent on the Ek Xux valiey socially, politically, and economically. The second is

that the two valleys were one - they only were divided geographically, but not

cogni tively .

Ibd&&ls

in the first model, if the AC valley was engaged in a dependent relationship with

Ek Xw, then it is nearly certain that the AC valley would fail as Ek Xux failed. That is

because there would be no more socio-economic and political fuel to keep the AC valley

fimctioning. The collapse for this model therefore would be the time of collapse for the

Ek Xux valley settlement.

In the second model, if the two valleys were one political identity, then the Ek

Xux valley and AC valley settlement would collapse together. Being one functioning

unit, both valleys would wperate with the larger valley wielding most of the political

power and being the ultimate controllet in the unit. The t h e of collapse for this model,

then, would be the t h e of collapse for the entire Ek Xux realm.

The lifetime for the nrSt model is approximately 162.54 years, whereas the

Lifetime for the second model is 160.79 years. The d.erence in the time of collapse

between these two models is only 1.75 years, unnoticeable in the archaeological record.

These lifetimes are so close to each other because the settlement of the AC valley makes

up such a negligible part of the total settlement in both valleys. The reason that the

second model has a slightly malla lifetime is that the settlement in the AC pocket is

mostly made up of domestic units with lower structure counts, or, altematively, domestic

uni& built later in the development of Ek Xux. To différentiate which of these models

would be more accurate in modeling the development of Ek Xux it will be necessary to

grapple with the data we have.

Since the AC valley settlement heeded Ek Xux administratively, yet dictated

policies on its own terms, then it suggests a relationship of understanding. If the Ek Xux

valley needed food, then surplus that was accumulateci in the AC valley would most

certallily be transportecl to the Ek Xux valley, although this seems unlikely because of the

size of the AC valley. Alternatively, it would seem that if AC valley were in need of

food, then the Ek Xwr valley would provide it with its suplus. Both valleys were within

the Ek Xwc realm and both cooperated with one another, headed by the site core in the Ek

Xux valley.

The hction that the AC valley served is difficult to ascertain. However, it no

doubt provided area for settlers to move into to support themselves later in the

development of Ek Xux. This was a response initially startecl probably because of the

growing population strain in the Ek Xux vailey. The fact that no settlement appears until

the fourth developmentd cycle, and that settlement was regulated, suggests that the AC

valley not only harbored overflowing settlers h m the Ek Xwt pocket but it was serving

its own special purpose. Could this purpose have been to grow food surplus for the entire

Fk XUYC realm, or could it simply have been the decisions made by the AC inhabitants?

The latter option seems the more plausible. If Ek Xux were d e r i n g fiom

insufficient food yield, is iinlike1y that Ek Xux set up AC for the purpose of increasing

food yield. This is because o f the AC valley's size, which is il1 suited for extensive

agriculture. If we accept developmental cycle theory, then one observation is clear - population began growing in the AC valley only fier over-population in the Ek Xux

valley. Once the AC valley began being populated, however, it constantly regulated itself

h m that point on. It will take t h e in excavating Ek X w and the settlement that

m u n d s it before an adequate explmation for the settlement pattern in these two valleys

presmts itself'.

Further Directions and Conclusions

T%nnne

A cntical prerequisite for model construction is the ability to test one's model.

Models in anthropology are often difficult to test because of the confushg and of€en

ambiguous language with which the original hypothesis is posited. Testability, an

integral feature of connrming the probabilistic nature of a hypothesis or model, can be

accomplished in two ways, verbally and numerically.

If the hypothesis or model is verbally constructed, then the results must be

verbally constructeci. As many know, v d a l communication rnay be appropriate for

description; however, when used to constnict and test models, misinterpretations may

arise causing discontinuity between the hypothesis and the test. The result is often an

ambiguous model.

If the hypothesis or model is numerically consûucted, then the remlts are often in

a numerical format. A model, when constcucted nmerically, can be tested in such a way

that the results are either confirmed or they are not. When tests and models are

consûucted numerically, then there are often fewer ways in which a result can be

misinterpreted. Reliability is one such numerical fbmwork where models can be tested

without the misiaterpretation that is ofien involved with verbally constnicted models. Of

course, numerically constmcted models and d t s tell us little if there is no verbal

explmation behind the mathematics, and it becomes necessary in anthropology to

integrate the two.

