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ARH
312Y – Archaeological Laboratory

Spatial
Analyses

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Apart from stratigraphy, the prime archaeological
evidence for context comes from spatial relationships, and archaeologists
depend on these relationships very heavily for their interpretations
of ancient human behavior, site-formation processes, and the
meaning of the archaeological record. Here we will explore spatial
analysis at various spatial scales. This summary will be longer
than usual, because this is a topic not covered in the published
version of the text. I apologize that I have not yet had time
to add any graphics

The cultural significance of spatial
patterning

Archaeologists often assume that patterns
in the spatial distribution of and relationships between artifacts,
features and other observable data have meaning in terms of activity
areas, the organization of households, camps and larger settlements,
and human use of landscapes. As we have seen (chapter 12), non-cultural
site-formation processes may also contribute to, or blur, these
patterns. Archaeologists have adopted a number of implicit and
explicit models for what cultural patterns in space should look
like at various scales and in various cultural and economic circumstances.

At relatively small scales, archaeologists
talk about tool kits and activity areas. An activity area represents
the place where one person or a few people carried out a single
activity, such as removing flakes from a core. Sometimes combinations
of tool types and other materials found within small clusters
should provide clues to the activities with which they were associated
– the recurring combinations of artifacts are sometimes called
tool kits – but usually identification of activity areas and
tool kits depends on the assumption that items were dropped where
they were used and never substantially moved prior to their discovery
by archaeologists. This occasionally happens, but usually site-formation
processes are much more complicated:

The traditional concept of “activity
area,” although perhaps useful in terms of observable activity
performance (e.g., in an ethnographic context), is not necessarily
a valid concept in terms of deposition. Simply put, people might
well perform “activities” in “areas,” but
there is no reason to expect them to map those areas with their
garbage; material products of activities may often be collected
in dump locations along with the products of other activities
performed in other areas (Rigaud and Simek 1991: 217).

Consequently, although it is still useful
to attempt to detect spatial patterns at this scale, analysts
must take these problems into account. In general, activity areas
are easiest to identify in cases where there was only one brief
occupation and little later disturbance, or where there was repeated,
intensive activity of a particular kind within a well-bounded
area, such as repeated food preparation within a room we might
call a “kitchen.”

At somewhat larger scales, archaeologists
often attempt to find the boundaries of work areas or households
or to understand how households may have been organized into
household clusters and neighborhoods.

At larger scales still, archaeologists
attempt to discover spatial structure in settlements. The archaeological
correlates of these communities are often assumed to be “sites,”
but in practice most archaeologists count as sites any apparently
concentrated cluster of artifacts on the landscape, including
small artifact scatters that could be the residues of isolated
single-activity areas as well as large cities. Defining which
sites should be considered the remains of communities, such as
villages, can be difficult in some instances, and fairly trivial
in others.

At the largest scales, archaeologists try
to understand why settlements and other types of sites are distributed
the way they are on the landscape, to discover what relationships
there may have been between sites, and generally how the people
who made and used the sites may have exploited the environment
or even conceptualized the cosmos. The pattern with which sites
are distributed on the landscape is called a settlement pattern,
while the way in which the sites interacted and jointly operated
within the society (or societies) that used them, economically,
politically, socially and ideologically, is called a settlement
system.

At the regional scale, geographers have
provided us with some models for settlement patterns with which
we can attempt to compare the distributions of known sites. This
kind of modelling has a much longer history than you would expect.
Most current models owe something to Central Place Theory, as
formulated by von Thünen (1826), and expanded by Christaller
(1933).

Von Thünen hypothesized that, other
things being equal, market forces and transport costs would encourage
different land uses at varying distances away from a city. Extensive
land use would take place only on the periphery, where transport
costs to the city were high, while intensive land use, such as
market gardening, would take place in a ring closer to the city.
This was an economic model for land use, with close links to
decision theory and cost-benefit analysis.

