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.

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.