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/cm^{3}, 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.

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 (

The volume ratio (

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 (

Refitting provides an approach that uses stone artefacts for evidence of actualised 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 (

The volume ratio was proposed by Phillipps (

The formula for calculating the volume ratio with the various previous methods used for calculating observed assemblage volume and original nodule 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 (^{3} to calculate volume for material classified as chert or obsidian, while others have used 2.53 g/cm^{3} for silcrete, and 2.64 g/cm^{3} for quartz (

Shapes and formula for estimating volume based on flake class and form (

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% (

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 (

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

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

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.

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

To test the accuracy of mathematical formula in quantifying total assemblage volume using photogrammetry as the comparative method

To test the use of standardised and non-standardised density to improve the accuracy and efficiency of quantifying total assemblage volume

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

Experiment two uses an archaeological sample of obsidian previously analysed with pXRF (^{3}).

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

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 (

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 (mm^{3}) |
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 (mm^{3}) |
71,707.4 | 14,731.7 | 118,026.8 |

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 (

The photogrammetry set-up utilised general procedures and principles outlined by Porter, Roussel, and Soressi (

The process of making a photogrammetric model:

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.

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

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).

The volume of chert calculated using hydrostatic weighing, and standardised volume using a value of 2.46 g/cm^{3} are plotted in ^{3} (

The plotted relationship between chert volume standardised using a density of 2.46 g/cm^{3} (mm^{3}) and chert volume calculated using hydrostatic weighing (mm^{3}).

The volume of obsidian artefacts calculated using hydrostatic weighing, and standardised volume using a value of 2.46 g/cm^{3} are plotted in

The plotted relationship between obsidian volume standardised using a density of 2.46 g/cm^{3} (mm^{3}) and obsidian volume calculated using hydrostatic weighing (mm^{3}).

Three different methods were used to reconstruct original nodule volume: the original Volumetric Reconstruction Method (VRM) developed independently by Middleton (^{3} 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 mm^{3} 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.

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

CORE ID | ORIGINAL NODULE VOLUME (MM^{3}) |
VRM (MM^{3}) |
PAE ± (%) | AVRM (MM^{3}) |
PAE ± (%) | FVRM | PAE ± (%) |
---|---|---|---|---|---|---|---|

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

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

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

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

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

METHOD | OBSERVED ASSEMBLAGE VOLUME (MM^{3}) |
MODELLED ASSEMBLAGE VOLUME (MM^{3}) |
VOLUME RATIO |
---|---|---|---|

851,098 | 970,518 | 0.88 | |

851,098 | 1,902,281 | 0.45 | |

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/cm^{3}. 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.

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

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 (

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/cm^{3} 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.

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).

The authors have no competing interests to declare.