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Research Article

Experimental Improvements to the Volume Ratio and Quantifying Movement Using Stone Artefact Analysis

Authors:

Stacey Middleton ,

University of Auckland, NZ
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Rebecca Phillipps

University of Auckland, NZ
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Abstract

Many conceptual frameworks of archaeological assemblages have assumed that stone artefact assemblages include all products of manufacture, use, and discard, although recent studies have indicated this is not always the case. The volume ratio is a method that examines the potential for the removal or addition of stone artefacts to an assemblage after manufacture. As humans transport material, and the movement of material effects the composition of assemblages, the alteration of an assemblage through the addition or removal of material can act as a proxy for mobility. This research uses three experimental assemblages to test the effect that different methods of volume quantification and reconstruction have on the calculation of the volume ratio. Results suggest observed assemblage volume is accurately and efficiently calculated using a standardised density of 2.46 g/cm3, while the modelled assemblage volume is relatively accurately calculated using either the Volumetric Reconstruction Method (VRM) or the Flake Volumetric Reconstruction Method (FVRM) with the potential for future research to further improve this methodology.

How to Cite: Middleton, S. and Phillipps, R., 2022. Experimental Improvements to the Volume Ratio and Quantifying Movement Using Stone Artefact Analysis. Journal of Computer Applications in Archaeology, 5(1), pp.152–168. DOI: http://doi.org/10.5334/jcaa.93
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  Published on 13 Oct 2022
 Accepted on 02 Oct 2022            Submitted on 29 Apr 2022

Introduction

Many methods of stone artefact analysis assume the spatial distribution and composition of stone artefact assemblages reflect the total products of manufacture, use, and discard at a single location (Dibble et al. 2017). Methods such as refitting have demonstrated that stone artefact assemblages are often missing elements from the reduction sequences of artefact manufacture, and therefore assemblages rarely contain the total products of manufacture (Turq et al. 2013). Several archaeologists have used other methods of stone artefact assemblage analysis to demonstrate the movement of artefacts to and from assemblages across landscapes (e.g., Davies, Holdaway, and Fanning 2018; Douglass et al. 2008; Holdaway and Davies 2019). This has prompted archaeologists to move away from assuming assemblages are complete to an understanding of the complex, dynamic processes that affect the formation of an assemblage (Dibble et al. 2017).

The volume ratio (Phillipps 2012; Phillipps and Holdaway 2016) provides a method to measure artefact movement to and from assemblages. The method approaches the archaeological record as a palimpsest of behaviour that has formed as a result of numerous discard events affected by formation processes. The volume ratio compares the total observed volume of artefacts at a single location to the modelled volume of the original selected nodules that would have been reduced (Phillipps and Holdaway 2016). Differences between these two figures can suggest the removal of stone material (volume) or the addition of stone material, and as the removal or addition of material acts as a proxy for the movement of people this acts as an empirical measure of movement. The modelling of the volume of original nodules can be achieved in several ways and previous research (Phillipps and Holdaway 2016; Middleton 2019) suggests this can have an impact on the outcomes of the volume ratio. Likewise, the calculation of the total observed volume can be calculated in a number of ways and has the potential to impact the volume ratio. Changes in measuring apparatus can provide one solution to improve the accuracy of these calculations, in addition to assumptions that underlie them. Refining the methodology is critical as the method can be used as a proxy for relative degrees of movement or mobility, which is crucial in understanding processes of settlement, occupation, migration, and relationships with place. Measuring relative degrees of movement within and between locations can allow for greater nuance when developing models of mobility (Phillipps and Holdaway 2016).

Background

Stone artefacts provide the ideal proxy to explore the “hard evidence” of movement as they are ubiquitous, durable, and were moved by people in the past. Movement has been empirically measured in the archaeological record using stone artefact analysis and a variety of concepts and methods. Previous understandings of the movement of material have included the concept of curation, often contrasted with expediency, introduced by Binford (1973, 1979) to explain the behavioural relationship between people, movement, and the use-life of objects described as the transport of material for anticipated needs. Curation thus encompasses a wide range of behavioural processes such as production, design, transport, maintenance, caching, and recycling, all to maximise the utility of a particular material (Bamforth 1986; Odell 1996; Shott 1996). These concepts were adopted to measure the technological organisation of individual tools and assemblages to interpret movement using economic principles (Nash 1996; Shott 1996). However, as Close (2000) discusses, the use of concepts such as curation and expediency, or logistical and residential mobility, highlight the difference between mobility and movement. Mobility can be considered to define the potential to move discussed in concepts derived from ethnoarchaeology that involve planning and strategies for future movement as well as actualised movement. Comparatively, movement can be considered as the realised consequence of mobility that has the potential to leaves traces in the archaeological record (Close 2000). While curation may provide insight into mobility (see Close 1996; Sellet 2006; Shott 1996; Sullivan 2016; Torrence 1983), our interest here is to develop methods to quantify human movement that is measurable using the archaeological record.

