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Modeling Settlement Patterns of the Late Classic Maya Civilization with
Bayesian Methods and Geographic Information Systems
Anabel Ford a; Keith C. Clarke b; Gary Raines c
a
ISBER/MesoAmerican Research Center, University of California, Santa Barbara b Department of
Geography, University of California, Santa Barbara c Reno, Nevada
First Published on: 29 May 2009
To cite this Article Ford, Anabel, Clarke, Keith C. and Raines, Gary(2009)'Modeling Settlement Patterns of the Late Classic Maya
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Modeling Settlement Patterns of the Late Classic
Maya Civilization with Bayesian Methods and
Geographic Information Systems
Anabel Ford,∗ Keith C. Clarke,† and Gary Raines‡
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*ISBER/MesoAmerican Research Center, University of California, Santa Barbara
†
Department of Geography, University of California, Santa Barbara
‡
Reno, Nevada
The ancient Maya occupied tropical lowland Mesoamerica and farmed successfully to support an elaborate
settlement pattern that developed over many centuries. There has been debate as to the foundation of the
settlement patterns. We show that Maya settlement locations were strongly influenced by environmental factors,
primarily topographic slope, soil fertility, and soil drainage properties. Maps of these characteristics were created
at the local scale and combined using Bayesian weights-of-evidence methods to develop probabilistic maps of
settlement distributions based on the known, but incomplete, distribution of Maya archaeological sites, both
domestic and monumental. The predictive model was validated with independently collected point-sampled
field data for both presence and absence, predicting 82 percent of undiscovered Maya sites and 94 percent of site
absence. This information should be of use in conservation planning for the region, which is under threat from
contemporary agricultural expansion. Key Words: Maya settlement, predictive modeling, weights-of-evidence.
Los antiguos mayas ocuparon las tierras bajas tropicales de Mesoamérica y produjeron una agricultura tan exitosa
como para sostener un elaborado patrón de poblamiento, desarrollado a lo largo de varios siglos. Se ha presentado
debate en lo que concierne a la fundación de los patrones de aquel asentamiento. Nosotros mostramos que las locaciones de los asentamientos maya fueron fuertemente influidas por factores ambientales, en especial la pendiente
topográfica, la fertilidad del suelo y las propiedades del drenaje de los suelos. Para representar estas caracterı́sticas,
se crearon mapas a escala local, combinándolos con el uso de métodos bayesianos de peso-de-evidencia a fin de
desarrollar mapas probabilı́sticos de la distribución de los asentamientos. Se tomó en cuenta la conocida aunque
incompleta distribución de los sitios arqueológicos maya, tanto domésticos como monumentales. El modelo predictivo fue validado con datos de campo independientemente obtenidos en puntos de muestreo para presencia y
ausencia, pronosticando el 82 por ciento de sitios maya sin descubrir y el 94 por ciento de ausencia de sitio. Esta
información deberı́a ser utilizada para planificar la conservación de la región, que se halla bajo la amenaza contemporánea de la expansión agrı́cola. Palabras clave: asentamientos mayas, modelación predictiva, peso-de-evidencia.
W
hen the ancient Maya civilization was at
its height in the Late Classic, from about
AD 600–900, a vast and complex system of
centers developed that included a tiered urban hierarchy of major and minor centers, household farms, and
remote buildings spread across the landscape. Populations of the southern Yucatan Peninsula—the greater
Petén surrounding northeastern Guatemala typifying
the Maya forest (The Nature Conservancy 2007)—
have been estimated to be as high as nine times that of
today. Currently, only a small fraction of the Maya settlements have been discovered, mapped, and analyzed.
Given this incomplete record, our research applied
methods that use the integrative power of geographic information systems (GIS) and Bayesian statistical modeling to predict the probable spatial distribution and
C 2009 by Association of American Geographers
Annals of the Association of American Geographers, 99(3) 2009, pp. 1–25 Initial submission, February 2006; revised submissions, March 2007 and April 2008; final acceptance, June 2008
Published by Taylor & Francis, LLC.
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2
Ford, Clarke, and Raines
number of Maya settlements from the subset of known
sites. The purposes of the modeling were to (1) assess the
influence of environmental constraints on ancient Late
Classic period Maya settlement and agriculture, (2) permit tests of the validity of the Maya settlement model in
the field, (3) allow the existing estimates of Maya population size and density to be assessed, and (4) propose
a map showing those lands with both undisturbed forest and numerous Maya settlements that have the most
to gain by conservation. Importantly, we offer the first
strong quantitative and spatial method for linking ancient Maya settlement patterns to ancient agricultural
patterns.
As an agrarian society, it is well documented that
the development of the ancient Maya transformed the
region known to conservationists as the Maya forest1
into a sustained and sustainable human landscape for
millennia. Although the development of the ancient
Maya is well researched, there remains debate over
the complexity of their subsistence adaptation and patterns of settlement distribution. The largest centers,
such as Tikal, arose in areas where no agro-engineering
feats have been identified, implying a constellation of
complex labor-intensive land use strategies that have
left no trace (cf. Nations and Nigh 1980; Nigh 2008).
The dense forest environment encountered today has
shrouded the archaeological view of the Maya landscape, one of the few ancient civilizations that emerged
in the now densely vegetated tropics (Bacus and Lucero
1999). The incomplete data on settlement distribution,
civic center locations, and land use stimulate debate
on ancient Maya population (e.g., Rice 1978; Turner
1990; Ford 1991b). In most cases, scholarship has ignored the quantitative relationship between the spatial
distribution of Maya settlements and its patterned interaction with the environment that controlled aspects
of everyday life. In this study, the significance of geographic resources to the Maya settlement and land use
patterns are considered for the culminating period of
the Late Classic when the ancient Maya civilization
was at its apex and nearly all habitation sites were occupied (Culbert and Rice 1990). We use the data fusion
capabilities of GIS with data from the recently developed University of California at Santa Barbara (UCSB)
Maya Forest GIS (ADL 2004). Using these data, we applied weights-of-evidence Bayesian statistical techniques
to explore the unknown components of the settlement
patterns as a supplement to those known to archaeology.
There is a substantial body of research and data on
Maya settlement and interpretations of patterns based
on surveys in sample areas of the region (e.g., Bullard
1960; Ashmore 1981; Fedick and Ford 1990). These
studies show that environmental factors played a role
in Maya site location, but the spatial implications of
these arguments have not been fully pursued. It is generally acknowledged that settlement densities were high
and that distributions should be related to agriculture
(Fedick and Ford 1990), suggesting a wide diversity in
agricultural pursuits (see Whitmore and Turner 2001).
These settlement data are used as a proxy for population
(Culbert and Rice 1990) and, by extension, land use.
Population estimates for the ancient Maya are most
often a starting point for discussions of land use and agriculture (e.g., Dahlin et al. 2005), with ranges from 100
to 1,000 persons per square kilometer or more, much
greater than existing densities in the same area. Major
centers, such as Calakmul, Tikal, and Caracol, have
proposed densities of 1,000 to 2,000 people per square
kilometer (Culbert and Rice 1990), equivalent to contemporary Sri Lanka. These estimated population figures are incompatible with other aspects related to
the steady expansion and development of the Maya in
prehistory (Turner 1978). Yet without a spatially distributed context for the Maya population, it is difficult
to validate the estimates (Turner 1990, 178–211). A
better understanding of the dimensions of settlement
patterns is required to understand settlement distribution and land use. This is the objective of our research.
The archaeological record is, of course, incomplete.
There are a number of reasons for this, but foremost
among them in the Maya context are (1) the difficulty
of exploring the mostly forested and isolated parts of
the region; (2) archaeology’s bias toward research on
the largest settlements; (3) the incomplete record of the
entire settlement context from peripheral farmstead,
household, and village to urban settings; (4) the variable nature of settlement data collection in the region;
(5) the lesser likelihood of survival of smaller settlements, and (6) the difficulty in surveying a geographically significant bounded unit such as a drainage basin.
Given these constraints, how can we interpolate the unknown Maya sites, both residential and civic, based on
the recorded partial record? One way to accomplish this
is with probabilistic spatial modeling. We chose to test
a predictive model of the patterns of Maya settlement
using the GIS at a local geographic scale of 1:50,000.
At this scale, we focus on field data collection in the El
Pilar area in the vicinity of Belize River (Figure 1). The
weights-of-evidence method was used to convert maps
for the area into probabilities of settlement using the
known point distributions of archeological sites from
the El Pilar area (Ford 1990, 1991a, 1992, 1993; Ford
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Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
Figure 1. Mesoamerica and the study area with application and
validation zone indicated.
and Fedick 1992). New field data were collected to validate the model. The results impact our understanding
of Maya land use in the past and resource management
for the future.