Christaller (1933) had noticed that, in
reasonably flat plains in parts of Germany, contemporary settlements
tended to be very regularly spaced. Furthermore, they tended
to be arranged in a hexagonal lattice, and in a hierarchy so
that a large town would occupy the center of a hexagon, six smaller
towns would occupy the hexagon’s corners, and small villages
would be located about halfway between each pair of towns. He
attributed this pattern principally to the economic efficiencies
that resulted from it under a market economy. For example, farmers
were able to locate themselves so that they had three markets
for their produce within a short distance of their farms, and
transport costs between towns could be minimized. Services that
consumers expected to use frequently were distributed thinly
and evenly over the landscape, while more costly services they
would use less often were located in central places, still within
a reasonable distance, but not as convenient as the more critical
services. Among the kinds of services that Christaller examined
were churches, post offices, telegraph offices, and government
agencies.

Central Place Theory seems applicable in
many places outside Germany as long as the terrain approximates
a flat, undifferentiated plain and settlement is heavily influenced
by market forces. In other situations we would at least expect
distortion of the classic hexagonal lattice. For example, where
there is a navigable river, transport costs are much reduced
near the river and the lattice becomes “stretched”
linearly along it. Johnson (1972) attempted to fit such a distorted
lattice to settlement patterns in ancient Mesopotamia, where
extensive canal networks would have been the least costly transport
routes, as well as the lifeblood of the settlements’ agriculture.

In general, however, Central Place Theory
has not had as large an impact on archaeology as you might expect
simply because it is often difficult to satisfy two more of its
assumptions: that all of the settlement locations are known and
that all of them were occupied simultaneously. Central Place
Theory is particularly ill-suited to analysis of data from spatial
samples; because typical archaeological surveys only examine
a patchy sample of the landscape and therefore miss a great many
sites, it is usually unreasonable to assume that we know where
all the sites are. In future, however, and particularly with
the aid of GIS (below), it is possible that Central Place Theory
will begin to fluorish in archaeology as a model with which we
might predict the location of undiscovered sites, and then do
new fieldwork to test the predictions.

Kinds of spatial analysis

No matter what the scale of archaeologists’
spatial investigations, they can choose among quite a number
of approaches to the problem of uncovering spatial patterns.
We may group many of these into the broad categories of point-pattern
analyses, grid-based distributional analyses, graph-theory approaches,
and Geographic Information Systems (GIS). In addition, we can
distinguish analyses that deal with one kind of phenomenon at
a time from ones aimed at discovering the relationship between
different phenomena over space.

In point-pattern analyses, the data involve
the locations of individual artifacts, features, sites or some
other observations in three-dimensional or two-dimensional space.
The purpose of the analyses can be to discern clustering of these
objects that might be related to activity areas, in the case
of artifacts, or social boundaries between sites, for example,
to reveal patterns in the way various classes of artifacts or
various attributes co-occur, which might tell us something about
tool-kits and activities, to discover the way in which artifacts
of known source were distributed to consumers, or to clarify
site-formation processes. In sites where the only evidence for
architecture consists of post holes, we may try to discern patterned
groups of post holes belonging to individual structures (Bradley
and Small 1985).

Point-pattern analysis

Point-pattern analysis has a very long
history in archaeology. In the late 19th century, many archaeologists
produced maps showing the locations of artifact finds in their
attempts to delineate the geographical boundaries of what they
regarded as archaeological cultures. In the 1960s, French prehistorians
made great strides toward the identification of spatial patterns
in the debris on Palaeolithic sites. As a student, I remember
being quite impressed by a film in which the overlapping distributions
of lithics, ash, cobbles, bones and even bear claws were used
to infer the outlines of huts and even (on the assumption that
phalanges and claws were attached to furs) sleeping areas. Until
recently, however, the delineation of such patterns involved
the subjective, visual examination of point-patterns on maps.
These inferences can be creative but, as with all analyses, are
influenced by the implicit preconceptions and explicit models
of researchers.

Carr (1991) shows how archaeologists with
two different conceptual models, one explicit, the other implicit,
obtain quite different interpretations of the debris at Pincevent,
a Magdalenian site in northern France that has produced radiocarbon
dates of about 11,000 bp. Faunal remains suggest that the site
was a reindeer-hunting camp occupied in late winter and spring.
The site’s excavators (Leroi-Gourhan and Brezillon 1966) interpret
the spatial patterns at “habitation no. 1” as the residue
of three interconnected, teepee-like huts, each with an indoor
hearth and a sleeping area (figure 17.3). Binford (1983: 156-60)
instead interprets hearths 2 and 3 as outdoor hearths that were
used sequentially, probably when the users moved in response
to a change in wind direction. One might be tempted to conclude
that this is a relatively minor distinction but many avenues
of research on the site, including estimates of population size
based on floor area and number of contemporary hearths, depend
on which interpretation (if either) is right.