Refitting provides an approach that uses stone artefacts for evidence of actualised movement (Close 1996). The refit of two artefacts from the same reduction sequence at different locations provide definitive evidence of movement (Close 2000). However, refitting has highlighted the difficulty of interpreting movement beyond individual instances of flake removal from a core, and the movement of these pieces from manufacture location (Foley, Spry, and Stern 2017; Morrow 1996). Refitting links the discard location of an individual flake to the discard location of the core from which it was removed and provides insight into reduction sequence. However, this only provides insight into point to point movement with the potential for multiple knappers to move and reduce a single nodule in different behavioural contexts throughout an artefacts’ use life (Dibble et al. 2017). Discussing and comparing movement through refitting creates problems when interpreting and quantifying this type of small scale behavioural processes within the temporal, behavioural, and spatial context of cumulative movement that effects stone artefact assemblage composition (Dibble et al. 2017; Holdaway and Davies 2019). Methods that empirically measure and compare direct evidence of movement that recognise the complexity of the archaeological record and assemblage composition are therefore explored here.

The Volume Ratio and Movement

The volume ratio provides a method that empirically measures the direct evidence of movement across areas at a scale appropriate to the archaeological record. The volume ratio combines the total debitage of a discrete archaeological area, indiscriminately incorporating non-retouched flakes and debitage (Holdaway, Douglass, and Phillipps 2014). The principles of these methods are specific to the movement and transport of material, shifting conceptualisations away from equifinal arguments connecting movement to retouched or “formal” artefacts (Douglass and Holdaway 2011; Douglass et al. 2008; Holdaway, Douglass, and Phillipps 2014). This allows for the empirical measurement and comparison of “actualised” movement shifting analyses away from vague, subjective concepts such as sedentism or mobility and equifinal correlations with “formal” artefacts. The application of the volume ratio allows for the analysis of movement strategies as a continuous phenomenon that occurs across the landscape (Holdaway et al. 2008). Movement strategies of people are assumed to be embedded within the movement and discard of material (Davies, Holdaway, and Fanning 2018). The volume ratio assumes that material can be moved throughout its use life but becomes incorporated into an assemblage upon discard, which can be volumetrically altered through the addition or removal of material (Phillipps and Holdaway 2016). The removal of material from a “complete reduction sequence” in different spatial and temporal contexts should therefore be quantifiable through the absence of material volume (Phillipps and Holdaway 2016). Quantifying the volume ratio therefore needs to be accurate if the issue of equifinality is to be removed from archaeological interpretations of movement and stone artefact assemblages. Errors from quantification, such as calculating original assemblage volume and reconstructing original core volume (discussed in depth below), can over or under represent the amount of material added or removed from an assemblage. This effects the accuracy of the volume ratio and error is therefore conflated with an increased or decreased amount of material moved from an assemblage, effecting our ability to interpret and compare different levels of movement across assemblages. This research aims to improve the quantification of the volume ratio to strengthen the methodology as a useful tool in quantifying movement and exploring the formation of stone artefact assemblages at a scale appropriate to the archaeological record.