The Geography of the Maya Forest
The Maya forest region, as defined by conservationists (The Nature Conservancy 2007), includes
the tropical lowland setting of the greater Yucatan
Peninsula including parts of eastern Mexico, northern Guatemala, and Belize (Figure 1). The region was
densely occupied in prehistory. Today, it is characterized by rolling limestone hills and ridges (Turner 1978),
most covered by a deciduous hardwood forest. This verdant growth thrives on an annual rainfall average of
1,000 to 3,000 mm that falls mainly from June to January. A dry season runs from January to June. Activities
today are seasonal, impacted by this wet–dry deluge
and drought sequence, as they were in the Maya prehistory (Haberland 1983; Ford 1986, 1996; Scarborough
1998; Lucero 2002; Peterson and Haug 2005; see also
Ewell and Sands 1987). The Maya forest, a biodiversity hotspot, consists of large protected areas (Nations
2006), but population expansion and associated farming
as well as commercial agricultural and cattle pasturage
are pushing the development frontier into the contiguous forest areas. Until recently, 85 percent (30,000 km2 )
of the Petén of Guatemala was covered with semidecid-
3
uous subtropical moist forest. Less than 50 percent now
remains (Sader et al. 2004).
Land clearing often reveals the location of archeological sites and leads to their destruction by erosion,
looting, and plowing. With the long-standing interest
in the Maya, the impact of tourism has been slight,
but larger sites with monumental architecture are often developed for tourism and some rank among the
greatest existing windows into the ancient Maya world.
Mapping of smaller ancient sites, although incomplete,
varies by country. Current trends to move to digital
coverage have produced a surprising amount of GIS
data that can be gathered from existing sources and
mapping agencies in Belize, Guatemala, and Mexico.
Despite the spotty nature of the accessible settlement
data in the Maya area, it is clear that, at the height of
the ancient Maya during the Late Classic, the number
of inhabitants of the region as a whole was significantly
greater than that of today[,] with little difference in
geographic resources. The general climate regime has
retained its wet–dry annual cycle within the context of
a general drying trend over the past 4,000 years (Deevey
et al. 1979; Hodell, Curtis, and Brenner 1995; Curtis,
Hodell, and Brenner 1996; Haug et al. 2001).2 It is also
evident that, despite the blanket population densities,
settlement and land use patterns were far from uniform
over the landscape (e.g., Turner 1978; Fedick and Ford
1990).
The ancient settlement distribution in the Maya
forest relates to a complex mosaic of regional land
resources (Fedick 1996; Ford 1986). Settlement densities are recorded as the highest in the well-drained
hills of the region (Bullard 1960; Puleston 1973; Rice
1976; Rice and Puleston 1981; Fedick 1989; Fedick and
Ford 1990). For the El Pilar Study area, 98 percent
of the residential sites tested dated to the Late Classic period (Ford 1992; Ford and Fedick 1992). This
is the period when the land use was at its greatest
and the overwhelming majority of sites were occupied
(Culbert and Rice 1990). The Late Classic is the period
that we considered in our modeling of ancient Maya
settlement.
The limestone ridge lands are concentrated in the
central areas of the Maya forest (Turner 1978). The
area is characterized by shallow and fertile Molisols
(also known as Rendzinas; Food and Agriculture
Organization of the United Nations [FAO] 2008) of
excellent quality (Fedick 1988, 1989), representing
between 1 and 2 percent of the world’s tropics, yet
nearly 50 percent of the soil around the ancient Maya
city of Tikal (Fedick and Ford 1990; see also Kellman
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4
Ford, Clarke, and Raines
and Tackaberry 1997, 82). Soil on these ridges is enriched by surface organics derived principally from leaf
litter (Kellman and Tackaberry 1997). The thin soil
covers broken limestone bedrock terrain and is superior for the hand cultivation methods that characterize traditional Mesoamerican farming (Fedick 1989;
Wilken 1987; Whitmore and Turner 2001), but it is
inappropriate for contemporary commercial farming
methods that focus on arable (i.e., plowable) lands
(Jenkin et al. 1976; Birchall and Jenkin 1979), a
fact of relevance to conservation risks in the region
today.
There is a distinct relationship between the availability of well-drained ridges, settlement density, and the regional Maya settlement hierarchy (see Fedick and Ford
1990). This is evident in the local settlements around El
Pilar, where extensive fieldwork of surveys and excavations has taken place (Fedick 1988; Ford 1990, 1991a;
Ford and Fedick 1992). Although it has been proposed
that this dispersed pattern can be explained by cultural
dimensions of political or economic factors (e.g., Freidel
1981), it has also been argued that the uneven distribution of land resources has influenced Maya settlement
patterns (Fedick 1989). Only a spatial examination of
resources can resolve this divergence.
The ancient Maya occupation of the central lowlands encompassing an area of at least a 100-km radius
around Tikal can be traced back 5,000 years (see Leyden 1987). Settlement data show an expansion over
the area, which appears to have followed rivers, then
lakes, and, ultimately, spread across the entire interior
(Puleston and Puleston 1972; Rice 1976; Ford 1986).
Evidence indicates that the interior Petén area around
Tikal dominated the study region in the Late Classic period between AD 600 and 900 (Marcus 1983, 1993; Ford
1986; Culbert, Levi, and Cruz 1990; Fedick and Ford
1990). Maya settlement and civic construction were at a
maximum at this time. The process of centralization was
sustained through AD 900, when the Maya civilization
“collapsed” (Webster 2002). Tikal and other major administrative and political centers witnessed abrupt halts
in public projects, although some continued through
the Terminal Classic Period (AD 900–1000). Settlement surveys between Tikal and Yaxhá (Ford 1986,
1991b), in the El Pilar area (Ford 1985, 1990, 1991a),
as well as in northern Belize (Pendergast 1981; D. E.
Z. Chase and Chase 1988; Hammond et al. 1998) attest to persistent occupation. In some areas, such as El
Pilar, monument building continued, only to cease in
the Postclassic (Ford and Orrego 1996; Ford et al. 1996;
Ford et al. 1998; Ford 2004).
Scholars have focused on the dramatic Classic Maya
collapse (e.g., Culbert 1973, 1988; Redman 1999;
Diamond 2005) and the search for the causes of the collapse has generated a substantial literature (see Webster
2002). Whatever the cause of the abandonment of the
great Classic Maya cities, the development of Maya social complexity was based on a gradual rise in population
and concomitant intensification of land use, including
farming of increasingly more difficult and marginal land
(Fedick 1992).
Early investments and development in the Maya forest landscape endured over time (see Whitmore and
Turner 2001, 111) and the ancient Maya civilization
integrated populations of the region over a span of
more than 2,000 years. Environmental dimensions offered attractions as well as constraints for the early ancestral Maya. Among these attractions is soil fertility
constrained by the critical problem of surface water
(Ford 1996). Subsistence strategies and cultural developments mediated constraints and agricultural diversity
sustained the steady growth of the Maya civilization
(Whitmore and Turner 2001, 100–107). Given the fine
scale evidence for precipitation variation over this long
period (Haug et al. 2001) coupled with the extensive
studies of the Petén lakes (Leyden et al. 1993; Curtis,
Hodell, and Brenner 1996; Islebe et al. 1996; Curtis
et al. 1998; Hodell, Brenner, and Curtis 2000; Brenner
et al. 2002; Rosenmeier et al. 2002), this endurance
reflects a flexible adaptation and robust strategies that
bridged periods of disturbance and extremes, such as
hurricanes and drought.
Despite the evidence that the Maya forest environment did support high settlement densities in the past
based on a sustained land use strategy, little effort has
been made to identify the balance that was attained
by the ancient Maya land use pattern. Instead, modern industrial strategies are proposed for development
that bear no resemblance to the past (for the Belize
River area, see Birchall and Jenkin 1979) and can
be seen as a destructive short-term trajectory in process (Turner 1990; Sever 1999; Sever and Irwin 2003;
Nations 2006). By identifying the spatial land use priorities of the ancient Maya, we can assess the contrast
of development planning used in the region. The success of the past strategies, the needs of contemporary
local populations, and the conservation demands of the
twenty-first century underscore the imperative to understand the basis of the past prosperity and sustainability of Maya agriculture.