With the model we have constnicted with Ek Xux there are several ways of

proceeding with tests. Our model hhges on two main assumptions. These are that the

developmental cycle was at work at Ek Xux, and that the reason that the ancient Maya at

Ek Xux abandoned settlement was due to insufncient agicultural land to accommodate a

rapidly increasing population. The concept of reliability, then, was the tool by which we

created a model with the given assumptions. 1 supported the reasons in making my

asswnptions and I reviewed the procedure involved in choosing a measurernent for

nliability. This being done, the model constructed cm be tested.

DccuDancv

The test for occupancy is based on the idea that the developmental cycle was at

work. Therefore, for a start, several mounds in both the Ek Xux and AC valleys, fiom

those in higher structure domestic units to those in lower structure domestic units, m u t

be excavated for occupancy figures. An inîradomestic-unit analysis must be conducted

as well as inter-domatic-unit analysis.

Crramics, organic material, and other artifacts associateci with specific structures

of different types must be dated to see if, in fact, domestic uni& of groups of many

structures are older than the domestic uni6 of groups of fewer structures. If this tendency

does seem apparent then an average gap between the construction of consecutive

structures within a domestic unit must be deduced. This figure will, of course, represent

the new figure for the developmental cycle of Ek Xw, taking the place of what we have

estimated to have been twenty years. The total occupancy of the settlement of Ek Xux

dropped substantially d e r approximately 9.0 developmental cycles. However, it m u t be

emphasized that some temporary residences no doubt continued throughout the Post

Classic.

The relationship between structure size (ie. stmcture basal area) and age must also

be tested. The structures with the largest basal areas in the domestic groups with the most

structures should be one of the oldest structures at the site, and the oldest in the

settlement. Similarly the lone mounds at Ek Xux should represent the moa recent

occupants at Ek Xux. Whether the structures that were built after the largest structure in

the domestic unit were comecutively the next largest structures in the unit may also be

tested given a fine enough dating criterion. This is not critical, though, for the structures

built a&r the first structure in the domestic unit are relatively the same size as was

predicted by Tourteliot at Seibal. Excavations should stili continue to interpret the order

of the construction of structures in the domestic units. However, until the time a

conclusive investigation of the relationship between site size and site ordering is

conducted, for the purpose of systematics 1 suggest that ordering follow basal area - that

is, h m largesi to smallest.

Collasse

The developmental cycle at Ek Xux was found to be the moa probabilistic

process at work arnongst the domestic units, and will naturally support the premise upon

which the mode1 was constructed. If lack of cultivable land for a rapidly increasing

population was the main cause of the collapse of Ek Xux, then we would expect that the

collapse of Ek Xux would happen when the hazard rate for the models equals one. Two

collapse models were suggested. One attached the t h e of collapse to that of Ek X w

vailey, and the other atîached the collapse to both valleys together. From what we know

of the settlement patterns, however, we believe that the latter collapse mcdel is the most

likely. Excavations, as with the test for occupancy, serve as the best tests for the collapse

of Ek Xwr. Since our prime motivator in the collapse is proposed as subsistence, then we

would expect that evidence of malnutrition would be ever more apparent der the tirne of

collapse or approximately 8.0397 developmental cycles. Evidence for malnutrition can

be detected in the bones of those who died after this time period, or in changes in the

natue of the faunal remains. Similarly, collapse is often associated with a decline in the

popularity of the elite. The elite in response rnight have been ûying harder than ever to

gain support by initiating a series of ceremonid rituals, a process that may be apparent in

the archaeological record of rituai or cerernonial structures. Dating the abandonment of

Ek Xux is another appropriate test that we may use to compare the test figures with.

T h e o f abandonment is uidicaîed by dating the last d e r visible in the archaeological

record. Evidence for collapse rnay also be visible in the hieroglyphic texts of vessels,

wbich rnay yet be discovered.