Calculating the Volume Ratio

The volume ratio was proposed by Phillipps (2012), and developed by Phillipps and Holdaway (2016), and Ditchfield et al. (2014) as an alternative or supplement to the cortex ratio (see: Davies, Holdaway, and Fanning 2018; Dibble et al. 2005; Ditchfield 2016a, 2016b; Douglass and Holdaway 2011; Douglass 2010; Douglass et al. 2008, 2021; Holdaway and Davies 2019; Holdaway et al. 2008; Holdaway, Douglass, and Fanning 2012, 2013; Holdaway, Fanning, and Rhodes 2008; Holdaway, Wendrich and Phillipps 2010; Lin, McPherron, and Dibble 2015, 2016; Parker 2011; Shiner, Holdaway and Fanning 2018). The volume ratio is a method similar to the cortex ratio but utilises volume rather than cortex and surface area to calculate the amount of material removed from an assemblage. This method assumes that material can be moved through various spatial, behavioural, and temporal contexts but becomes incorporated into an assemblage upon discard, which can be volumetrically altered through the addition or removal of material (Phillipps and Holdaway 2016). Unlike the cortex ratio, the volume ratio does not assume that nodules are fully cortical when procured and reduced, but instead assumes a negative relationship between original nodule volume and flake removal (Dibble et al. 2005; Phillipps and Holdaway 2016). The volume ratio is therefore necessary for lithic sources that may not have a fully cortical nodule prior to reduction, as in Aotearoa, New Zealand (Moore 2015; Phillipps 2012). This method of artefact analysis is applicable to a range of archaeological areas including surface scatters and stratigraphic deposits (Holdaway and Davies 2019; Phillipps 2012). As shown in Figure 1, the volume ratio is calculated by dividing the total observed assemblage volume by the modelled assemblage volume. A volume ratio of 1 would indicate that all products of reduction are represented in a location, while under or over 1 represents the addition or removal of material, or equally a value of 1 could represent an equilibrium in the addition or removal of material from an area (Davies, Holdaway, and Fanning 2018).

The formula for calculating the volume ratio with the various previous methods used for calculating observed assemblage volume and original nodule volume
Figure 1 

The formula for calculating the volume ratio with the various previous methods used for calculating observed assemblage volume and original nodule volume.

Calculating Observed Assemblage Volume

The observed assemblage volume is derived by calculating the total volume of flakes, cores, and tools in an assemblage. The observed assemblage volume has been calculated using three main approaches: mathematical formulas, density either using a standardised unit or individual object densities, and photogrammetry or laser scanning (Dibble et al. 2005; Ditchfield et al. 2014; Lin et al. 2010; Phillipps and Holdaway 2016). Observed assemblage volume calculated using mathematical formulas assign geometric shapes to flake classes and forms to calculate volume as in Phillipps and Holdaway (2016) (Figure 2). This method is generally employed when weight has not been measured or photogrammetry/laser scanning is not feasible due to time and access. Dibble et al. (2005) proposed the use of an average density of 2.46 g/cm3 to calculate volume for material classified as chert or obsidian, while others have used 2.53 g/cm3 for silcrete, and 2.64 g/cm3 for quartz (Douglass et al. 2008; Douglass and Holdaway 2011). The use of hydrostatic weighing to calculate density, and therefore volume, has proven to be an accurate and efficient method to calculate artefact volume (Armitage 1971; Reeves and Armitage 1973). However, an average value to standardise density and volume calculations has not been experimentally demonstrated to accurately calculate volume for chert and obsidian. Results from Lin et al. (2010), Middleton (2021), and Ditchfield (2016a) found digital methods, such as photogrammetry or laser scanning, accurately measure the volume and surface area of stone artefacts.

Shapes and formula for estimating volume based on flake class and form (Phillipps and Holdaway 2016: Figure 6)
Figure 2 

Shapes and formula for estimating volume based on flake class and form (Phillipps and Holdaway 2016: Figure 6).

Calculating Modelled Assemblage Volume

The original nodule volume, used to calculate modelled assemblage volume, has been variably calculated through numerous methods: using the total assemblage volume divided by the number of cores, the upper quartile of core volume, the dimensions of unifacial cores with thickness increased by three, using a sample of raw material from the survey of local material in proximity to the studied archaeological area, or using regression analyses with width increased by 60% (Ditchfield et al. 2014; Lin, Douglass, and Mackay 2016; Phillipps 2012; Phillipps and Holdaway 2016) (Figure 2). These methods provide varying approaches to reconstruct original nodule volume and calculated modelled assemblage volume. Methods that involve raw material survey are appropriate when raw material sources are known, and these sources are represented in the archaeological sample. However, this method relies on arguments of uniformitarianism. Uniformitarianism is implicated in the assumptions of the relationship between distribution, size, and shape of exploited nodules found in archaeological assemblages (Lin et al. 2019a, 2019b). This assumes past nodules are morphologically the same as nodules found in the present and have not been altered by geological processes, and surveys can account for variability of nodule selection across various reduction sequences and raw material sources. Methods that calculate the original nodule volume by dividing assemblage volume by the number of cores has been critiqued for the assumption the number of cores found represents the original number of nodules or cobbles used (Finkel and Gopher 2018). The modelling of original nodule volume must therefore reconstruct the volume of material removed from cores through the process of reduction.