To what extent does the fundamental geographic
setting of the ancient Maya civilization account for its
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
adaptation? Our research focuses on geographic data as
a means to isolate the subsistence economy from the
political and social factors. We use geographic variables
that directly influence agriculture, past and present
(Jenkin et al. 1976; Birchall and Jenkin 1979), and include field improved digitized 1:50,000 maps of the soils
(based on Fedick 1988, 1989, 1994). We focus on settlement patterns of the Late Classic period, the apogee
of the Maya civilization, representing the accumulation
of two millennia of Maya accomplishment.
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Weights-of-Evidence Analysis
The premise of our model is that an actual map of
ancient Maya sites and settlement distribution consists
of a set of all locations, including the subsets of locations that remain unknown and locations of known
archeological settlements. The actual distribution cannot be known but can be modeled probabilistically, and
by focusing on strictly geographic variables we avoid
basic weaknesses of proxies identified in earlier predictive models (see Kohler and Parker 1986). The settlement distribution is assumed to spatially reflect mapped
distributions of major geographic and environmental
factors. Among these are topographic slope, soil fertility, soil drainage, and proximity to water sources.
These factors each contribute independently to the location of all settlements, but in different degrees. These
amounts, or weights, are the basis for the use of weightsof-evidence (Monts-Homkey 2000; Ford and Clarke
2001; Raines, Bonham-Carter, and Kemp 2000; Sirjean
2003; Monthus 2004). Weights-of-evidence origins are
in mining geology (Bonham-Carter 1999). The essential tools were integrated into a GIS software package,
ESRI’s ArcView 3.2 and later ArcGIS (Sawatzky et al.
2004), and extended into a broader analysis package
called ArcSDM.
Weights-of-evidence methods are Bayesian methods. They involve a given point distribution, assumed
to be a sample or incomplete representation of a spatial distribution that is the consequence of the combined influence of multiple influential factors or themes,
represented as binary or categorical maps. The thematic maps are usually reduced category sets, or classified fields, processed by buffers or other map-based
transformations. The influences can be positive or negative (i.e., a map class is prohibitive to the sample
rather than causative) but must be independent of each
other. These thematic maps, when overlain with the
point sample, result in an expected statistical density
for each class. The explanatory significance is compared
5
to random variation; that is, does a particular class increase or decrease the likelihood of finding a positive
sample by a significant amount. Each map contributes
explanatory power to the point distribution proportionally (the weight). By assembling the sum of the weighted
contributing factors as a map overlay, a probabilistic surface representing the likely complete distribution density can be generated and used in modeling, simulation,
and forecasting.
Weights-of-evidence analysis follows six steps:
1. Select known points of features to be modeled,
such as Maya sites.
2. Select thematic maps that are suspected to
contribute to the explanation of the point
distribution.
3. Using the correlation analysis tools of weights-ofevidence, convert selected map layers to binary or
categorical form in the most predictive manner.
4. Test for conditional independence comparing
prior and posterior probabilities by class combinations, eliminating those maps that do not contribute explanatory power.
5. Create a set of weights to use for each layer using
Bayesian methods.
6. Develop posterior probability and the associated uncertainty maps using the weighted layers
(Bonham-Carter 1994; Raines 1999).
Any model is, of course, only as good as its ability
(1) to be calibrated and validated to reflect past and existing data; (2) to summarize and simplify a real system
to allow experiments and test hypotheses; (3) to allow aggregate investigations that would not be possible
by testing parts in isolation; and (4) to be transportable
across scales or regions. The weights-of-evidence model
allowed us to forecast where to expect and not expect
Maya settlements, promoting an independent means of
validation. The model also allows us to see the relative
importance of environmental factors in Maya settlement location choices. The probabilities can then be
used as environmental weights in a settlement simulation. Although the actual application is not directly
transportable, because the weights are derived for each
case empirically, the approach is applicable universally
and the posterior probability layer can be input into
further models.
Each input map is converted into two or more categories based on the data. Of the detailed 1:50,000 soil
classes on the UK Overseas Development Administration (ODA) survey of the Belize Valley (Jenkin et al.
1976), we condensed characteristics of soil drainage and
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6
Ford, Clarke, and Raines
soil fertility into four categories: good, moderate, poor,
and very poor. The number of categories for a continuous variable, such as percentage topographic slope,
was determined using the software and some simple
measures. The weights-of-evidence method then combines layers and categories spatially to determine which
points in the evidential theme, in our case, archeological sites, fell inside or outside of the regions on the map.
The weights were computed both as layer/class contributors to a distribution and their opposite; that is, they
“repel” the evidential theme.
The computation of positive weights (W+) reflects
the possibility of the presence of sites if the theme is
present. If the positive weight itself is positive (W+ >
0) in the presence of the class or theme, we will find
more sites than chance would determine. If the positive weight is negative (W+ < 0), then presence of
the theme means fewer sites than what chance would
determine. If W+ is equal to zero, the class or theme
does not influence the location of sites. In this neutral
case, the computation shows that it is not an evidential theme and so should be excluded from the model.
Negative weights (W−) are the complement. If the negative weight is negative (W− < 0), the class or theme
is a good negative indicator, whereas if (W− > 0),
we would expect that in the absence of the class or
theme on the map, we will find more sites than what
chance would suggest. Contrast is the difference between the positive and the negative weights (C = W+–
W−) and is a measurement of the correlation between a
particular class or theme and the training points, which
in our case are the known archeological sites. If contrast
for a theme is high, then that theme in general is a good
predictor. Weights are log ratios of conditional probabilities and expressed in continuous decimal fractions.
The ArcSDM weights-of-evidence software provides
for the computation of a table of class weights, the contrast, and an estimate of the variance of the contrast.
This allows statistical tests of significance of the evidential themes, allows the computation of uncertainty,
and permits trial-and-error testing of class and layer
combinations to build strong models. A final output is
the sum of the posterior probabilities for all contributing classes and layers in the form of a map showing their
spatial distribution. The result is a map of the spatial
predictive model of the dependent variable.
UCSB Maya Forest GIS
Research began with the collection, integration,
harmonization, preservation, and distribution of the
scattered environmental and settlement data from the
greater Maya forest region. The result was collected
into the UCSB Maya Forest GIS, a data repository for
the greater Maya forest region of Belize, Guatemala,
and Mexico. Data contributed by agencies and scientists have been combined into a regional GIS (Ford and
Clarke 2000) and encoded with Federal Geographic
Data Committee standard metadata for archiving and
redistribution via the Alexandria Digital Library (ADL;
Smith and Frew 1995; ADL 2006). The Maya Forest
GIS data are available through the online library of
ADL.
Our original compilation on CD (Ford and Clarke
2000) was based on the GIS developed at the regional scale by the Paseo Pantera Consortium for
the U.S. Agency for International Development. Integrated with this are digitized maps of topography
and soils, Sader’s (1999) land use data for the Petén,
geo-referenced Landsat MSS satellite images, the local GIS database developed by Fedick (1989) on soils
based on the UK ODA map for the entire Belize River
valley at the resolution of 1:50,000 (topography, soil,
geology), as well as the Late Classic period settlement
data from Ford’s Belize River Archaeological Settlement Survey (BRASS) project at the resolution of
1:2,000 (1983–2003) and a 1998 1:6,000 photomosaic
of the El Pilar Archaeological Reserve for Maya Flora
and Fauna (Girardin 1999). This first version (Ford
and Clarke 2000) has been shared with collaborators in
Belize and Guatemala and published on the Internet by
the SCS Belize Country Conference (Ford and Clarke
2002). A key recent addition for this research has been
90-m-resolution digital topography from the National
Aeronautics and Space Administration Shuttle Radar
Topographic Mapping program (Sifuentes 2005) that
provides seamless slope coverage for the entire Maya
region. Many of these data themes provided the input
weighting layers for the weights-of-evidence modeling.
The specific characteristics of the input data are listed
in Table 1.
