A distinction has often been made between two schools of thought, formalists and substantivists, about the way trade and exchange should be modeled. The former approach works within the paradigm of market economics. Here, all exchange transactions can be viewed by economic rationalism, based on cost efficiency. Falloff models presented in the section below are based on cost efficiencies. The substantivist school, on the other hand, views exchange as embedded in social and economic processes. This approach allows an investigation into social groups and social change. In reality, archaeologists draw from both approaches to model ancient interregional exchange.
Archaeologists analyze the distribution of an object from its source or production area to its consumption site in order to model the type of exchange that took place. In some instances, the nature of the society participating in the exchange system is inferred, such as egalitarian versus chiefdom, or nonhierarchical versus hierarchical. Popular among archaeologists is the use of falloff curves and modes of exchange. By plotting the frequency of an item against distance from its source (falloff curve), Colin Renfrew observed different distribution patterns which he attempted to relate modes of exchange or access. Some of these modes included reciprocity, down-the-line, and central place exchange.
How were falloff curves and modes of exchange related? Down-the-line exchange and reciprocity led to an exponential falloff in abundance, away from the source or production center. The term ‘Law of monotonic decrement’ was coined to account for this falloff in the frequency of an item away from the source. Attempts were also made to define an object’s value by the slope of the curve. Small slope equates with high value goods, such as spondylus shells in Europe, Maya jade, and Oaxaca iron ore mirrors. These modes were equated with an egalitarian society (semi-sedentary agriculturalists and hunter-gatherers; nonranked; nonhierarchical).
Central place exchange, on the other hand, was seen as directional (no exponential linear falloff) and should lead to multinodal falloff curves, and is indicative of redistribution.
Central place relates to the movement of goods towards one place or center, from which they are then distributed. Redistribution has been related to complex chiefly societies (hierarchical, ranked, and/or stratified societies). Examples of such societies given by archaeologists include early states such as the Maya, Egypt, Near East, or chiefdoms such as Hawaii.
Although problems occur with equifinality, that is, different modes of exchange produce similar distributions, this approach is important as it relates the measurement of archaeological material away from the source, to trade and exchange modes, and the structures of societies.
A good example of changes in inter-regional exchange systems can be seen in the distribution of obsidian in the western Pacific over 20 000 years. Here distribution patterns changed over time indicating changes in the socioeconomic configurations of these regional exchange systems. Patterns in the distribution of obsidian can be best modeled using either ‘down-the-line exchange’ models, or social connectivity.
For instance, the distribution of obsidian during the late Pleistocene and early to mid-Holocene is best explained by down-the-line exchange as there is an exponential falloff in abundance away from the source. The first evidence for the extraction and distribution of obsidian is found in the late Pleistocene site of Matenbek, New Ireland. In the bottom units dated to between 20 000 and 18 000 years ago, nearly 80% of obsidian came from the Mopir source and the rest from Willaumez Peninsula sources (see Figure 3). Matenbek lies over 350 km from the nearest Mopir obsidian source, and just over 400 km from the Willaumez Peninsula sources. The distribution of obsidian is best explained by the extraction of obsidian from the closest available source, and subsequent down-the-line exchange between semi-sedentary populations. This would account for the small appearance of Talasea obsidian and the dominance of Mopir in this assemblage.
However, taking an exponential falloff pattern alone could lead to erroneous models being developed. For instance, at 3300 years ago obsidian was distributed beyond the Bismarck Archipelago to Fiji in the east as part of the colonization of this region by Austronesian speaking peoples. Obsidian was brought out into the Pacific as part of that colonization process, yet it continued to be exchanged among Lapita communities. If the volume of obsidian is measured, then there is an exponential distribution from its source. Yet, by analyzing the assemblage in detail, differences are seen. The earlier Lapita assemblages show an expedient technology not seen in the earlier pre-Lapita or later assemblages away from the source regions. These assemblages had the largest pieces of obsidian and lacked bipolar flaking. Such an expedient technology is not expected from a down-the-line exchange network.
The distribution of this West New Britain obsidian could have been a result of either direct procurement or the movement of obsidian through a smaller number of hands. The movement of this obsidian was argued to be an indicator of a formal exchange network that was an adaptive mechanism in the colonization process forming a ‘lifeline’ back to a homeland. In this context, exchange is an adaptive strategy for colonists moving east and a means of maintaining social ties. When this lifeline is no longer needed, then exchange with homeland areas would cease.