Proposed Methods for Calculating Original Nodule Volume

The method, known as the Volumetric Reconstruction Method (VRM) assumes the dimensions of flakes in an assemblage will be suitable to model the dimensions of negative flake scars produced on the core (Lombao et al. 2020). The addition of average flake platform thickness or flake thickness to core dimensions are used to calculate volume using geometric formulas similar to shapes produced through various knapping strategies (Figure 3). This method of estimation was shown to strongly correlate with original nodule volume. However, the estimation tends to variably underestimate original nodule volume for each knapping strategy (Lombao et al. 2020). The VRM substitutes the maximum dimensions of a core into the formula for a sphere or an ellipsoid (dependent on the reduction strategy). The maximum dimensions of the core are corrected using the average flake thickness. As Figure 3 shows, the principle of this method assumes that the average flake thickness reconstructs volume lost through the removal of flakes during the reduction of a nodule.

The principles of volumetric reconstruction for the VRM using the geometric formula for an ellipsoid (left) and sphere (right)
Figure 3 

The principles of volumetric reconstruction for the VRM using the geometric formula for an ellipsoid (left) and sphere (right).

The Adjusted Volumetric Reconstruction Method (AVRM) is a novel development of the VRM. This acknowledges that while the VRM accounts for volume loss, this does not consider reduction intensity. As a factor that effects the intensity of flake removal and therefore volume loss from a core, accounting for reduction intensity is crucial in reconstructing original nodule volume. The AVRM thus incorporates the average dorsal scar count of complete flakes to further correct the dimensions of cores to account for volume lost through varying reduction intensities. As shown in Figure 4, the maximum dimensions of a core are substituted into a geometric formula with the average flake thickness multiplied by the average complete flake dorsal scar count. The principle of this method assumes that as cores are reduced evidence of previous flake removals are erased (Braun et al. 2005; Douglass et al. 2017; Lombao et al. 2019). The AVRM therefore reconstructs volume lost through the reduction process by multiplying flake thickness by dorsal scar count to account for volume lost through the erasure of flake scars.

The principles of volumetric reconstruction for the AVRM using the geometric formula for an ellipsoid (left) and sphere (right)
Figure 4 

The principles of volumetric reconstruction for the AVRM using the geometric formula for an ellipsoid (left) and sphere (right).

The Flake Volumetric Reconstruction Method (FVRM) is a method of volumetric reconstruction that accounts for volume loss that uses core scar count and dorsal scar count as proxies for reduction intensity and volume loss. This method uses the observed core volume and the average volume of flakes in an assemblage to reconstruct original nodule volume. This principle relies on the preservation of negative flake scars on cores and complete flakes to measure volume loss as shown in Figure 5. The core scar count is multiplied by average dorsal flake scar count and summed with the core scar count to calculate the lost number of flakes. The product of this calculation is multiplied by average flake volume to calculate the amount of volume lost through flake removal. This is added to the observed core volume to derive the original nodule volume. The FVRM therefore adds the observed core volume to the modelled flake volume loss to reconstruct the volume of the original nodule.

The FVRM principles of volumetric reconstruction showing a flake (left) and the core it was removed from (right) with the areas highlighted showing negative flake scars, and therefore volume lost from the original nodule through reduction
Figure 5 

The FVRM principles of volumetric reconstruction showing a flake (left) and the core it was removed from (right) with the areas highlighted showing negative flake scars, and therefore volume lost from the original nodule through reduction.