Our study area includes the diverse characteristics
of the greater Maya region: well-drained ridge lands,
poorly drained lowlands, wetlands, as well as the rare
alluvium. The majority of the El Pilar study area is composed of well-drained ridges (Fedick 1989; Fedick and
Ford 1990), featuring the characteristic limestone ridges
with the shallow and fertile Molisols that surround the
nearby Maya centers of Tikal, Yaxhá, and Naranjo (20–
50 km distant). Like Tikal, the limestone ridges around
the major center of El Pilar are noted for their absence
of surface water and compose nearly 35 percent of the
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
7
Table 1. Input data for the weights-of-evidence analysis
Theme
Scale
and extent
Soil fertility
El Pilar area
Resolution
1:50,000 vector
4 classes
4 classes
1:50,000
4 classes
4 classes
1:50,000 vector
40 m contours
Slope percent (percent),
below and above 16
percent
1:50,000 vector
Perennial and
intermittent
streams
Distance buffers
1:50,000 vector
1:2000
1:50,000
All
Major or minor civic
center/residential
sites
undifferentiated
Distance buffers
1 class
Topography
El Pilar area
Digitized paper map
(Jenkin et al. 1976)
Digitized paper map
(Jenkins et al. 1976)
Paper official topo 40 m
Rivers and streams
El Pilar area
Belize data
Paper official topo 40 m
Lakes and water bodies
Archaeological sites
El Pilar area
Site local
Soil drainage capability El Pilar area
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Map source
Belize data
Paper official topo 40 m
Belize River
Archaeological
Settlement Survey/El
Pilar Institute of
Archaeology
area (Ford 1992). The ridge lands are the concentration
of the settlements and the location of the largest Maya
center in the area, El Pilar, situated 10 km from the
Belize River (Ford and Fedick 1992, 45). The El Pilar
study area includes only a minor presence of closeddepression wetlands, generally a significant component
of the landscape of the entire Maya area (Fedick and
Ford 1990; Dunning et al. 2002).
The landscape of the El Pilar area features the Belize
River, one of the few rivers that run east from the central Petén. Rivers, and for that matter any surface watercourses, are scarce in the Maya region (Scarborough and
Gallopin 1991; Scarborough 1994, 1998; Ford 1996;
Lucero 2002). This makes the examination of the El
Pilar area important. The alluvium of the El Pilar area,
including the settlement of Barton Ramie (Willey et al.
1965), is notably fertile, yet makes up less than 5 percent of the study area (Fedick 1988, 1989; Fedick and
Ford 1990; Ford 1992). Although likely a critical component of the earliest agricultural adaptations (Powis
et al. 1999; Lohse, Awe, and Griffith 2006), the imposed growth limits are evident given the later periods
of occupation that concentrate in the abundant ridge
lands north and into the interior. The valley provides
a very restricted area for expansion and development;
consequently, it does not constitute a major focus of
Late Classic Maya occupation (Ford 2006).
The importance of water cannot be overemphasized
(Scarborough 1994; Ford 1996). Unchecked, surface
Classification
Transform
water is quickly absorbed into the limestone bedrock
and follows invisible and inaccessible aqueducts within
the limestone. Our examination of the El Pilar area will
provide a means of identifying the priority of watercourses for Maya settlement patterns.
Regional examinations of major centers have suggested a number of underlying factors contributing to
location. These include local and long-distance trade,
political competition, and access to critical resources
(Marcus 1973, 1993; Fry and Cox 1974; Rice 1981;
Freidel 1986; Sabloff 1986; Ashmore 1991; Demarest
1992; Martin and Grube 1995, 2000; Fox et al. 1996;
Foias and Bishop 1997). Patterns of spacing have been
considered along with center size and site sustaining
area (Marcus 1976). Our research examines geographic
variables most useful from the agricultural perspective.
Early agricultural occupations have been recognized
as later settlement concentrations and ultimately the
focus of Maya civic centers (Ford 1986; Fedick and
Ford 1990). Thus, our predictive modeling targeted
archaeological patterns as a whole, residential and civic,
reflecting the agrarian foundations of the Maya. We
considered all archaeological signatures, complex and
simple residential units as well as major and minor monumental centers together, as seen in Table 1.
From the numerous data contained in the Maya Forest GIS (ADL 2006), a subset of our environmental
data layers defined by the northern drainage catchment
of the Belize River were extracted and clipped to the
8
Ford, Clarke, and Raines
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Figure 2. Location map for the application zone and validation zone
showing the training samples from the
Belize River Archaeological Settlement Survey and Global Positioning
System field data site locations.
extent of our study area (Figures 1 and 2). The subset
and input layers were selected at the local scale and
extent as listed in Table 1 and are shown by the outline
polygon in the southwest of Figure 2. The study area is
located between the Belize–Guatemala border and the
Belize capital of Belmopan and focused on the north
side of the river. The area extends from the western
limestone ridges and hills to the eastern lowlands and
wetlands. All data themes of the GIS were consistently
registered to WGS84 using the Universal Transverse
Mercator coordinate system in zone 16 North.
The weights-of-evidence module used here was an
extension to ArcView 3.3 as an Avenue script utility
that is introduced into ArcView as a regular extension
and becomes an additional menu on the main ArcView
software toolbar. The extension has been rewritten and
extended and is now available as a more general analytical package and for other versions of the ESRI
GIS software (ArcSDM; Sawatzky et al. 2004). Using the tool involves following the weights-of-evidence
steps outlined earlier. The tool includes a means to
experiment with layer combinations, layer independence, category aggregation, and statistical fitting of the
model. After sorting and preprocessing statistical tests
of different class breakdowns, we reduced the combinations to a workable set of four principal classes and
themes: soil fertility, soil drainage, slope, and distance
to watercourses.
The soil layers were based on the four described soil
suites and subsuites in Birchall and Jenkin (1979) and
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
Table 2. Soil fertility ranking
Fertility Cation exchange
class
capacity
Base saturation
1
2
3
4
High
High
Moderate to high
Variable
Phosphate
pH
Low
Low
Low
Low
5.8–8.2
4.1–8.2
4.2–8.3
3.5–7.6
High up 100%
High
Moderate to high
Variable
9
tured by Horton stream order. Watercourses were thus
defined as any perennial stream or river.
Our set of four principal classes and themes of soil fertility, soil drainage, slope, and distance to watercourses
were included in this study as the evidential layer inputs
for investigating the geographic conditions of Maya settlement (Figure 3). They are as follows:
r Theme 1: Soil fertility. Classes: good, moderate,
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poor, very poor.
are detailed in Fedick (1988, 179–202). The suites are
based on landforms and the subsuites based on location. The locations include alluvial parent material in
river valleys with young, mature, and poorly drained
soil; limestone on the ridges, escarpments, and plains
that vary based on parent location; Pleistocene coastal
deposits primarily of sand and clay; and wetland areas
flooded in the rainy season based on limestone or acid
rocks (Birchall and Jenkin 1979, 13).
According to the field results of Birchall and Jenkin
(1979) and Fedick (1988), we ranked soil fertility
from 1 (fertile) to 4 (infertile). Soil fertility rank
is based on cation exchange capacities (CEC), base
saturations (Ca2+ , Mg2+ , K+ , and Na+ ), along with
phosphate and pH levels as identified in Birchall
and Jenkin (1979) and employed by Fedick (1988,
1989). We summarize the fertility classification in
Table 2.
Based on the analysis of Birchall and Jenkin (1979)
coupled with the field survey of Fedick (1988, 1989),
we were able to classify drainage characteristics of the
soil. We ranked drainage from 1 (good) to 4 (poor).
Soil permeability, infiltration, and clay content form
the basis of our ranking, summarized in Table 3.
The themes of slope and watercourses were defined
based on the 1:50,000 scale maps digitized as GIS layers
as well as the Shuttle Radar Topographic Mapping
(SRTM) data. We defined slope in percentages. In considering access to water, based on statistical tests, we
explicitly eliminated as explanatory variables distance
to the major river, distance to lakes, and distance struc-
Table 3. Soil drainage ranking
Drainage
class
Permeability
range (m/d)
Infiltration
rate (m/d)
Clay
content
1
2
3
4
∼0.34–0.85
∼0.2–0.7
∼0.06–0.35
∼0.1–0.3
2.9–5.0
0.8
0.12–0.22
0.18
30–40%
20–70%
40–85%
up to 90%
r Theme 2: Soil drainage. Classes: good, moderate,
poor, very poor.
r Theme 3: Slope (percentage). Classes: integer percent, reduced to above and below
16 percent.
r Theme 4: Distance to watercourses (meters).
Classes: integer meters, tested in 100 m bands,
reduced to 0 to 500 m, 500 to 1,000 m, and greater
than 1,000 m.
The choice of weights-of-evidence model weights
was based on the statistics, especially the number of
points explained by the weighted combination. The
grid size for the model was one hectare, with an area
of application of 83.59 km2 in the local case. The
archaeological sites layer included 262 sites in the
evidential theme. The analysis was repeated, first with
the application zone surrounding El Pilar and next with
the validation zone for the entire El Pilar/Belize River
area of 1,290.11 km2 , constituting a major portion of
western Belize. The relationships between the two areas
are shown in Figure 2 and 3. This formed the basis of our
analyses.
