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Simulating Lithic Raw Material Variability in Archaeological Contexts: A Re-evaluation and Revision of Brantingham’s Neutral Model

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Abstract

This paper presents a systematic re-evaluation of Brantingham’s (American Antiquity, 68(3), 487-509, 2003) neutral model of raw material procurement. I demonstrate that, in its original form, the model is ill-suited to the identification of archaeologically visible patterns, as it can only simulate processes governing the composition of toolkits and these differ substantially from those influencing the composition of discard records. I discuss and implement a series of modifications, and provide a detailed analysis of discard records produced under revised model definitions. On this basis, I argue that qualitative similarities in patterns generated by the neutral model and those evidenced in archaeological contexts cannot be used to prove, or disprove, the adaptive or functional significance of raw material variability (cf. Brantingham 2003). However, I show that the revised model can be used to detect deviations from neutral expectations quantitatively and within well-defined error ranges. I outline a new set of predictions for what archaeological variability should look like under the simplest procurement, transport, and discard behaviors, and argue that deviations from each of these may be traceable to specific behavioral domains (e.g., biased mobility, raw material selectivity). I also demonstrate that (a) archaeological sites or assemblages do not offer an adequate proxy for the average composition of ancient forager toolkits; (b) assemblage richness is, by itself, a very poor predictor of occupational histories; and (c) that the common practice of calculating expected frequencies from distances to sources is flawed, regardless of how such distances are measured.

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Notes

  1. Binford (1979: 259) argued that lithic raw material procurement was embedded in basic subsistence activities, but there is no reason to suspect that it may not also have been embedded in non-subsistence activities which may not be visible archaeologically (e.g., Gould and Saggers 1985: 122).

  2. While there are a series of ethnoarchaeological accounts of lithic procurement (e.g., Binford 1979; Gould and Saggers 1985; see also the review by McCall 2012), the studied populations had access to modern means of transport (e.g., Gould and Saggers 1985: 120), and even in the case of Binford’s study of the Nunamiut, which provided the basis for his “embedded procurement” argument, it failed to consider variables that are critical in understanding procurement behaviors (see Cole 2002: 54).

  3. As discussed by Sillitoe and Hardy (2003), there is certainly evidence to suggest that we may be overestimating the “true place [of lithics] within the material culture of which they formed part” (Sillitoe and Hardy 2003: 555).

  4. Information on toolkit states was still recorded for the first 200,000 time-steps, but only for diagnostic purposes.

  5. Note that Brantingham’s own reported modal and maximum transport distance values are also inconsistent with his predicted ratio of 3 to 4. Indeed, Brantingham (2003: 499) first argues that “the neutral model predicts that maximum raw material transport distances should be three to four times the foraging radius d” (italics mine), but in his discussion of archaeological parallels, he states that “[m]aximum transport distances are expected to be three to four times the distance represented by the internal mode” (Brantingham 2003: 501; italics mine). It is unclear why Brantingham equates foraging radii with internal modes (Brantingham 2003: 503), given that the foraging radius value he uses is 10 (e.g., Brantingham 2003: 499) and the modal value is 5 (Brantingham 2003: 498). Using the actual modal value he provides, the maximal to modal distance ratio is 8.6, not the 3–4 value used in his analysis of archaeological parallels.

  6. Note that the model provides only one and very weak mechanism for allowing such “random samples of different sizes” (Brantingham 2003: 493) to be drawn from the toolkit, namely the 1/9 probability that the agent will remain at the same location for two consecutive time-steps, discarding two items from the same toolkit at the same location. While arbitrarily obtaining toolkit samples larger than one by simply querying it for multiple items is technically possible, doing so would violate the definitions of the model (i.e., discard rates) and would provide meaningless results.

  7. It should be noted that Brantingham discusses patterns evidenced in toolkits states sampled over time, not in space (i.e., at a specific grid coordinate). This is probably because, as shown in the text, the definitions of the model prevent such spatial sampling.

  8. The distance an agent may cover in a given number of time-steps is equal to the number of time-steps, regardless of direction, because diagonal movements carry no penalty; in other words, under the mobility rules stipulated by Brantingham, the hypotenuse of a right triangle is equal in length to the other two sides. Thus, the distance between two sources located at x = ±5 and y = ±5 from each other is 5 grid cells.