Binford uses as a model for interpreting
the Pincevent site a pattern he observed among Alaskan Nunamiut,
which he calls the “Men’s” Outside Hearth Model (figure
17.4). According to this model, several men sat in an arc around
the upwind side of the hearth (to avoid smoke), and dropped small
waste, such as small flint chips from flintknapping and small
bone fragments, in their immediate vicinity, but threw larger
debris that would get in their way as they worked or make sitting
uncomfortable either over their shoulders or across the fire
in front of them. This pattern of behavior created a “drop
zone” in an arc near the hearth and two “toss zones”
farther from the hearth. When Binford overlaid a scaled version
of this model on the distribution maps from Pincevent habitation
no. 1, he concluded that the model’s drop zone “fits exactly”
with the distribution of lithic debris (figure 17.5). Certainly
the largest concentrations of such debris are in arcs around
the hearths, as the model would predict, although Carr (1991:
231) draws our attention to other, smaller but well-defined arcs
that Binford’s model does not address. Binford found much poorer
fit of his model to the bone distributions, and Carr (1991: 232)
notes that this probably results from the fact that the distribution
includes both large bones and small fragments. Binford instead
opts to explain the poor fit as the result of overlapping toss
zones from different episodes of hearth use, oriented differently
because of changes in wind direction. Even this does not account
for the bone distribution very well, and some of the backward
toss zones are nearly empty of bone. As Carr notes (1991: 234),
often large bones and lithics occur in the drop zones, and not
in the toss zones where the model predicts they should be, while
the boundaries of the toss zones appear too crisp to be the result
of casual tossing (figure 17.6), which should result in a gradual
diminishing density of debris away from the hearth area (1991:
235-36).

Leroi-Gourhan and Brézillon (1966),
by contrast, studied the debris patterns, noticed the abrupt
changes in the density of debris, and implicitly fit them to
a hut model. A very satisfying way to account for the fact that
concentrations of debris seemed to form very distinct arcs was
to infer that the debris had been kicked or swept against some
kind of barrier, such as a tent wall. A number of different lines
of evidence help to corroberate this interpretation. Red ocher
appears to have been sprinkled on the floor just prior to occupation,
and its stains also stop abruptly at the arcs defined by chipping
debris, while the areas that Leroi-Gourhan and Brézillon
suppose were swept, as indicated by very low debris density,
also lack ocher (figure 17.7). Refitting burin spalls to the
burins from which they were struck shows that the spalls found
in an arc of debris for one of the putative huts often fit burins
found in the drop zone of another alleged hut, or vice versa
(figure 17.8). The same can be said of refit flakes and cores
(figure 17.9). Although there are other ways this could happen,
this distribution of refits is consistent with the idea that
debris in all three “hut” areas was swept together,
in several different sweeping episodes. “This pattern would
have been generated if work around one hut’s hearth had been
followed by the sweeping of the resulting debris against the
walls of another hut, which would have been standing at the same
time” (Carr 1991: 246). The orientation of debris also supports
the hut model. The long axes of many of the larger bones and
lithics run parallel to the arcs that mark the possible hut walls
(Carr 1991: 246). The distribution of large flint nodules and
a hummock of sediment at fairly regular intervals along the arcs,
particularly on the western side that would have been exposed
to the prevailing wind, makes sense if they were used to anchor
tent poles or weigh down a tent skirt, and, it is important to
remember that the site was occupied in winter during a very cold
phase of the Pleistocene, not a very good time to do work requiring
manual dexterity, such as burin production, out-of-doors (Carr
1991: 246-47). Even the microstratigraphy of the three hearths
matches, with two carbon-rich lenses separated by a thin lens
of sediment, which would be unlikely if the hearths were not
used simultaneously.