Analyses and Results: Predicting Ancient
Maya Settlement
The predictive modeling of ancient Maya settlement
patterns focused on the archaeological survey data of the
BRASS/El Pilar surveys, the source of the training sites
for the predictive model (Ford 1991b, 1992). The locations of the training sites were based on 1:2,000 scale
composite maps of archaeological sites, residential and
civic (Ford and Fedick 1992). The modeling exercise
was divided into the two phases. First, we used existing data from the surveys to define the application zone
(83.59 km2 ) and developed the initial model. Second,
we expanded the initial model from the application
zone to the validation zone (1,290.11 km2 ) for the field
corroboration. This phased examination provided the
basis of our model development and the field tests.
10
Ford, Clarke, and Raines
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Figure 3. El Pilar application and
validation zone input maps for the
weights-of-evidence model. A: slope;
B: distance to streams; C: soil drainage;
D: soil fertility.
The application zone for the El Pilar area was gridded by the software at 100 m resolution (one-hectare
cells). For the 262 surveyed archaeological training sites
(predominantly residential and including civic centers;
see Table 1 and Figure 2), the expected a priori probability of encountering a site in a cell was calculated as
0.0313. As defined in Table 4, contrast indicates that
soil fertility has the strongest spatial correlation with
training sites, followed by proximity to watercourses.
Soil drainage and slope are approximately equal factors,
both of less importance than soil fertility and proximity
to watercourses.
Table 5 shows the criteria used to select the evidence
layers and the thresholds defined by the weights analysis. Soil fertility and drainage are ordered data, each
with four ranks. In both cases the highest ranks were
defined as the optimal predictor of training sites. Slope,
an ordered measure of slope angle, was analyzed using
the cumulative ascending method to define a 16 percent slope as the optimal maximum slope preferred by
the Maya, as indicated by the training sites. Slope has
the lowest confidence, where a value of 1.6316 would
indicate an approximate level of confidence of 95 percent. This significance test is approximate, as it is based
on all of the data rather than a random sample.
In the first test of our model in the application zone,
197 sites were explained with the weighted evidence
model. Sixty-five of the 262 points had a posterior
Table 5. Criteria and thresholds for the chosen
weighting model
Evidence
Table 4. Weights table for the application zone
Evidence
Soil fertility
Watercourse proximity
Soil drainage
Slope
W1
W2
0.6813
0.6314
0.6015
0.0193
−0.9796
−0.4575
−0.2391
−0.8032
Contrast Confidence
1.6609
1.0889
0.8407
0.8225
11.2877
8.7517
6.5745
1.6316
Soil fertility
Criteria
Preferred
high-fertility soils
Watercourse proximity Near to the river but
not too close
Soil drainage
Preferred
well-drained soils
Slope
Preferred low slopes
Threshold
Class = Good soil
fertility
500–1,000 m from
river
Class = Good soil
drainage
Less than or equal
to 16◦
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
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Table 6. Categorical weights table for proximity to
the rivers
Distance (m)
Contrast
Confidence
STUD CNT
100
200
300
400
500
600
700
800
900
1,000
1,100
1,200
−1.1785
−0.9705
−0.4319
0.0055
0.5389
0.8825
0.6473
1.5585
1.5633
1.27
−0.1194
0.2465
0.2199
0.2159
0.1935
0.1892
0.1838
0.1976
0.258
0.216
0.2425
0.2994
0.589
0.5925
−5.3599
−4.4953
−2.2317
0.0291
2.9316
4.4652
2.5089
7.2158
6.4479
4.2426
−0.2027
0.416
probability less than the prior probability and therefore
were not explained by the weighted evidence model,
resulting in a 75.2 percent overall explanatory level.
Of these sixty-five unexplained points, forty fell in the
first slope class (0–9 percent) and grouped in clusters at
the south of the BRASS survey transect near the minor center Yaxox, in the preferred watercourses Class
2; that is, within 100 to 500 m of a watercourse.
The analysis of the proximity to watercourses is particularly interesting, as the data show that the Maya
preferred to live close to, but not too near, watercourses
(Table 6). This might have been to avoid areas of flooding along the rivers and streams, as is supported by field
observations, and with a consistent avoidance of wetlands. The actual buffer interval was defined by using
a categorical weights table. Note that the weights are
well defined because the distance intervals are large.
In analyses with narrower distance intervals, the selected interval was mostly of positive contrast, but there
were occasional negative contrasts inside the interval
(Sirjean 2003). This is a consequence of the sample
size of the training set. This particular evidential layer
and its analysis represent a unique contribution of this
research project and are potentially useful for others
working with weights-of-evidence. Rarely is a single
influential theme both a positive and negative contributor to the explanation of a distribution (Table 6), with
distance forming the key variable.
All evidence was generalized within the context of
the weights-of-evidence to optimize prediction into binary classes (i.e., predictive or nonpredictive), by selecting the maximum contrast that had a confidence level
of 90 percent or greater based on an approximate Student’s t test. The soil fertility, soil drainage, and slope
were all analyzed by the appropriate cumulative weights
11
measurement to define the threshold for good and bad
evidence as summarized in Table 5. Slope weights analysis was done using the cumulative ascending method
because the question asked of the data was this: What
was the maximum low slope preferred by the Maya farming settlements? Soil fertility and drainage were appropriately analyzed by cumulative ascending because the
ordered ranks were numbered with one as the highest
rank. This ordered numbering sequence dictates using
cumulative ascending weights analysis to answer the
question of how good of a soil would the Maya farmer
use. The answer for both fertility and drainage was Class
1, or good. The proximity to watercourses weights analysis was done using a unique categorical weights analysis
supported by testing the reclassification of the evidence
with categorical weights (results are shown in Table 6).
Conditional independence is always an issue when
using a Bayesian method such as weights-of-evidence.
The rule is to accept a conditional independence
value greater than 0.85. In our test, the overall conditional independence test reported a value of 0.97.
This overall test is considered conservative, and thus
there is no conditional independence problem in our
model. The chi-square pairwise test indicates a weak
conditional dependence between soil fertility and soil
drainage and between soil fertility and proximity to watercourses. The overall test, however, indicates no significant problem of conditional independence. These
conditional dependencies are reasonable because fertility and drainage and the favorable linear buffered region
around the watercourses are probably moderately associated. These considerations, however, do not change the
model because the intended use of the model is to rank
areas.
Our results in the application area are supportive.
We were able to predict 75 percent of the sites based
on the combined environmental inputs. The next step
was to perform the field tests of the model.
Validation of the Predictive Model
of Maya Sites
Field validation tests expanded the results of the El
Pilar application zone to the entire Belize River validation area (Figure 4). The continuous weights were
classified into four categories (very high, high, low, very
low) and applied to the validation area. The exercise
to confirm the predictive model of ancient Maya sites
focused on specific zones of interest based on the topography and the model results themselves. Three zones
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12
Ford, Clarke, and Raines
Figure 4. Weights-of-evidence posterior probabilities for the El Pilar application and validation zone.
were defined for the field validations. Zone One represents areas comparable to those of the BRASS/El Pilar
surveys with a similar geography. Zone Two is located
south of the BRASS/El Pilar surveys in the area between the Mopan and Macal River branches of the
Belize River. The last zone, Zone Three, was focused
on the valley north of Barton Ramie, where the predictive model shows serpentine shapes of contrasting poor
and moderate prediction for Late Classic archaeological
sites (see Figure 4), similar to the location of the area
of unexplained sites of our model in the application
zone.
Each validation zone was visited, canvassed, and surveyed in the field. We located areas within each zone
for the validation tests by vehicle. Once oriented, the
selected area was covered by foot. Sites were recorded
with ESRI’s ArcPad running on a Compaq iPAQ with
a NAVMAN Global Positioning System (GPS) sleeve,
while displaying the weights layer in the GIS. These
data were then compared with the model and evaluated in terms of reliability.
The first validation zone was focused on the northwestern area of the model, north of El Pilar around Cadena Creek. This zone is very similar to the geography
around the major center of El Pilar. Today, Zone One
is largely in plough and pasture with good access by allweather roads maintained by the Mennonite commu-
nity of Spanish Lookout. Concentrating on the places
with the strongest predictability for sites, we plotted
the unmapped Maya residential sites and minor centers
encountered in the many cleared fields. Predictably, a
high density of sites characterized the locales with high
probability weights. Most ancient Maya residential sites
were found within 20 to 30 m of each other. Several minor centers were identified as well. This density of sites
in this zone is typical of the densely settled areas of
the Maya lowlands and leads one to imagine an intense
occupation of these high-probability areas. Other probability areas were canvassed as well, and all sites were
recorded.