In this papa 1 synonymously use the tenns hypothesis and model. 1 do this

because, particularly in studying social phenomena, 1 see no differwtiation between the

hypothesis and model. Models descnbing social behavior must be loosely constructeci

because of the numerous socio-cultural variables that constitute society. A model that ;s

loosely constnicteâ, however, must be tested, and is therefore equivalent in definition to a

hypothesis, for what is a hypothesis but a generalization based on observaticn, which in

him must be tested? In most sciences, the model holds a higher credibility than a

hypothesis because it has bem tested and therefore assumes a truth. For social

phmornena, I beiieve that a model whether tested once or several times must be

wntinuously testeci' a model of social phenomena is therefore always in a state of flux as

a hypothesis. I differentiate a firmly established rnodel fiom an ordinary model in that a

-y established model has been tested at l e s t once; an ordinary model - or simply, a

model - may not have been tested.

In studying social phenomena, it is essential that once a supportable hypothesis is

formulated, or equivalently, a model of social behavior constructed, that what has been

proposed be tested. In this paper 1 fom a hypothesis supporteci by the available data. 1

also propose tests that can be canîed out in the near fbhire that may add support to the

hypothesis proposed. Tests should, however, not stop ihere. Tests should continue until

we are nearly certain that they would recur given identical conditions. Often, we are not

given a chance to test the same hypothesis in an identical siîuation; this is the difficulty

with using a hypothetico-deductive approach to social phenomena. However, initially, at

least up through the fint test, I believe it is possible to utilize deductive reasoning in

conjunction with inductive reasoning to arrive at a firmly established model.

In the harder sciences it is possible to utilize a deductive approach throughout

one's research because there exist infïnitely identical phenomena to test. OAm this is the

case because it is the researcher who controls for the conditions. With social phenomena,

because thcm are so few instances in which there exist testable phenomena under

identical conditions, the researcher must be satisfied often with only one attempt at

testing the hypothesis. M e r which, if it is necessary, the researcher must proceed to

correct the hypothesis according to the results of the tests. The corrections to the

hypothesis, however, must remain indennitely, because it is rare for another phenornenon

in identical conditions to present itself in one's lifetime. Perhaps, that is the ciifference

between archaeology as a "science" and O ther sciences. Because archaeologists study

phenornena that necessitate t h e to unfolci, t h e is needed to apply a deductive approach.

It may be that archaeologists have not corne to the realization that archaeology may

conceivably be a science, but one much different fiom the harder sciences.

Archaeologists, Ullfortunately, use the harder sciences as a model for "science",

which is inappropriate for archaeological research. Archaeology, as a science, is a

discipline in which conclusions cannot be obtained within a lifetime's work. It is a

science that may necessitate several lifetimes and several Lifetimes more to amve

evennially at a M y established model. 1 do not think that we fWy comprehend or

appreciate the time span with which archaeologists work. If archaeology is a science, it is

a science that needs expanses of time for theones to be supported by enough identical

instances to be substantiated. The hard sciences are more gratifying, because within an

individual's lifetime, one can arrive at a theory that describes a recurring phenomenon.

For archaeologists, such gratification will remain eiusive, because one's research will be

data for another's work, which will be data for another's work, until theones describing

social phenornena are finally reached.

Since al1 our work as individuah is cumulative, we seek at least to reach a

"pendhg theory". Our conditions that we have established must be explicit and the

phenomenon that we are attempting to rnodel m u t be fully described. Hypotheses must

be more than the hypotheses of otha sciences. In essence, other sciences have the tirne to

make mrs, because their hypotheses can be retested. Archaeologists, however, do not

have this lwury. Hypotheses must be ngorously constructed after which tests may be

speczsed that would enable the modeler to gain additional support for the model. These

models, then may or may not have to be reconstnicted, depending on the results of the

tests.

It is hoped that this papa serves as an example of a work in the beginning phase

of this ideal. It is also hoped that after testing' and possibly d e r reconstructing the

model presentecl, the work will provide insight guiding other research under similar

conditions. Further research will either reinforce my model or will necessitate that it be

reconstnxcted once again.

