The influence of time averaging and space averaging on the application of foraging theory in zooarchaeology

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Abstract

Use of models derived from foraging theory to explain variation in prey-abundance indices over time and space, evidenced in the zooarchaeological record, is common in western North America. Such use presumes that models derived from ecologically scaled observations are applicable to archaeologically scaled observations. The influence of time averaging and space averaging, whether inherent in the zooarchaeological record or resulting from analytical lumping, on interpretations of changes in relative availability of prey is demonstrated with real data to mask fine-scale variation. The critical issue that must be addressed at the beginning of any application of foraging-theory models is the specification of the spatio-temporal scale of the research question.

Introduction

For more than 20 years, Americanist zooarchaeologists have called on foraging theory [58] to provide models of human-resource use [3], [68]. Even biologists have occasionally applied such models to zooarchaeological materials [35], [55]. During the 1990s, use of these models in western North America resulted in the development of a set of methods for monitoring the history of human resource use as evidenced by the zooarchaeological record [8], [9], [10], [11], [15], [19], [32], [33], [34], [50], [51], [63]. Some of the more interesting implications of these models concern the fact that pre-industrial humans had significant influences on prehistoric faunas the world over; these implications have now been abundantly confirmed by the zooarchaeological record (summarized in Ref. [29]). In particular, as a result of their selective exploitation of prey taxa that provided either or both low costs and high returns, humans with primitive technologies often caused changes in faunal diversity (taxonomic richness and evenness), independent of changes in climate. Therefore, humans sometimes had to alter what they were exploiting as a response to a change in the availability of animal prey that they themselves had caused.

Many significant new insights into the past have been provided by applying foraging theory to zooarchaeological problems. Yet such application is not always straightforward and thus the voice of caution hasoccasionally been heard. For example, many studies conclude that changes in the list of exploited prey to include more small, low-value prey taxa were the result of human exploitation depressing the availability of large, high-value prey taxa. The voice of cautionrequires that this explanation be substantiated by disconfirmation of alternative causes of depressed prey availability, such as changes in technology, changesin how technology was used, and environmentally or climatically driven changes in taxonomic abundances [30]. Further, it has been pointed out from anOld-World context that zooarchaeological abundances of Linnaean taxa do not always reveal changes in prey availability with respect to particular spatio-temporal coordinates [59]. Finally, it has been noted that the traditional means of quantifying prey abundances—the number of identified (faunal) specimens (NISP) per taxon—entails various epistemological and interpretive difficulties [66]. Importantly, analytical techniques have been and are being developed for addressing a number of these issues [18], [31], [60], [61], [67].

One potential difficulty for which there presently isno obvious analytical solution is that, as Grayson and Delpech [31, p. 1119] put it, if one is to apply explanatory models derived from foraging theory to the zooarchaeological record, “concepts that are meant to apply in ecological time must be translated to archaeological time.” In particular, they underscore the fact that with respect to prey-choice or diet-breadth models, where either is measured as the number of taxa exploited or taxonomic richness (NTAXA), the time period represented by a zooarchaeological assemblage results in NTAXA comprising the maximum number of taxa exploited during the total duration of time represented by that assemblage. Paraphrasing their example, if five taxa are exploited over 99 years, but those five taxa plus five additional taxa are procured in the 100th year, then diet breadth rendered as NTAXA for the assemblage resulting from that 100 years will be 10—the maximum number of taxa exploited (see also Ref. [12]). The significant point of this example is that variationbetween the first 99 years and the 100th year will be masked by the fact that multiple annual assemblages have been lumped by the formational history of the zooarchaeological assemblage. It is the effect of such lumping, whether along the temporal dimension, the spatial dimension, or both, that is one concern here.

A second concern is that there is another potential difficulty not previously mentioned in the pertinent literature. It resides in the variable typically referred to as sample size. The influences of sample size rendered as NISP are often acknowledged, and most zooarchaeologists who apply models derived from foraging theoryto their data take steps to account for sample sizewhen taxonomic richness or taxonomic abundance is measured with NISP (see Ref. [20] for a particularly important method in this respect). No zooarchaeologist I am aware of, however, has considered the potential influence of sample size rendered as the number of analyzed spatio-temporally distinct assemblages—what I will term NASM—of faunal remains, which arguably comprises a measure of sample size at a different scale than NISP.

The third and final concern resides in the fact that zooarchaeological assemblages comprise samples ofdifferent portions of the spatial and temporal continua. For discussion purposes I refer to these portionsas contexts, irrespective of size or duration. Eachassemblage of faunal remains occupies a unique context in terms of its spatial and temporal coordinates. The influence of the number of unique spatio-temporal contexts included in an analysis on interpretations of changes in prehistoric foraging is only now beginning to be examined (see subsequently). I refer to the frequency of these contexts generally as NCTX, the number of spatial contexts as NCTXspace, and the number of temporal contexts as NCTXtime. Note that sometimes NASM = NCTX, but the more typical relation will be NASM > NCTX as a result of analytical lumping. In this article, I explore some of the effects that NASM and NCTX have on analytical results produced by application of methods derived from foraging-theory models and used by zooarchaeologists working in western North America.

Section snippets

The usual method

I will not review the reasoning behind the application of foraging-theory models to zooarchaeological data here, as there are numerous such discussions now available [8,9,30]. It suffices to note that as used in western North America, the typical basic model—the prey-choice model—is that human foragers will preferentially exploit the largest prey first because these taxa are the most valuable. The model further holds that if valuable prey decrease in availability and thus the frequency at which

Materials and methods

For purposes of detecting the influences of spatio-temporal lumping on analyses and interpretations, the ideal situation would be to have assemblages meeting three criteria. First, the assemblages would be from various geographic locations in one physiographicarea. Such cases are commonplace in western North America where many archaeological projects havebeen undertaken under the auspices of cultural-resource management. Second, each assemblage would be of sufficient size in terms of NISP to

Results

To examine the influence of spatio-temporal lumping of assemblages, I first calculated the three AIs for all 31 assemblages. Here, NASM = 31, NCTXspace = 1, and NCTXtime = 30; Fig. 1;comptd;;center;stack;;;;;6;;;;;width> shows the scatterplot for the nonartiodactyl index. All three indices tend to increase over time—the slopes of the best-fit regression lines are positive—suggesting that the overall trend was for the abundance of artiodactyls to increase relative to small mammals (r=0.15), fish

Discussion

The general significance of the example discussed above for applications of models derived from foraging theory (or any explanatory theory) to zooarchaeological data should be clear. On the one hand, the manner in which zooarchaeological samples are lumped by space or by time—whether taphonomically or analytically—may reveal regionwide trends precisely because that lumping masks spatio-temporal variation within the region. Lumping data without consideration of the included spatio-temporal

Conclusions

The observation of Grayson and Delpech [31] that the application of models derived from foraging theory requires the translation of ecological time into archaeological time must be expanded to include the notion that those applications must also translate ecological space into archaeological space. Such translations have, to date, not been accomplished by literally converting or rewriting the ecological model in terms of archaeological variables. Rather, the models have simply been applied to

Acknowledgements

I thank M. J. O'Brien, M. C. Stiner, and twoanonymous reviewers for comments on an early draft.

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