2.3.1. Quantitative approaches to regional exchange

An influential approach to long-distance exchange was developed by Colin Renfrew and his colleagues (Renfrew, et al. 1968) who asserted that the spatial distributions of a raw material like obsidian could be used to infer not only extent of interaction, but mode of exchange. In subsequent investigations these distance decay relationships were further explored and in 1977 Renfrew defined the Law of Monotonic Decrement (LMD):

In circumstances of uniform loss or deposition, and in the absence of highly organized directional (i.e., preferential, nonhomogeneous) exchange, the curve of frequency or abundance of occurrence of an exchanged commodity against effective distance from a localized source will be a monotonic decreasing one (Renfrew 1977: 72).

Here, and in other publications, Renfrew (1975;1977) and Hodder (1974;1978;Hodder and Orton 1976), sought to interpret exchange relationships and the friction of distance from the shape of "fall-off curves" where the abundance of material is plotted against cost, usually distance from the source. The novelty in this approach is that it sought to determine "types" of exchange that substantive anthropologists had placed in evolutionary sequence using explicit, formalist measures of abundance and cost. These distance decay graphs included "Down-the-line" exchange thought to represent reciprocity, "freelance" trade representing barter, and even laissez-faire capitalism. More general and robust characterizations were described as well. For example, low value, often cumbersome goods were shown to have different distance decay profiles than prestige-goods exchange (Hodder 1974;Hodder and Orton 1976: 124).

Other scholars adopted this approach and in places like Mesoamerica the method held promise because obsidian sources were abundant, and material from many sources were, for the most part, visually distinct (Braswell, et al. 2000). Raymond Sidrys developed a "Trade Index" that, he argued, showed that major ceremonial centers acquired obsidian in volume from greater distances.

Figure 2-5. Log-Log fall-off curve of obsidian density (grams of obsidian/m3 of fill). Line 1 is a regression line derived from major ceremonial centers while line 2 is derived from minor centers (Sidrys 1976: 454).

The axes of the fall-off graphs are on linear, power or logarithmic scales. Depending on the data available, interaction can be measured by using absolute or relative measures. Abundance of a non-local good at site A is assessed in absolute terms using weight of material from site A divided by estimated population for site A, or abundance is measured in relative terms using percentage by weight or artifact count from site A in the total raw material class for that site (Earle 1977: 6;Renfrew 1977: 73).

In his work with Neolithic Near Eastern obsidian Renfrew (1969: 157) specifies that areas less than 300 km from the geological source area, at least for Neolithic modes of exchange, are in the "supply zone" because obsidian represents over 80% of the material in lithic assemblages at sites found in that zone. Areas beyond the 300 km band Renfrew refers to as the "contact zone" and it is in that area that he argued the shape and angle of the fall-off curve could provide insights into prehistoric economy. The "interaction zone", or universe of study, for a sourceable material was defined by Renfrew to be the area within which 30% or more of the obsidian was derived from a single obsidian source. A similar approach was taken with Mesoamerican obsidian in the Oaxaca area by Jane Wheeler Pires-Ferreira (1976: 301) but in this case a 20% threshold was used to define the interaction zone. There appears to be no ethnographic basis for the source, contact, or interaction zone threshold values used by Renfrew and others.

In the course of further exploration of the parameters associated with fall-off curves, serious weaknesses were identified that limit their utility for identifying forms of exchange solely on the basis of the shape of the curve. Hodder (1974;1978;Hodder and Orton 1976: 127-154) simulated a large number of simple random walks and found that generally similar fall-off curves could be produced by different combinations of variables, a condition known as equifinality. In other words, a Gaussian artifact distribution that results in a fall-off curve that Renfrew would have described as "down-the-line exchange" could as have been the result of random walks. Hodder and Orton (1976: 142-143) found that the more convex curves have higher a values and that these are the result of a greater number of short steps usually associated with highly portable value goods. Ammerman et al. (1978: 181-184) explored the fall-off curve with simulation studies and found that in the interpretation of down-the-line models one must consider the accumulated effects of time over the long-term. Further, they argue that accumulation rates in archaeological studies of down-the-line systems can modeled by using realistic estimates of "passing" and "dropping" of artifacts in distribution systems. Critical evaluations of the utility of fall-off curves demonstrate that Renfrew's goal of distinguishing reciprocity, redistribution, and market exchange from two-dimensional graphs was overambitious. It has been shown, however, that the relative shape of fall-off curves can aid in differentiating high value commodities from bulky, utilitarian goods. These graphs are valuable for highlighting variations from the LMD, and these deviations can point towards avenues for further data exploration. Hodder and Orton (1976: 155-160) suggest applying trend surface analysis to distribution data, an approach that was implemented in the 1970s raster-based computer mapping package SYMAP. Trend surface analysis and geostatistics have become considerably easier using modern GIS methods.