In total, we identified 225 sites in Zone One, all
previously unmapped. Of the total, 122 of the sites,
or 54.2 percent, were recorded in the areas of very
high probability and a further 55 or 24.4 percent in
the high-probability area. Sites were also located in
the lower probability areas: 35 or 15.5 percent in the
low-probability areas and 13 or 5.7 percent in very
low-probability areas. Most of the sites in these lowprobability areas are near areas of high probability,
suggesting some imprecision or generalization of edge
locations in the evidential themes. Considering together areas of very high and high probability, recorded
sites account for 76.8 percent of all sites of the validation test. The model proved reliable in this zone.
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Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
The second validation zone we examined was the
area south of the El Pilar area between the Mopan and
Macal Rivers. Zone Two is marked by difficult broken
terrain and steep hills that are not well reflected in the
digital elevation model (DEM) for the region. Nevertheless, eighty-one new sites were located, of which
seventy-four were in the high-probability areas, accounting for 91.3 percent of the documented sites in this
zone. The remaining seven sites, or 8.6 percent, were located in the low-probability areas. The model predicted
correctly all the locations of newly identified sites. In
addition, the high-probability areas correspond to those
mapped in the area of the Chan site (Robin 2002). In
this area no sites fell in the very low-probability area.
The model predicted well the occurrence of sites by
probability.
The third validation zone we considered was east of
the El Pilar area bordered by the Belize River where the
first archaeological surveys of the area were conducted
around Barton Ramie (Willey et al. 1965). This is where
the model shows serpentine areas of low probability
next to areas of high probability based on watercourses.
This model pattern comes from the relationship of sites
to watercourses, where the majority of site locations
fall between 500 and 1,000 m from a watercourse (see
Table 6). Yet in the case of Zone Three, both areas have
poor soils, generally a poor predictor of site locations.
Only three sites were found in the vast expanses of Zone
Three. Of these sites, one was in the high-probability
area (33.3 percent), one was in the low-probability area
(33.3 percent), and one was in the very low-probability
area (33.3 percent). None were located in very highprobability areas.
Although there are very few sites in Zone Three,
they are evenly divided among the high-, low-, and
very low-probability classes. Only one site, or 33.3 percent, was located in a high probability area, and two,
or 66.6 percent, were located in low-probability areas,
suggesting some uncertainty in the predictability in this
13
very lightly settled zone. All the sites were situated
on the margins of the defined zone. The one site in
the high-probability area was located 13 km north of
the river near limestone ridges know as Yalbac Hills.
The other two were located close to the Belize River.
These results suggest that work on the precise nature
of the influence of drainage and Maya site location still
needs to be addressed. Nevertheless, barely 1 percent of
the all the newly recorded validation sites were identified in the large expanse of Zone Three.
In conclusion, the predictive model of ancient Maya
sites held up well to the field validation tests. We located and recorded 315 sites in the validation tests
and 82 percent of these sites fell in the very high and
high-probability areas as mapped by the weights-ofevidence model. These newly recorded sites were divided relatively evenly between probability areas: very
high with 39 percent and high with 43 percent (Table
7). The very high-probability areas are densely settled;
there were 122 recorded sites in only 5.6 percent of the
study’s areal extent. The high-probability areas were
more spread out and included 136 sites recorded in 19
percent of the study area (Table 7). Together these
258 new sites, accounting for four fifths of all validation sites, were predicted for only 24.6 percent of the
study extent. The remaining 18 percent of the sites
were distributed in areas of low and very low probability. Only forty-three sites (14 percent) were recorded in
the area of low probability, and only fourteen sites (5
percent) were located in the very low-probability areas.
Sites in the low-probability areas were distributed across
32 percent of the study, yet the few sites in very lowprobability areas cover nearly 43 percent of the study extent (see Table 7). Thus, our model could exclude 42.7
percent of the study area based on geographic predictors with 96 percent confidence that no sites would be
found.
It must be borne in mind that these figures reflect
the uncertainty of the data collection and assimilation,
Table 7. El Pilar/Belize River area settlement distribution by probability class
Posterior probability
Class 1: 0.1039 to 0.225 black
Class 2: 0.0314 to 0.1039 dark gray
Class 3: 0.0087 to 0.00313 light gray
Class 4: 0.0 to 0.0086 white
Total
Percent
masked area
in class
Number of validation
points (newly mapped
sites) in region
Percent
predicted
sites
5.55
19.09
32.63
42.74
100
122
136
43
14
315
39
43
14
4
100
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14
Ford, Clarke, and Raines
limitations of data resolution, and assumptions of the
Bayesian model. Alternative interpretations are possible. For example, the negative watercourse proximity
results could be the consequence of the destruction of
Maya settlements by flooding and thus not caused by
Maya settlement preferences. Still, the strength of the
preference for other factors, especially soil fertility, cannot be easily discounted. Thus, we see that our weightsof-evidence model proves very reliable for predicting
ancient Maya sites.
These results support the validity of the model in
predicting the major proportion of Late Classic Maya
archaeological sites, a time when at least 98 percent
of residential units and all of the civic centers in the
study area were occupied (Ford 1990, 1992; Ford and
Fedick 1992; see also Culbert and Rice 1990). In a
general review of the residential sites found in the
high-probability areas, we note that they are relatively
large, complex, numerous, and dense. Sites that occur
in the lower probability areas are small, widely dispersed, and often close to a sharp probability boundary
with the higher probability areas. Thus, based on the
field validation test, we conclude that our four-factor
environmental model explained the location of the
majority of Late Classic Maya sites. Taking model
probabilities of greater than 0.0314 as “high” and
including 24 percent of the area (see Table 7), then
the model predicted the occurrence of 82 percent or
252 of the 315 newly identified validation sites. In
addition, we have demonstrated that the exclusion
of probabilities less than 0.0086 making up nearly 43
percent of the area would still recover the majority of
96 percent of the sites. These are strong results.
Implications
The combined geographic themes were selected for
their reflection of agricultural factors in the choice of
site locations. In our research, we confirmed the conditional independence of the geographic variables with
regards to the training sites, critical to the overall tests.
The geographic themes were each contributors to the
model and the combined themes of the predictive model
can account for the majority of sites based on the validation field tests. The strong influence of soil fertility
among the four themes is particularly relevant, supporting the view that agricultural strategies were at the
foundation of Maya settlement patterns and development. Watercourses were relatively important, but more
significant was that distances were found to be neither
very close nor too far. Drainage and slope also played
roles, ranked below fertility.
Our investigation of the predictive model for ancient
Maya sites provides a means to evaluate land use patterns of the Late Classic Maya. Consistently, the results
of our model implicate geographic motives for site location. These choices match contemporary smallholder
farming choices for residence locations and underscore
the importance of farmer choice in the selection of residential site locations. These locations would be the
natural focus for the development of civic centers that
would have responded to established settlement areas.
In this examination, sites have been predicted based
on geographic variables and highlight the value of
geography in explaining site locations. Although the
agricultural basis of Maya settlement patterns has been
appreciated, the spatial relationships had not been rigorously explored until now. Of particular importance
here is the power of GIS to synthesize and coregister
maps, supporting the analytical results and their validation in the field. Consequently, this examination
brings to the fore the value of the weights-of-evidence
method of evaluating multiple variables across space,
demonstrating the combined contribution of geography
and the value of agricultural choices to the settlement
patterns of the ancient Maya.
With the weights-of-evidence method, we have isolated features of the geography in the Maya area that
account for the majority of the archaeological sites, both
residential and monumental. The areas of strongest
probability of sites include only 24 percent of the entire
validation area (see Table 7). As can be seen in the
maps, these areas occur in scattered patches throughout
the El Pilar area (Figures 4 and 5). In other words,
82 percent of the sites discovered in the validation
tests (252) are found in dispersed high-probability areas without concentrating in any one particular area,
such as adjacent to the Belize River or near the major
center of El Pilar. This is noteworthy as the earliest surveys surmised that the Belize River exerted
significant influence on Maya settlement (Willey et al.
1965).