Certainly, careful visual examination of
point patterns, in combination with other sources of information,
can sometimes result in quite vivid reconstructions of some of
the activities that produced them but, as in the Pincevent example,
we can sometimes say that one reconstruction seems more plausible
than another, but the measure of plausibility is rather subjective.
How clustered do the items have to be do be considered “clustered?”
How dense do the clusters have to be to be “concentrations?”
How abrupt does the falloff in density have to be to be considered
“crisp?” At what scale should the clusters exist to
be culturally meaningful? All these questions pose difficulties
for point-pattern analyses even when site-formation processes
are fairly straightforward and well understood.

Some people have tried to refine point-pattern
analysis and address at least some of these questions by taking
a more quantitative approach. During the last two decades one
of the principal uses of point-pattern analysis has been in the
attempt to recognize clustering of the points quantitatively.

The most common technique that archaeologists
have used in this attempt is Nearest Neighbor Analysis.
This technique is very easy to apply in cases where its assumptions
are valid. We must assume that our point-map does not omit any
points (therefore we cannot use a sample of a larger population
unless it is a fairly large and spatially contiguous cluster
sample), and that all the points (whether artifacts, features
or sites) are contemporaneous. Then, for each point, we simply
measure the linear distance (r) to the nearest neighboring point,
and we average all these distances to obtain the mean distance
to nearest neighbor and the standard deviation on this distance.
When the points are highly clustered, this mean distance to nearest
neighbor is relatively low, when they are randomly distributed
it is intermediary, and when they are evenly distributed, it
is high. But how high is high and how low is low? To standardize
our measure we then divide it by the theoretical mean for a random
distribution of points — or 2 * the square root of rho, where
rho is the density of points on the map or (n-1)/A and A is the
area.

Our measure of the degree of randomness
in the distribution (R) then simply becomes the ratio of the
observed and expected mean distances: mean r (observed)/mean
r (expected).

The result consistently ranges between zero (highly clustered),
through 1.0 (random) to a little over 2 (evenly distributed).

Where the assumptions of Central Place
Theory can reasonably be applied, and where our analyses indicate
a relatively even distribution of sites, one of the tools we
can use to detect the hexagonal (or some other) structure is
to construct Thiessen polygons. To do this we simply draw
line segments between each pair of settlements (figure 17.11),
and then draw more line segments that bisect the first ones at
a 90o angle. We then erase the first set of line segments as
well as any parts of the second set that extend past the point
of intersection with others. In a more complicated scenario,
we can attempt to account for differential weight of settlements
(e.g., large central places might be expected to have more territory
than small villages) by intersecting the first set of line segments,
not at their halfway points, but at a length away from each settlement
that is proportional to the settlement’s relative “importance.”
We can measure this importance in a number of ways – population,
site size, number of services, proportion of elite goods – and
if, for example, we are trying to find the boundary between a
two sites with an importance ratio of 2:1, the perpendicular
would be placed two-thirds of the way from the most important
site (Hodder and Orton 1976: 59-60, 78-80).

Another form of simple point-pattern analysis
has been popular among archaeologists studying regional settlement
systems, but has recently been largely displaced by GIS (see
below). This analysis involves patterns, not between the locations
of the points, but in the relationships between the points and
various environmental attributes, such as soil type, elevation
above sea level, and distance to permanent water sources. Even
quite early archaeologists noticed these kinds of environmental
associations, such as the apparent tendency for Linearbandkeramik
(LBK) sites to be located on loess soils in Europe (Buttler 1938).
In the more modern form of these analyses, the actual associations
between site locations and various environmental types are compared
with the distribution you would expect if the sites were located
randomly on the landscape. In other words, the question in the
case of LBK sites is, “are LBK sites located on loess soils
more often than we would expect to happen by chance?” If
the association is purely by chance, we would expect, on average,
that the proportion of sites on loess would be the same as the
proportion of space that is covered by loess. Since the environmental
categories constitute a nominal scale, we can compare the observed
and the expected site distributions with a one-sample chi-square
test. Essentially, the value of chi-square is high when there
are very large differences between the observed and expected
values; in the example here, LBK sites are found so much more
often on loess soils than we would expect to happen by chance
that we would tend to conclude that there really is a preference
for the sites to be located on loess soils. Of course we should
be careful about the possibility that our sample of sites could
be biased by factors of differential preservation or by the research
habits of their discoverers, and should ensure that we are not
violating any of the chi-square tests’ assumptions.