  9. For the purposes of the GLM simulation, time-steps were counted from the first discard event onward; thus, the first discard event represents the first simulation time-step.

  10. Cell size was increased by one whenever a given time-step resulted in a higher maximum cell size than previously observed.

  11. The Python code for the generation of the raw data as well as the R code for all analyses are included in the Electronic Supplementary Material (ESM2).

  12. Multiplying the maximum cell size observed across all 500 simulations (30) by the maximum size of the toolkit (100) would yield but 3000 items.

  13. Two other aspects of the model may also prove problematic. First, random mobility cannot guarantee access to lithic sources (or indeed sites), and as argued by Oestmo et al. (2014) and also shown by my analyses (see ESM 1), this brings into question the survivability of foragers. However, the model makes no provisions for lithic recycling, which would allow foragers to recover previously discarded items, and it is in any case unclear whether access to lithic materials was as critical in the past as commonly assumed. While future revisions of the model could, and should, include provisions for non-random or semi-random mobility, whereby agents are allowed to gravitate around resources or sites, random mobility can nevertheless be accepted as a baseline. The second problematic aspect pertains to the number of modeled foragers: clearly, a single forager was not responsible for the formation of the archaeological record, and inter-agent communication likely played a major role. However, preliminary analyses revealed no differences between models run with multiple or single agents, and allowing for inter-agent communication would dramatically increase the complexity of the model. Therefore, as with random mobility, the patterns generated by a single agent provide an adequate baseline for interpreting the record and evaluating the effects of new variables that may be included in the model at a later stage.

  14. The frequency of moves in each of the nine possible directions was consistent with those expected under conditions of random draws from uniform distributions (simulation A, χ 2 = 2.8047, df = 8, p = 0.946; simulation B, χ 2 = 6.9466, df = 8, p = 0.542; simulation C, χ 2 = 5.1084, df = 8, p = 0.746); the same was true with regards to the selection of items for discard: the distribution of p values for the observed versus expected frequencies of selected discard indices at different toolkit sizes was uniform across all three simulations, with simulations A, B, and C yielding significant tests in 4.04, 5.05, and 3.02 % of cases respectively at an alpha level of 0.05.

  15. The choice of four nearest neighbors is arbitrary and is used here only to illustrate certain patterns. The optimal number of nearest neighbors to use will depend on the relationship between the global density of sources, the size of the toolkit, and the specified discard rates. Mean distances are used because a fixed number of neighbors is considered, and considering median distances would result in outliers being essentially ignored which, in this particular context, is not desirable.

  16. The pattern is more irregular around source b′ simply because of the lower sample sizes.

  17. The initial placement of the agent, as well as its mobility and discard behaviors, were fully and independently random in each simulation, as per the model’s specifications.

  18. Consider that, in order to attain a modal representation of 34 unique raw material types per cell, as is the case in the discard record of simulation A, effective exploitation areas of roughly 1700 grid cells (i.e., a linear radius of approximately 23 grid cells) are required at the specified resource density of 0.02 (i.e., 5000 sources on a 500 × 500 grid).

  19. This theoretical maximum is ill-defined by Brantingham: it cannot be considered in terms of assemblage size, which Brantingham seems to imply, because the number of discarded items found in the assemblage may exceed the number of physically available sources, and it cannot be considered in terms of the number of physically available sources without limiting inquiry to a given area, and it is unclear how large that area should be.

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Acknowledgments

I would like to express my gratitude to Will Archer, Sam Lin, Marcel Weiß, Dawit Desta, Harold Dibble, and Shannon McPherron for their insightful comments on earlier drafts of this manuscript, and to Mike Richards for the encouragement and for making this research possible.

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  1. Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Deutscher Platz 6, 04103, Leipzig, Germany

    Cornel M. Pop

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Pop, C.M. Simulating Lithic Raw Material Variability in Archaeological Contexts: A Re-evaluation and Revision of Brantingham’s Neutral Model. J Archaeol Method Theory 23, 1127–1161 (2016). https://doi.org/10.1007/s10816-015-9262-y

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