The geographic preference for settlement in the limestone ridges is significant in that this geographic landform is a dominant characteristic of the entire Maya
region from the El Pilar area west across the greater
Petén of Guatemala and north to the modern state of
the Yucatan, Mexico. The exploration of this modeling strategy for other study areas as well as the region
as a whole might prove promising in identifying largescale regional patterns of Maya land use. How much the
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
15
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Figure 5. Examples of sites in high-probability areas from the application area, A: Latón, B: Alta Vista, and C: Bacab Na.
weights of the contributing factors vary with scale and
region is a topic for future research.
The areas that evince the very lowest probability of
sites include more than 42 percent of the El Pilar area
(see Table 7) and yielded very few sites (fourteen, or
5 percent) in the field validation tests. Interestingly,
these zones found in the El Pilar application area show
both low density and small sites. Within the El Pilar surveys of the BRASS project, examples of such
sites underscore the varied land use objectives of the
Maya.
Examples of small sites in very low-probability areas around El Pilar were identified and tested in the
BRASS survey (Ford 1990, 1991a, 1992; Ford and
Fedick 1992). The sites are uniformly diminutive and
excavations suggest that they were specialized in nonagricultural activities. Artifacts collected from excavations, for example, on the Yaxox transect (Figure 6),
Figure 6. Examples of sites in very low-probability areas from the application area: Near the major center of El Pillar (left image) and north
of the minor center Yaxox (right image).
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16
Ford, Clarke, and Raines
indicate some of these were small-scale stone tool production sites that expanded in the Late Classic into
the poorly drained lowlands adjacent to a chert quarry
(Ford and Olson 1989); these areas were quickly abandoned in the Terminal Classic (Fedick 1989). A similar
expansion pattern is noted for the very low-probability
area adjacent to El Pilar (see Figure 6) where sites are
recorded after the initial Preclassic, clearly related to
the presence of El Pilar with its early construction dating to the Middle Preclassic (Ford 2004) and its growth
and expansion thereafter. Thus, occupation in some of
the lowest probability areas reflects other factors that
might not relate to agriculture. Whereas sites around El
Pilar may simply be infilling, the case of the Yaxox sites
might be related to entrepreneurial economic specializations where resources, such as chert for stone tools
or clay for ceramics, are found (cf. Brumfiel and Earle
1987).
Critically, our model demonstrates that ancient
Maya populations that were living in the Late Classic
period were not homogeneously distributed. There were
specific areas that were preferred and general areas that
were avoided for Maya settlement. The majority of sites
were concentrated in the areas favorable to smallholder
agriculture where fertility, watercourses, drainage, and
slope supported farming. These features of the local
geography are scattered, primarily based on parent geology, and occurred in less than one quarter of the study
area (24 percent). An overwhelming majority of sites,
82 percent, were identified in these high-probability
areas. This result has significant implications for the
development of population estimates. If, as in the El
Pilar case, the majority of sites that are used as proxy
for population are concentrated in a small percentage
of the land area, then projections of population need to
be adjusted significantly downward and should exclude
the majority of the landscape.
Although there are scholars who have clearly recognized the geographic preferences of the ancient Maya for
the well-drained ridges (Turner 1978; Dunning 1996;
Dunning et al. 1998), there are Maya scholars who
project high population densities evenly across a region for the Late Classic Maya (Haviland 1969; A.
F. Chase and Chase 1987; Dahlin et al. 2005; Healy
et al. 2007; except Webster 2005). Our results, consistent with Turner and others (Turner 1978; Whitmore
and Turner 2001), support the understanding of land
use in developing population estimates (see also Turner
1990). In other words, part of the problem of understanding Maya land use comes from the way in which
populations are estimated. Population estimates might
be high in areas of settlement, but these are limited by
geographic factors related largely to farming choices,
as shown in our spatial model. The predictive model
for the Maya sites of the El Pilar area provides a clear
spatial view of the settlement and by extension population distribution. Not only should population densities
be focused on areas that have a strong probability for
occupation, but because these populations are largely
agrarian in nature, these will tend to be the areas where
agriculture would be practiced. Our predictive model
provides the essential spatial criteria for making such
assessments.
Translating our map results for the ancient Maya
into land use and agricultural practice is an important
step. To undertake this exercise, we first compare our
predictive model to that of the Western model of contemporary development priorities. Given the prosperity
apparent for the ancient Maya, how do the priorities of
the predictive model for ancient Maya settlement compare with the contemporary development model? The
answer to this is facilitated by the fine-scale and detailed
soils research and agricultural undertaken in the Belize
River area published in the 1970s (Jenkin et al. 1976;
Birchall and Jenkin 1979). This agricultural assessment
was undertaken within the context of a development
scheme promoted by the United Kingdom and consistent with the United States for emerging economies
since the last half of the twentieth century (Boserup
1965; Bray 1994; see also Fukuoka 1978; Mollison 1988;
Nash 2007).
Following Fedick’s digitized classifications of these
data and our field update and verification of the soil
polygons, we evaluated the priorities of the UK ODA
recommendations based on “suitability for arable use”
(Birchall and Jenkin 1979, 5; Jenkin et al. 1976,
215), explicitly defined as geographic characteristics
amenable to plowing (Jenkin et al. 1976, 215–16).
With these data, we were able to compare the results of our model of ancient Maya settlement priorities based on Prehispanic Maya hand cultivation
dependent on stone tools (Denevan 1992) and rainfed systems (see Whitmore and Turner 2001) to that
of the contemporary development model based on
mechanical cultivation dependent on technological
systems.
To evaluate the relationship of the two models, we
employed the attribute in the table of the 1:50,000 soil
maps that ranked land capability class (Jenkin et al.
1976, 215–23). For the development model, we simplified the nine classes of the ODA study to four classes
(1–4, high to low development priority) to compare
Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
Table 8. El Pilar/Belize River area development class
Development
class
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Class 1: Black
Class 2: Dark gray
Class 3: Light gray
Class 4: White
Percent
area
in class
Mean posterior
probability,
Set 1
Mean posterior
probability,
Set 2
5.8
51.5
16.5
23.2
0.0546
0.0014
0.0418
0.0653
0.0578
0.0014
0.0459
0.0671
with the Maya model (Table 8), based on the actual
weights-of-evidence posterior probabilities (see Table
7). Two sets of random points were generated to populate each of the four development classes with one
hundred points using Hawth’s tools (Spatial Ecology
2008). The total 400 points per set were intersected
between class in the development model and posterior probability for the Maya model. The probability
of finding a Maya settlement within each set of the
four development classes was calculated based on the
weights-of-evidence statistic and plotted for both sets of
random numbers. The results of this test are presented in
Figure 7 and Table 8.
Overall, the contemporary development classes show
little in common with the Maya model. Excluding
the top 6 percent of the potential development area,
there is an inverse relationship with respect to the
Maya model. The most dramatic distinctions come from
the comparison of the lowest development class assigned for the limestone hills preferred by the Maya
Figure 7. Comparison of the Maya
model probabilities with the development model priorities.
17
and the high development class assigned to the poorly
drained lowlands virtually avoided by the Maya (see
Figure 7).
Although the highest development priority areas,
Class 1, proved a relatively good predictor of Maya sites
(but hardly comparable to the weights-of-evidence) and
shares some qualities in common with the Maya model,
this class represents less than 6 percent of the study area
and includes principally the restricted well-drained alluvial areas that offer value for hand and mechanical
agriculture (Figure 8). Development Class 2 accounts
for over 50 percent of the landscape of the study area
with an assessed high potential for contemporary development, yet this high development class is the poorest
predictor of Maya sites with mean weights-of-evidence
probability in the very low-priority areas for the Maya
(Table 7). Conversely, the lowest development priority
(Class 4) is the best predictor of Maya sites, incorporating 23 percent of the study area largely located in the
hilly terrain with thin soil (Figure 8). Thus, the contemporary development model that prioritizes based on
arable land does not explain the ancient Maya land use
strategies.
In considering alternatives to explain the Late
Classic period Maya settlement model, Maya ethnographic and ethnohistorical data are important (Villa
Rojas 1945; Redfield and Villa Rojas 1962; Hernández
Xolocotzi, Bello Baltazar, and Levy Tacher 1995;
Zetina-Gutiérrez and Faust 2006). These cases show
that our predictive model shares much in common
with the time-honored traditional practices of farmers
18
Ford, Clarke, and Raines
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Figure 8. The development model
(left) with an example of Class 1 development priority that overlaps with
high Maya settlement probability at Bacab Na (right above) and Class 4 development priority and very low Maya
settlement probability at Latón (right
below).
in the Maya region today. The choices of soil, drainage,
and slope characterize traditional land use techniques
(Nations and Nigh 1980; Fedick 1995; Beach, Farrell, and Luzzadder-Beach 1998; Levasseur and Olivier
2000; Gómez Pompa et al. 2003; Levy Tacher, Rivera,
and Rogelio 2005). Even the contemporary forest itself
shows the signatures of ancient impacts with a plethora
of economic plants (see Balick and Cox 1996; Balick,
Nee, and Atha 2000; Campbell et al. 2006; Ford 2008;
see also Balée 1994). Moreover, these high settlement
density areas identified in the predictive Maya model
exhibit considerable homogeneity of species indicated
by high beta diversity (Campbell et al. 2006), reflecting a strong human impact of centuries of cultivation
of tree-dominated plots despite current abandonment
(see also Peters 2000).