As the result of this snidy, 1 hope that some light was shed on the dynamics of site

formation and collapse at an ancient community in the Maya Mountains. 1 believe that

utilizing the concept of reliability has been a usefbl tool. If the generated tirne intervals

Eom the mode1 correspond to the actual time intervals that can be obtained through

excavation, then it may be possible to d e t e e what caused the demise of Ek Xux and

produce, for the nrst the, a simulation of a site's dynamics through time. If the time

intervals do not comspond, then it wiH be necessary to make the suggested changes in

the mode1 and test it again on a different subset of sita in the Maya Mountains. As new

data aise, we must be ready to incorporate them in our hypotheses and test again. i t cm

be a tedious procedure, but the benefits are significant not only for our understanding of

the ancient Maya but also for our understanding of ancient complex societies everywhere.

Cycte 1 128.25

Stnicture Area CurnAm 89 12825 128.25 87 68 19635 91 67.5 263.75 n 44 ~ 7 . 7 5 56 31.25 339 90 30.1875 368.1875 88 28.75 397,9375

135 18.0625 416 140 16 432

Cycle 2 508.375

Cycle 3 767.875

Cycte 4 1 521.702

Area CumArea 82.875 82.875

58 140.875 56.1875 1 Q7.0625 53.625 250.6875

3ô.8125 289.5 37.125 326.625

30.1875 356.8125 30 386.8125

Stnicture Area CumArsa Sirudure Area C u m h 25 284.4825 284.4825 157 248.tSïf 249.1511 26 279.7275 56491 158 71.65607 320.8132 22 259.3225 823.5325 285 21 -85588 342.6691 23 246.3825 1069.915 159 17.48471 360.1538

23' 246.3825 1316298 180 15.61 135 375.7651 27 163.8 1480.098 161 15.61 135 391.3765

Cycle 5 2623.666

Structure Area Cum.Area Structure Area Curn.Area Slriicture Area Cum.Area 48 82.875 82.875 O 135.125 135.125 80 52.5 52.5 49 50.75 133.625 C 83.375 218.5 . 81 46.875 99.375 50 35.75 169.375 P 83.25 301.75 62 46.5 145.875

133 23.75 193.125 A 43.875 345.625 99 22 167.875 1 34 17.5 210.625 B 32 - 377.625 . 146 16.625 184.5

Stnicture Area Cum.Area SInicture Area Cum.Area 13 179.705 179.705 110 125 125 11 80.ûô5 260.39 109 107.625 232.625 12 64.7625 325.1525 111 68.0625 300.6875 14 39.05 364.2025 1147 56 356.6875 9 29.0975 393.3 112 45.5 402.1875

Structure Area CumAma Structure Area Cum.Area Structure Area Cum.Area 106 1 55 1 55 101 69.75 69.75 142 102.125 102.125 108 73.5 228.5 100 40.625 110.375 60 86 188.125 113 37.375 265.875 102 4025 150.625 143 60.9375 249.0625 107 36 301.875 1 03 31.5 182.125 6 1 15 264.0625

Stnidure Area CurnJuea Structure Ama CurnAea Structure Area Cum.Area 173 103.5894 103.5894 184 91.79471 91.79471 225 107.4737 1 O1 -4737 172 84.30126 267.6907 182 38.56002 130.3547 226 82.4279 183.9016 174 18.73361 286.6243 183 37.46723 167.822 227 78.99341 262.895 171 15.61135 302.2356 294 13.73798 181.5599 228 6822150 331.1166

Cycle 7 6283.613

Structure Area Curn.Area Structure Area CumArea Structure Area Cum.Area 117 80.4375 80.4375 115 73.625 73.625 T 87.5 87.5 118 68.0625 148.5 116 63 136.625 U 63 150.5 119 22.5 171 148 25 161.625 24 23.75 174.25

Structure Area Cum.Area Stnidure Area CumArea Sîructure Area CumAea 39 68.25 6ô25 67 305 105 83 81 81 38 59.8125 128.0625 65 74 179 84 40.25 121.25 40 30 158.0625 66 31.5 210.5 85 5.625 126.875

Structure Area Cum.Area Structure Area CurnArea Structure Area Cum.Area 76 56.1875 50.1875 58 156.3125 156.3125 82 60 5 60.5 75 35.75 91.9375 59 62 218.3125 141 33.75 94.25 78 34.5 126.4375 55 36.75 255.0625 124 21.375 115.625