Experimental Dataset and Methods

Three experimental and archaeological datasets are used to test each aspect of the volume ratio. The experimental goals are as follows:

  1. To test the accuracy of mathematical formula in quantifying total assemblage volume using photogrammetry as the comparative method
  2. To test the use of standardised and non-standardised density to improve the accuracy and efficiency of quantifying total assemblage volume
  3. To test the three methods (VRM, AVRM, FVRM) of original nodule volume reconstruction to improve the calculation of modelled assemblage volume

Experiment one is tested using an experimental assemblage produced by Douglass et al. (2008). Two silcrete reduction sequences were selected from the experimental assemblage, with 18 flakes and one core in the first reduction sequence (assemblage one), and 47 flakes and one core in the second reduction sequence (assemblage two). The resulting sample of the experimental assemblage totalled 65 flakes and two cores, representative of two reduced cobbles. Models were constructed for each flake and core (photogrammetric methods discussed below). The volume of the 67 3D models were recorded using the measure surface area and volume tool in Agisoft Metashape 1.5.5 (Agisoft 2019). The form and class of the flake were classified to determine the formula used to calculate estimated volume of complete flakes (Phillipps and Holdaway 2016). Measurements were taken at the maximum length, width, and thickness of flakes and cores to substitute into the mathematical formula.

Experiment two uses an archaeological sample of obsidian previously analysed with pXRF (McBride 2019), and a reference collection of chert from natural sources (Moore, Sheppard, and Prickett, unpublished manuscript). The archaeological sample is from Waitapu, Ahuahu (Great Mercury Island) and represents a sample of obsidian (n = 665) that has been sourced to eight source locations in Aotearoa, New Zealand as shown in Figure 6. The chert sample is a reference collection that represents a sample of chert and sinter (n = 227) surveyed from 16 source locations as shown in Figure 7. The density of each object was calculated using hydrostatic weighing where an object is weighed in air (in grams), and then weighed while suspended in a liquid of known density (Armitage 1971). The density was calculated by substituting the air weight, water weight, and density of water at a given temperature into the formula for the density of a solid object (Mettler Toledo 2000). The volume of each object was calculated and compared against volume calculated using the standardised density for obsidian and chert (2.46 g/cm3).

Map showing the location of obsidian sources/regions (circles) and study sites (triangles)
Figure 6 

Map showing the location of obsidian sources/regions (circles) and study sites (triangles).

Map showing the location of chert sources in the chert reference collection (adapted from Moore, Sheppard, and Prickett, unpublished manuscript)
Figure 7 

Map showing the location of chert sources in the chert reference collection (adapted from Moore, Sheppard, and Prickett, unpublished manuscript).

Experiment three is tested using an experimental assemblage that was reduced and modelled to test the proposed methods for calculating original nodule volume. Three chert cores of different material type and quality were sourced from raw material surveys conducted on Ahuahu, Great Mercury Island. These cores were reduced with various manufacturing goals and were reflexively altered as material was tested for its viability in producing the manufacturing goal (Table 1). Flakes were removed using a hammerstone and each strike was defined as a reduction attempt. After each reduction attempt, the core was modelled using photogrammetry following procedures outlined below. These models were used to measure the relationship between volume, surface area, and flake scars throughout the reduction process. The resulting data are used to explore the possibility of reconstructing volume loss using the properties of flakes and cores in order to refine the calculation of modelled assemblage volume.

Table 1

The manufacturing goals, core volume, and flake metrics for Experiment 3.


CORE NUMBER CORE 1 CORE 2 CORE 3

Manufacturing Goal Drill points and drill point blanks Large flakes with long cutting edges Drill points

Original Volume (mm3) 871,651.3 1,659,654.4 868,255.2

Total Flake Number 90 75 68

Maximum Flake Dimension (mm) 27 35 25

Final Volume (mm3) 71,707.4 14,731.7 118,026.8

Photogrammetric Methods

This research follows current trends in modelling, particularly for lithics, that uses either laser scanning or photogrammetry to quantify lithic attributes to develop methodologies and test archaeological questions (Clarkson 2013; Clarkson, Shipton, and Weisler 2014; Li, Kuman, and Li 2015; Li et al. 2018; Lin et al. 2010; Shipton and Clarkson 2015a, 2015b). Physical attributes of lithics such as surface area or dimensional metrics have been accurately quantified in experimental and archaeological contexts using photogrammetry to refine methods such as the Cortex Ratio or the Scar Density Index (Clarkson 2013; Lin et al. 2010). The approach used in this research follows this methodological direction in photogrammetry to quantify volume and other metrics to refine the volume ratio.