2.3.2. Other Distance Decay studies

Approaches to the study of attenuation with distance were applied in a variety of other regions worldwide, and these studies have been ably summarized by Torrence (1986: 10-37). A valuable theme in these studies has been the exploration of deviations from Renfrew's Law of Monotonic Decrement, and suggestions for improvement of distance decay models. Gary Wright (1970) proposes that predictions made by the LMD could be improved by controlling for variations in consumption through time and between types of consumer sites, and he emphasizes that investigators consider the influence of alternative materials in the study area, such as the effects of local flint on demand for imported obsidian. Wright (1970;Wright and Grodus 1969: 47-52) also advocates using weight of a non-local good as a measure of abundance, rather than count or percentage of each artifact class. For time periods prior to the domestication of beasts of burden in the Near East, when the weight of artifacts was borne directly by human carriers, weight would more likely influence behavior and discard patterns. Renfrew also considers weight in his analysis, but he observes that weight would be influenced by stylistic and functional factors.

Geographical relationships are considered in more detail in subsequent research. Jonathon Ericson (1977;1977;1981;1982) conducted an exhaustive study of California obsidian distributions and, by focusing on deviations from the LMD, and using regression analysis, he was able to assess the strengths and weaknesses of the approach. Ericson uses trend surface analysis available in the early raster-based mapping system SYMAP to produce maps showing isometric distributions of obsidian types in consumption sites (Ericson 1977: Figures 1-4). In comparing this form of analysis with Renfrew's distance decay graph distributions Ericson states that "in two-dimensional analysis only the magnitude of an observation and its distance from a source is considered, the spatial position of the observation is not considered in its local context; and this simplification masks significant variability in the data" (Ericson 1977: 110). Ericson's density maps demonstrate that, while distance from source is a primary determinant of obsidian type, the distributions of obsidian consumption locations are not symmetrical around the source areas. Ericson explores the spatial relationships by superimposing trail systems, alternative material distributions, and ethnolinguistic group boundaries (Kroeber 1925) on the obsidian consumption density maps and finds that these spatial phenomena influence obsidian distributions.

Similar to Ericson's implementation of trend surface analysis, Findlow and Bolognese (1982: 60-70) perform a SYMAP analysis using the percentage of lithic assemblages represented by obsidian throughout their study region. Their maps are useful in that they show the changing territoriality and direction of obsidian procurement through time in the region. However, as their obsidian percentage isolines only display aggregated obsidian versus not obsidian data, and do not differentiate between source types of obsidian, the maps are difficult to interpret in terms of exchange distances from the sources through time.

Quantitative data available for Ericson's (1977: 121-123;1977: 249-257) analysis include isotropic distance calculations between discard locations and geological source areas, and estimated population by consumption area. A multiple linear regression analysis using the percentage of obsidian from a single source showed that, as stated by the LMD, the distance from the source had the highest predictive power. However, the estimated population in a given consumption area had only slightly less power in predicting the source of the obsidian being used than did distance to the closest source, and the distance to the second closest obsidian source had virtually no predictive power. Ericson interprets these data in terms of the degree of utilitarian use of a commodity and level of necessity for the average person in the community. Thus, in the proximity of the geological source of a raw material widely used in the community, the source types with high population levels in the immediate vicinity of the source would have been more widely used in exchange systems (Ericson 1977: 120).

An improvement in the calculation of effective distance with an incorporation of the influence of topographic relief in the cost accumulation with fall-off curves was first explored by Findlow and Bolognese (1980;1982). In their study in the U.S. Southwest the authors manually develop the linear solutions known today in GIS as "Least-cost paths" or, as Findlow and Bolognese (1980: 239) express it, "the line between the site and the source that at once minimized distance and topographic relief". They find that when these paths are used in the cost function then variability is accounted for more strongly than when using an isotropic distance estimate.

The technology of transport can dramatically alter the effective distance, and changes in mode of transportation have been proposed as explanations for variability in distance decay curves through time (Hodder and Orton 1976: 113,117-118;Renfrew 1977: 73). Torrence (1986: 122-123) reviews the issue and she also discusses boat transport (1986: 135-136). The adoption of river and sea-going vessels in Mesoamerica are discussed by Sidrys (1977: 103-105), and in the Mediterranean by Ammerman (1979;1978). Gary Wright (1970) mentions the importance of considering the weight of transported material for the period before the domestication of cargo animals and the availability of caravan trade networks in the Near East. Similarly, working in the Andes, Richard Burger and his co-authors (2000: 348) consider the impact of camelid domestication and llama caravan networks on obsidian distributions.

The prediction, following the LMD, that artifact size or weight should diminish with distance from the source area (Wright 1969: 47-52;Wright 1970;Wright and Grodus 1969) is not necessarily supported in cases where the form of the artifact, such as projectile points or bladelets, take precedence over effective distance from source. Angela Close (1999) found that at early Neolithic sites in southwestern Egypt flint backed bladelets, even very close to the source, were produced to be very narrow due to hafting requirements, defying the prediction of LMD. Close (1999) also found that among the late Neolithic sites unretouched, unbroken flint debitage did not conform to the LMD either, a situation that she attributes to the probable use of domestic cattle in transporting flint cores (Close 1996). With formal tools, such as projectile points, artifact form may take precedence over size. Hofman (1991) found with Folsom points that did not diminish in size with distance from the raw material source. However, incidence of resharpening can be expect to increase with distance from the source, affecting tool size (Andrefsky 1994).