Structure Area Cum-Area Structure Area CumAea StnictUre Ares Cum.Area 195 68.84603 68.84603 253 115.524 115.524 121 124 124 194 47.77072 1 16.61 68 251 80.0862 195.6102 120 63.9375 187.9375 196 15.61 135 132.2281 252 .37.46723. 233.0774 122 31.5 219.4375

Structure Area Cum.Area Strudure Area Cum.Area Slrucfure Area Cum.Area F 108.5 108.5 129 71.6875 71.6875 127 83.25 83.25 G 52.5 161 130 10 81.6875 126 39 122.25

Structure Are8 CumAree Structure Area Cum.Area Structure Area Cum.Area 139 52.5625 52.5625 70 61.875 61.875 144 47.25 47.25 138 50.315 102.9375 7$ 37.5 99.375 145 31.5 78.75

Structure Araa C u m h a Structure Area Cum.Area Structure Area CumArea 64 68 68 53 50 50 1 36 39 39 63 61.625 129.625 54 34.125 84.125 137 28.5 67.5

Structure Area C u m h Sltucture Area Curn.Area Structure Area CumArea 69 43.75 43.75 44 102.5 102.5 151 62.44538 62.44538 68 40 83.75 43 39.875 142.375 152 42.46286 104.9082

Structure Area C u m h Structure Area CumAea Structure Area Cum.Afea 153 262706 2622706 155 28.10042 26.10042 250 62.44538 62.44538 154 15.61 135 41.83841 1% 18.73361 46.83403 249 37.467 23 99.91261

Cycle 9 161 78.93

239 240

. 241 242 243 244 245 246 24 7 292 293 296

Total

Cycle 1 231.6724

Structure Area Cum.Area 286 231.6724 231.6724 288 140.8143 372.4867 284 139.8777 512.3644 289 89.76524 602.1296 285 56.35696 658.4866 287 39.96504 698.4516

Structure Area CumArea Structure Area 272 139.0971 139.û971 279 421.5063 421.5063 273 88.51633 227.6134 278 157.3624 578.8687 275 62.28927 289.9027 276 150.8056 729.6743 274 53.3908 343.2935 277 122.0807 851.155 271 53.07857 396.3721 280 31.84714 883.6021

Cycle 3 1318.847

Cycle 4 1 824.03

Structure Area CumArea Structure Area Cum.Area Slruclure Area Cum.Area 260 50.42465 50.42465 267 81 -95956 81.95956 282 69.93883 69.93883 259 32.78383 8320848 266 68.22158 150.1811 281 59.94757 129.8864 258 29.19322 112.4017 268 32.4716 182.6527 283 44.96067 174.8471

Cycle 5 2486.731

Structure Area Cum.Area Structure Area Cum Area Structure Area Cum Area 262 34.96941 34.9694 1 269 105.3766 105.3766 290 21 85588 21 .a5588 263 32.62771 67.59712 270 88.51633 193.8929 291 18.26527 40.121 15

Slnicture Area Cum.Area 300 107.7183 107.7183 299 104.1277 211.846

Cycle 6 3330.993

Structure Area 254 21.23143 255 54.95194 256 62.28927 257 12.64519 261 18.26527 264 131.1353 265 68.68992

Total 369.2083

Fig. 1 - Map of Belize with Major Sites and the Maya Mountains (drawing by Rita Granada).

GULF OC HONDURAS /

I square = I squared ki lometcr

Fig. 3 - Survey Map of ihc Ek Xux Site Core

Fig. 4 - Survey Map of Ek Xux Scttlement around the Ek Xu* Site Corc.

mg. 8: Satlement Area as a Fundon of fIme (CyclesJ. From top to Bottom: Ek Xux Realm, Ek Xux Valley, AC Valley

FIg. 10: Reliabtlity 8s a Function of Time (Cycles) for Ek Xux Valley

Ag. 12: Reliabllity as a Functlon of nme (Cycles) for Enffre Ek Xwr Realm

Ag. 16 Failure as a Function of Time (Cycle@ for Ek Xux Valley

Flg. 17: Fallum as a Fundon of Time (Cycles) for AC Valley

mg. II: Faltum as a Function of TIme (Cycles) for Entire Ek Xux Realm

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