The photogrammetry set-up utilised general procedures and principles outlined by Porter, Roussel, and Soressi (2016). Objects were fixed on a stand with plasticine. The object and stand were placed on a Syrp electronic turntable within a white photography tent with a white or black velvet background. The stand included a two-dimensional target pattern placed at known, measured co-ordinates to provide a reference system for scaling at the model construction phase and measure error in the calculation of volume (Galantucci, Guerra, and Lavecchia 2018). The black or white velvet background removed any external objects or textures and allowed for focus on the target object. The object was flooded with light at each angle visible to the camera to remove differential shadows and light exposure caused by the movement of the object (Porter, Roussel, and Soressi 2016). Four videos were taken for each object to capture the entire surface area of an object. The videos were imported and processed in Agisoft Metashape 1.5.5 (2019) to create the final model (as shown in Figure 8).

The process of making a photogrammetric model: (a) the creation of tie points, (b) a density cloud, (c) mesh, (d) aligned top and bottom meshes, (e) and final model with texture
Figure 8 

The process of making a photogrammetric model: (a) the creation of tie points, (b) a density cloud, (c) mesh, (d) aligned top and bottom meshes, (e) and final model with texture.

Experimental Results- Observed Assemblage Volume

Experiment One- Formulas and Photogrammetry

The 3D modelled volume, calculated using photogrammetry, was used as a baseline to compare the accuracy of calculated volume using 3D shape formulas for flake and core classes. Table 2 shows that on average, formulas based on shape tend to overestimate volume. The overestimations are moderate for proximal, distal, and complete flakes with normal and blade forms. Calculations are overestimated by less than 100% of the modelled flake volume. The overestimations for angular fragments, and complete flakes with expanding forms are relatively high with estimations more than 100% of the modelled flake volume. Cores have a comparatively low overestimation with calculated volume overestimated by 12%. The complete flake class with contracting form tends to underestimate flake volume by 38% of the modelled volume.

Table 2

Average percentage difference between formula calculated volume and 3D modelled volume.


ARTEFACT CLASS FORM AVERAGE DIFFERENCE (%)

Complete Flake Contracting –38

Complete Flake Expanding 127

Complete Flake Normal 51

Complete Flake Blade 60

Proximal Flake 81

Distal Flake 85

Angular Fragment 113

Core 12

Overall, the summary statistics in Table 3 show that formulas tend to overestimate volume by 65%, with a large standard deviation of 84.52%. This is reflective of the wide range of volume percentage differences ranging between 199% and –104%. As Figure 9 shows, when plotted the difference is highly variable particularly for smaller flakes with a cluster of flakes at 200% representing the flakes with the highest error (complete flakes with expanding form). This is further validated by percentage differences in total assemblage volume with formula calculated volume overestimating 3D modelled volume by 192%. The findings of these differences may affect the calculation of total assemblage volume, and therefore the accuracy of the volume ratio.

Table 3

Summary statistics for the difference between formula calculated volume and 3D modelled volume.


N MEAN SD MEDIAN MIN MAX SE

67 64.6 84.52 51.3 –103.93 199.42 10.33

The plotted relationship between modelled 3D volume and percentage of difference between calculated volume (Method 2) and modelled volume (Method 1)
Figure 9 

The plotted relationship between modelled 3D volume and percentage of difference between calculated volume (Method 2) and modelled volume (Method 1).

Experiment Two- Standardised and Non-Standardised Density

The volume of chert calculated using hydrostatic weighing, and standardised volume using a value of 2.46 g/cm3 are plotted in Figure 10. These values are highly correlated with a rho value of 0.99 and a p value of <0.0001. The average percentage difference between the standardised volume and the hydrostatic volume can be used to represent the general error of a standardised density to calculate volume. This gives an average error of 1.2% for the calculation of chert volume using a standardised density value of 2.46 g/cm3 (Middleton 2021). When the two populations are compared using a Wilcox non-parametric t test there is no significant difference between the two values and therefore quantification methods (p = 0.89).

The plotted relationship between chert volume standardised using a density of 2.46 g/cm3 (mm3) and chert volume calculated using hydrostatic weighing (mm3)
Figure 10 

The plotted relationship between chert volume standardised using a density of 2.46 g/cm3 (mm3) and chert volume calculated using hydrostatic weighing (mm3).