The gravity model was another approach borrowed from geography and applied to the study of regional artifact distributions (Chappell 1986;Hallam, et al. 1976;Hodder 1974;Renfrew 1977: 87-88). Gravity models are used in situations where artifacts made from raw materials from a number of competing sources are found in a given consumption site. The claim is that the approach quantifies the "attractiveness" of a given material type over other types available to the consumers in a site by comparing actual proportions with expected proportions of the material given the predictions of the LMD. However, as Torrence (1986: 27) observes, "in reality, the gravity model is merely a means for describing and comparing distributions which are already reasonably well documented." While gravity models could be useful in parsing complex temporal patterns in raw material use in production and consumption at a given site, the approach does not provide a means of inferring the character of exchange relationships between consumption sites in prehistory.

Throughout the 1970s, the regional exchange literature shows an increasing awareness of the limitations of a purely spatial approach to inferring modes of exchange through formal geographical regression analysis. Renfrew's ambitious models linking geographical distance-decay with substantive modes of exchange connected to an associated evolutionary socio-political level, were meant to be sufficiently general to operate through time and in different cultural contexts. However, from simulation studies and from archaeological applications, researchers observed that it was necessary to incorporate supplementary information along with the geographical data on long-distance exchange and consumption, in order for distance decay studies to be useful. The view that chemically derived exchange data must be considered in association with information about archaeological context was first expressed by Wright (1969) and was widely echoed in the contributions to Ericson and Earle's (1982) volume "Contexts for Prehistoric Exchange" as well as in later volumes on exchange including Ericson and Baugh (1993) and Baugh and Ericson (1994). Preserving the strengths of geographical analyses from the 1970s period of investigation and combined with a greater consideration of artifact form, regional variation in reduction strategies and site-specific contexts of consumption, offers a fruitful way forward.

2.3.3. Site-oriented studies of exchange

As obsidian moved farther from its source, the size of the pieces traded progressively decreased and the relative value increased. ...Small blades were obtained simply by smashing a large block with a stone, while in time blades were broken into smaller fragments to obtain newly sharp edges (Harding 1967: 42).

Establishing consistent links between the types of social structure and the forms and organization of production in association with exchange was the approach taken by Ericson (1982) and, most explicitly, by Torrence (1986). By investigating the standardization and error rates in blade reduction strategies at obsidian production sites on the Greek island of Melos, Torrence was able to evaluate the degree of specialization involved in the quarrying and production of obsidian at the source.

In her review of archaeological site-oriented studies of exchange, Torrence (1986: 27-37) uses a few major themes to characterize site-oriented investigations. These themes include measures of abundance, source composition percentages, and the variability in archaeological context and artifactual form of import.

2.3.4. Discussion

A period of vigorous exploration of spatial models of exchange followed on the initial availability of chemical characterization methods in the 1960s. In addition to responding to new proveniencing methods, these developments also reflected a convergence between formal analytical models borrowed from quantitative geography (Haggett 1966;Harvey 1969) and the spatial models of processual archaeology in the early 1970s. As the potential and the limitations of the formal geographical approaches have became more evident, archaeologists have been able to take stock of the insights from that period (Bradley and Edmonds 1993: 5-11;Clark 2003: 32-42;Hodder 1982;Torrence 1986: 10-37, 115-138).

Exploration of a variety of promising measures and ratios for regional analysis is one of positive products of these regional distance decay studies. For obsidian distance decay, the ideal analytical situation would involve a variety of metric measures for each artifact, and the chemical type would be known for every artifact of sourcable material. While such detailed analyses have not been generally available, analysts have made do with other measures such as visual assessment of obsidian type (although it is unreliable in many regions) and relative measures of abundance. These measures of abundance include: (1) proportion of obsidian in total lithic assemblage by count or weight, (2) proportion of obsidian flakes to other artifact classes like ground stone or ceramics, and (3) density of obsidian by excavated volume of soil. A variety of additional inventive measures were explored during this period. Further details from consumption contexts, such as variability in material type by spatial and temporal provenience, are important for regional studies, although acquiring consistent and comparable measures from various archaeological projects can be difficult.

Technological innovations promise to lend greater support to both chemical characterization and geographical analyses in coming years. Developments in GIS and other spatial technologies have greatly facilitated the management and analysis of spatial data. An associated technological development is portable chemical characterization devices such as portable X-ray fluorescence (XRF) units. It is likely that, in the not-too-distant future, XRF analysis will become a routine part of lab analysis for many archaeological projects (Jeff Speakman, May 2006, pers. comm.), a development that will significantly expand the archaeological significance of quarry studies and geographical relationships between production and consumption locales.

In sum, the confluence of spatial technology with the widespread use of non-destructive chemical characterization methods in archaeology will likely result in the emergence of a rigorous proveniencing and spatial analysis sub-discipline in archaeology in coming years. The foundations of this sub-discipline were explored in the 1970s but with greater refinement in theoretical approaches to exchange and the organization of technology, as well as the issues of artifact variability, and the consumption contexts of exchange, one may expect significant contributions from regional analysis in coming years.