Smallholders today who practice traditional farming strategies emphasize trees in their “forest gardens”
and demonstrate the conservation of soil productivity,
water retention, promotion of biodiversity, and support for birds and other animals (Gómez Pompa, Flores,
and Sosa 1987; Gómez Pompa and Kaus 1990, 1999;
Hernández Xolocotzi, Bello Baltazar, and Levy Tacher
1995; Griffith 2000; Ferguson et al. 2003; Ford 2008; see
also Wilken 1987). In this way, our predictive model
provides a link from ancient Maya settlement patterns
to contemporary ecological, botanical, and agroforestry
studies.
The traditional farming techniques provide a basis
for interpreting the ancient Maya site selection patterns (cf. Teran, Rasmussen, and Cauich 1998). The
land use priorities identified in our predictive model
maximize access to a combination of agricultural areas and vary the intensity of land use based on agricultural potentials across a wide sustaining area. The
different land use strategies would be adapted to local productive capacities (Hernández Xolocotzi, Bello
Baltazar, and Levy Tacher 1995), from polycultivated
high-performance milpas (Wilken 1987) to shaded
tree orchards with understory cover crops and productive palms as found in home gardens and outfields today (Gomez-Pompa and Vazquez Yáñez 1981;
Corzo Marquez and Schwartz 2008). These differing
levels of land use intensity would be reflected in the
settlement size, composition, and density. Permanent
residential units would be focused in the high productive areas, with seasonal and intermittent use of
low productive areas, while avoiding the least productive areas for agricultural pursuits (see Zetina-Gutiérrez
and Faust 2006; Zetina-Gutiérrez 2007). This is the
infield–outfield model espoused by Netting (1977) and
others.
In summary, we see the results of the predictive
model of Late Classic Maya settlement as a critical basis for reexamining current themes of ancient Maya
development and demise, for considering more diverse
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Modeling Settlement Patterns of the Late Classic Maya Civilization with Bayesian Methods and GIS
subsistence adaptations, and for a reassessment of population levels. This first test at modeling ancient Maya
settlement patterns has resulted in patterns that spread
settlements and populations out into the mosaic of limited preferred zones of dense occupation of green communities (Voorhies 1982; Graham 1998), large areas
with light occupation, and a proportion of the area with
little or no evidence of occupation (see Fedick 1988).
With these results we can begin to model land use and
population levels that would best explain the patterns
of the predictive model.
Further, the predictive model provides a foundation
for examining the value of geographic variables at larger
and smaller scales. Extending the model to the regional
level for the whole lowland Maya area at, for example,
1:250,000, could provide insights into the variations
of land use across the Yucatan Peninsula. We have
recently developed a soil coverage theme for fertility
and drainage of the entire Maya area (Sifuentes 2005).
These new themes provide an opportunity to scrutinize
the preference for farming sites in the region and to
consider changes over time.
The results of our predictive model are promising,
demonstrating that areas with Late Classic Maya settlement focused in environmental settings that support intensification of hand cultivation, avoiding areas that are
difficult for these labor-based agricultural systems. The
example from the El Pilar area reveals that the agricultural landscape is dispersed and fragmented, spreading
the sites and populations out into large and small areas
preferred for settlement and agriculture with no pattern of focus on rivers. Because the whole society was
agrarian and dependent on the management of food
production, our predictive model suggests that farming
choices outweighed other factors in the development
of the overall landscape. Wider testing of this model
will help to better understand the diversity across the
ancient Maya landscape.
Conclusion and Discussion
Late Classic Maya settlement distributions were arrived at over a long period of time. The patterns we
have discovered are likely the product of adjustments
to the overall characteristics of the landscape. From this
study’s perspective, however, it is not relevant whether
the patterned results were deliberate or based on centuries of trial and error. Overall, what our results show is
that four geographic and environmental factors predict
82 percent of the Maya sites in the high-probability ar-
19
eas. Furthermore, fully 96 percent of the settlement, a
vast majority, can be predicted for less than 60 percent
of the El Pilar study area.
Our conclusions are moderated by the uncertainties embedded in our data and in the assumptions of
the Bayesian model. Given that the model is probabilistic, it might be difficult to use it for population
density forecasts. A critical value is how many settlements are missing from the record. Exogenous estimates
from cultural records or other sources could, nevertheless, be used with the model to simulate possible
population distributions. Replication of this model in
other local areas of the Maya lowlands would be important to build a broader database in support of our
model. In addition, testing its validity at other scales,
such as the greater region-wide scale, would provide
another basis for interpreting land use and population
distribution.
We propose that the probabilities computed for the
model here can be used as surrogates or proxies for
land use intensity and population distribution. Simple aggregation and integration would be sufficient to
test the contemporary hypotheses about Maya population sizes and distributions. Thus, the foundation model
developed here for the El Pilar area could shed light
on Maya farming sustainability as well as the infamous
Maya “collapse.”
Predictive models will become increasingly useful as
more of the Maya archaeological record is destroyed.
Although the likelihood of finding new major centers
is not high, there must remain thousands of unmapped
and unknown lesser centers, and certainly numerous
farm and house sites that could be located with this
tool, as our validation efforts have shown. Modeling
geographic preferences could be a means of initial archaeological surveys for areas that have had little attention, such as the Lacandon forest of Chiapas, Mexico.
Given the broader implications, we believe that the
use of GIS data with Bayesian methods offers value to
predictive mapping of archaeology in the Maya forest.
Additional factors, perhaps religious and political, not
to mention economic, are likely to explain variation
from the expected patterns, and better environmental
data would improve the current example. Finally, we
see a great potential of wider application of the model,
perhaps to the whole Yucatan region, as well as a narrower one at a major center such as El Pilar, among
the next steps. Of most interest for such future tests is
that the factor weights of the new models will show
how environmental influences vary by geographical
scale.
20
Ford, Clarke, and Raines
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Acknowledgments
This research owes its inception to the generous
Research Across Disciplines program sponsored by
UCSB’s Office of Research under Vice Chancellor
France Cordova. The project benefited from the early
investments from UCSB students Erica Gardener and
Aric Monts-Homkey. Engineering interns from École
Supérieure des Géomètres et Topographes (Le Mans,
France), including Anne Girardin, Elise Sirjean, and
Florent Monthus, improved this work with their dispassionate fieldwork and GIS knowledge while discovering
the patterns of the ancient Maya landscape. We also
thank Belize’s Institute of Archaeology and particularly
John Morris and Jaime Awe for their continuity of support of the research at El Pilar. We are equally grateful
to the communities around El Pilar for their generosity
and assistance throughout our field endeavors. We, of
course, alone are responsible for our works.
Notes
1. The term Maya forest refers to the moist forest ecosystems of the lowland tropical parts of Maya culture area
located between 15.45◦ N and 19◦ N latitude and 88◦ W
and 91◦ W longitude at elevations below approximately
300 m (see also Whitmore and Turner 2001, 24, Table
2.1).
2. There has been considerable controversy on the subject of climatic change and the Maya area. Nonetheless,
the general climatic regime is characterized as tropical
with a wet–dry annual sequence that has continued over
the recent Holocene period (Curtis et al. 1998; Hodell,
Brenner, and Curtis 2000; Brenner et al. 2002; Rosenmeier et al. 2002; Neff et al. 2006). This period had
included significant punctuated variations of deluge and
drought, particularly in short-term precipitation changes
that would have impacted the Maya (e.g., Haug et al.
2001; Peterson and Haug 2005).
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Correspondence: ISBER/MesoAmerican Research Center, University of California, Santa Barbara, CA 93106–2150, e-mail: ford@marc.
ucsb.edu (Ford); Department of Geography, University of California, Santa Barbara, CA 93106–4060, e-mail: [email protected] (Clarke);
940 Sumack Reno, NV 89509, e-mail: [email protected] (Raines).