The key here is to be sure to compare the
observed distribution with the distribution expected from a random
pattern of dots. Archaeologists sometimes forget this when, during
exploratory analysis of point patterns, they notice what seems
to be an interesting pattern.

For example, Coinman et al. (1988) notice
extreme clustering of Palaeolithic sites at low and high elevations
in the tributaries of Wadi al-Hasa, in southern Jordan, and attempt
to explain them by fitting them to a general model of a settlement
system with small camps in part of the year, seasonally coalescing
into large “aggregation camps” or base camps to take
advantage of a seasonally available resource while participating
in large-group social activities. Coinman et al. (1988) notice
that, when you plot site size against elevation for the Wadi
al-Hasa tributaries, you find a few, mainly small, sites at low
elevations, usually no sites at intermediary elevations, and
mixtures of large and small sites at high elevations. This seems
to satisfy the model if the large sites at high elevations represent
the aggregation camps and the small sites at high and low elevations
represent dispersal camps at different seasons. However, they
do not compare this distribution to an expected distribution
under a random model. The clear separation between low and high
sites is easily explicable by the substantial cliffs that separate
the narrow valley bottoms of Wadi al-Hasa’s drainage from the
ridge-tops and broad plateaux above them (1988: 61, 64) and make
it virtually impossible for open-air sites to occur at intermediary
elevations, which occupy only a small percentage of the research
area. It is equally impossible for large sites to occupy the
narrow valley bottoms unless they are extremely linear in shape.
The large sites at higher elevations are probably actually palimpsests
of overlapping, deflated, small sites that wind has collapsed
into a surface that is nearly continously “paved” with
lithics (Banning 1988: 17). Coinman et al (1988: 51, 54, 61)
recognize that these are problems, and make some attempt to take
the availability of different elevation zones into account (1988:
58, 63). The point of using this exploratory study as an example
is that a comparison to a random distribution would have been
an easy way to see whether the apparent pattern had anything
to do with prehistoric cultural practices.

In another case, Alan Zarky (1976) attempts
to determine whether prehistoric sites at Ocós, Guatemala,
were located to take particular advantage of certain resource
zones by comparing the known site distributions with “expected”
ones, much as just suggested. To do this he uses the one-sample
chi-square test that we already saw, however briefly, in connection
with grouping methods (above, pp. 41-43). He applies the chi-square
test in a way that violates the test’s assumptions, but we can
use this example to show how one could compare the environmental
contexts of point-patterns with those expected under a random
model before going on to illustrate a better method based on
spatial sample elements.

Zarky’s analysis is predicated on a number
of assumptions. First, is the assumption that the 36 archaeological
sites to which the analysis pertains constitute a random sample
of the population of sites for the periods under study. In fact,
however, the data come from a random sample of spatial units
(Plog 1968), not a random sample of sites, so Zarky is treating
these sites as a cluster sample (see above, pp. xx-xx). Second,
the chi-square test requires a sample size large enough that
no more than about one-fifth of the cells in the table have expected
frequencies below 5. Zarky finds that his analysis, which employed
a large number of cells so that he could test for several environmental
variables at once, had far too many cells with low expected values
(1976: 127). Third, the chi-square test that Zarky selects to
compare the known distribution of sites with a random distribution
assumes that the observations consist of counts, and presumably
this is one reason that Zarky has decided to use numbers of sites,
rather than measures on some spatial unit, for his analysis.
However, although he recognizes this limitation, he also recognizes
that it is the proportion of some resource area that lies within
the site’s catchment that is really of interest, not just the
presence or absence of that resource at or close to each site
(Zarky 1976: 120-119). Consequently, he attempts to modify the
chi-square test by counting sites with two resource zones within
their half-kilometer catchment areas as half-a-site for each,
those with three resource zones as three one-third-sites, and
so on. He suggests that this “a good approximation”
and satisfies the assumptions of the chi-squaretest (Zarky 1976:
126) but, in fact, this tinkering with the method is not statistically
valid. Rather than try to adapt the chi-square test, he should
have used a test that was well suited to measures on spatial
areas.

But first, let us assume that the 36 sites
do represent a random sample to illustrate how the chi-square
test could have been used to evaluate a simpler hypothesis without
such tinkering. Let our hypothesis be that the location of Middle
and Late Formative sites gave them preferential access to the
resources of Mangrove …

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