The volume of obsidian artefacts calculated using hydrostatic weighing, and standardised volume using a value of 2.46 g/cm3 are plotted in Figure 11. The standardised and hydrostatic volume is highly correlated with rho value of 0.999 and a p value of <0.0001. When total assemblage volume is calculated using volume from hydrostatic weighing and standardised volume the average error between the two samples is 3.5% (Middleton 2021). When the average error rate is considered, and the two populations of standardised and hydrostatic volume are compared using a Wilcox non-parametric t test, there is no significant difference between the two quantification methods (p = 0.47). When the volume calculated using hydrostatic weighing is used as an accurate modelled assemblage volume and the standardised density as the total assemblage volume this provides a volume ratio of 1.

The plotted relationship between obsidian volume standardised using a density of 2.46 g/cm3 (mm3) and obsidian volume calculated using hydrostatic weighing (mm)
Figure 11 

The plotted relationship between obsidian volume standardised using a density of 2.46 g/cm3 (mm3) and obsidian volume calculated using hydrostatic weighing (mm3).

Experiment Three Results- Modelled Assemblage Volume

Three different methods were used to reconstruct original nodule volume: the original Volumetric Reconstruction Method (VRM) developed independently by Middleton (2019) and Lombao et al. (2020), the Adjusted Volumetric Reconstruction Method (AVRM), and Flake Volumetric Reconstruction Method (FVRM). The original nodule volume of the core was calculated for each method, and percentage of average error was calculated using the percentage difference between the original nodule core volume and the modelled original nodule volume (following Lombao et al. (2020) and Middleton (2019)). As shown in Table 4, the AVRM overestimates original nodule volume providing the highest overall percentage of average error. The average error is highest for the reconstruction of volume for Core 1, 3, and total modelled assemblage volume with error ranging from 56% to 113%. The VRM method has the lower percentage of average error for the calculation of original nodule volume for Core 1 and total modelled assemblage volume, which is overestimated by 36% and 4% respectively. However, Core 2 has a relatively high percentage of average error with an 115% underestimation of original nodule volume. This increases the range of overall percentage of average error for the VRM to between 4% and 115% giving an overall difference of 39,045 mm3 for the calculation of modelled assemblage volume. This error range is the lowest of the three methods. The FVRM overestimates the original nodule volume for Core 1, 3, and modelled assemblage volume with error ranging from 11–107%. This error rate is slightly above the VRM method with a difference of 110,761 mm3 for the calculation of modelled assemblage volume. The VRM and FVRM both have the highest rates of error for Core 2 with an underestimation by 115% and 107% respectively. The reduction of Core 2 shows the most rapid volume loss of the three cores. The high reduction intensity and production of numerous large flakes would have increased the likelihood of erasing previous evidence of flake removals. The AVRM accounts for the high reduction intensity of Core 2 with the lowest error rate for original nodule volume at 56% underestimation.

Table 4

Comparisons of volumetric reconstruction methods and the percentage average error (PAE ±) in the calculation of original nodule volume.


CORE ID ORIGINAL NODULE VOLUME (MM3) VRM (MM3) PAE ± (%) AVRM (MM3) PAE ± (%) FVRM PAE ± (%)

1 228,878 330,474 36% 763,649 108% 471,835 69%

2 458,956 124,788 115% 258,155 56% 139,772 107%

3 243,639 515,256 72% 880,477 113% 430,627 56%

Total 931,473 970,518 4% 1,902,281 69% 1,042,234 11%

Table 5

The comparison of observed assemblage volume to the modelled assemblage volume calculated using each volumetric reconstruction method.


METHOD OBSERVED ASSEMBLAGE VOLUME (MM3) MODELLED ASSEMBLAGE VOLUME (MM3) VOLUME RATIO

VRM 851,098 970,518 0.88

AVRM 851,098 1,902,281 0.45

FVRM 851,098 1,042,234 0.82

The VRM, AVRM, and FVRM provide the formula to calculate the original nodule volume, and subsequently modelled assemblage volume within the formula for the volume ratio. As each flake knapped during the reduction process was collected and weighed, the total observed assemblage volume should be close to the original nodule volume. Some volume loss should be due to small shatter and the standardisation of density using the value of 2.46 g/cm3. The total modelled assemblage volume is the cumulative total of the original nodule volume of the three cores. The subsequent volume ratios should be close to 1, indicating the majority of material volume remains within the sample. Table 5 shows the calculation of the volume ratio using the VRM, AVRM, and FVRM. The previous calculations of percentage of average error for the VRM, AVRM, and FVRM indicate that the VRM should provide less overall error in the calculation of modelled assemblage volume compared to the AVRM and FVRM. The volume ratio for VRM is 0.88 and FVRM is 0.82. While this is close to the value of 1 expected by an accurate volume ratio these methods tend to overestimate assemblage volume. Comparatively, the AVRM volume ratio of 0.45 is significantly lower than the VRM and FVRM and has a high percentage of average error with 76% difference between observed assemblage volume and modelled assemblage volume.

Discussion

This study refines the volume ratio method using experimental data to explore improvements to the calculation of observed and modelled assemblage volume. Results from experiment one showed that mathematical formulas tend to variably over or underestimate observed assemblage volume and presumably affect the calculation of the volume ratio. These findings are similar to Lin et al. (2010), which also found a significant overestimation of calculations compared to modelled surface area. However, due to the increased dimension of volume compared to surface area, these differences are greater and more variable. While these results are pronounced due to the small sample size these results provide an insight into the inflation of artefact volume as a result of the use of geometric formula. The results of the summary statistics further indicate that when volume estimations are calculated using 3D shape formulas, volume estimates can be highly variable in the over or underestimation of volume. As demonstrated in experiment two, when a standardised density value for chert and obsidian is used this can provide an accurate and efficient method of quantifying observed assemblage volume.

The results of experiment three demonstrate the improvement of the calculation of modelled assemblage volume using the VRM or FVRM. While the improvements to observed assemblage volume accurately provide a volume ratio of 1, the results of this experiment indicate the modelled assemblage volume using the VRM or FVRM does not yet provide an accurate volume ratio of 1. As the FVRM is a novel method of reconstructing original nodule volume, future revisions may include other flake or core metrics such as platform angle, flake length and thickness, alongside negative flake scars on cores to improve this method of volume reconstruction and therefore the volume ratio. However, this study has demonstrated the value in accounting for reduction intensity for the reconstruction of original nodule volume and with further experimentation there is promise in a novel and accurate method of volumetric reconstruction in modelling assemblage volume.

The results presented here suggest there is value in refining the methods for calculating the volume ratio and increased availability of tools such as photogrammetry in conjunction with experimental archaeology should facilitate continued improvement. The volume ratio is a useful measure for empirically assessing relative differences in movement across a range of spatial and temporal contexts that addresses the contemporary conceptualisations of the archaeological record. This small initial study has explored how assemblage characteristics can be used to empirically measure movement using the archaeological record. Future research would replicate these experiments with a larger sample size under multiple transport scenarios to test this method in an archaeological context. The use of simulations has demonstrated the viability of such methods to empirically measure movement and the formation of stone artefact assemblages through the modelling of the Cortex Ratio (Davies, Holdaway, and Fanning 2018). However, the volume ratio has yet to be tested using simulations with an archaeological application and this provides the ideal future avenue for this method.

Conclusion

The experimental results found that the calculation of volume using mathematical formulas tended to inaccurately quantify volume and overestimated the quantification of total assemblage volume. While a standardised density of 2.46 g/cm3 did not significantly alter the calculation of observed volume and provides an accurate and efficient alternative to hydrostatic weighing, photogrammetry, or geometric formula. The experimental reduction set tested the reconstruction of the original nodule volume using a variety of methods. The VRM and FVRM were found to be two methods that increased the accuracy of reconstructed original nodule volume and therefore modelled assemblage volume. However, further research would refine the accuracy of the modelled assemblage volume to accurately reflect a volume ratio at or close to 1. The potential of the volume ratio to address the formation processes and its outcomes evident in archaeological assemblages is significant given current shifts in ontological approaches and conceptual understandings of the archaeological record. The volume ratio has the potential to provide a model of movement appropriate to the scale of the archaeological record that can be compared across various temporal and spatial contexts.

Acknowledgements

The recent archaeological investigations are part of the Ahuahu Great Mercury Island Archaeological project, which is a collaboration between Waipapa Taumata Rau (the University of Auckland), Tāmaki Paenga Hira (Auckland War Memorial Museum), Sir Michael Fay as a representative landowner, and Ngati Hei of Wharekaho. This research was supported by the Royal Society of New Zealand Marsden Fund (18-UOA-058).

Competing Interests

The authors have no competing interests to declare.

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