Elysandre Puech

Marion Bamford

Guillaume Porraz

Aurore Val

Isabelle Théry-Parisot

Evaluating sampling methods in charcoal-rich layers and high diversity environment: a case study from the Later Stone Age of Bushman Rock Shelter, South Africa

Keywords: Anthracology, Southern Africa, Sampling strategy, Sampling bias, Sample representativeness, Environmental representativeness, Temporal and spatial resolution, Species richness, Species diversity, Fragment size distribution

In southern Africa, archaeobotanical studies are intrinsically linked to prehistoric investigation and the discipline of anthracology has already proved its potential for palaeoenvironmental and palaeoecological reconstructions. While the region benefits from particularly good preservation of macro charcoal remains in its sites, anthracological studies remain underexplored and the methodological framework still needs to be developed and adapted to the diverse southern African ecological contexts. Here we provide a review of sampling methods and sample representativeness and we compare it with wood charcoal analyses performed in southern Africa. We used the charcoal-rich layers from the Later Stone Age sequence of Bushman Rock Shelter (BRS) to elaborate a sampling strategy producing samples that can both be analysed in a timely manner and that are statistically representative of the whole assemblage. In light of our results, we discuss the relevance of applying anthracological methods developed in European contexts. The evaluation of the taxa richness, diversity and size distribution at BRS leads to the recommendation of the identification of at least 500 charcoal fragments per stratigraphic unit. Thick layers should be split into two distinct samples, one comprising the top half and the other one the bottom half of the layer. The analysis of thin layers with limited charcoal abundance necessitates increasing the surface of sampling. All size-classes should be analysed to avoid any sampling bias.

Introduction

The potential of charcoals as palaeoenvironmental proxy is now widely acknowledged (e.g. [START_REF] Chabal | La représentativité paléo-écologique des charbons de bois archéologiques issus du bois de feu[END_REF][START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF][START_REF] Figueiral | A review of charcoal analysis as a tool for assessing Quaternary and Tertiary environments: achievements and limits[END_REF]. Scattered charcoals from secondary deposits, i.e. long-term and "synthetic" deposits (sensu Théry-Parisot et al., 2010a) are traditionally preferred for the investigation of past woody vegetation since a higher diversity of taxa tends to be represented and thus better reflects the local environment [START_REF] Chabal | La représentativité paléo-écologique des charbons de bois archéologiques issus du bois de feu[END_REF][START_REF] Asouti | Reconstructing woodland vegetation and its exploitation by past societies, based on the analysis and interpretation of archaeological wood charcoal macro-remains[END_REF]. However, charcoal assemblages from other types of deposits, such as fireplaces, still provide both environmental and cultural information as long as the modality and context of accumulations are considered and with the adoption of a strict sampling and quantification method [START_REF] Asouti | Reconstructing woodland vegetation and its exploitation by past societies, based on the analysis and interpretation of archaeological wood charcoal macro-remains[END_REF]Théry-Parisot et al., 2010a;[START_REF] Delhon | Les assemblages de charbons "concentrés" : une piste pour améliorer leur représentativité. (Charcoal concentrations: a new track for improving their reliability)[END_REF].

To assess the use of charcoal fragments as a tool for palaeoenvironmental reconstruction, several anthracological studies have investigated the question of the optimal number of samples and fragments that should be analysed to provide statistically significant results (e.g. [START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF][START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF][START_REF] Chabal | L'anthracologie[END_REF][START_REF] Asouti | Reconstructing woodland vegetation and its exploitation by past societies, based on the analysis and interpretation of archaeological wood charcoal macro-remains[END_REF]. Saturation curves estimating the species richness of a given assemblage are used primarily to ensure that the required minimal number of charcoal fragments is analysed [START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF]. This minimum number of fragments is attained when a clear stabilisation level is reached, defining a "saturation point". This saturation point ensures that the species richness of the whole assemblage is well represented in the sub-sample analysed.

In synthetic deposits, the species richness of the assemblage is considered to be similar to the species richness of the local environment and thus, the saturation point also ensures the ecological representativeness. However, palaeobotanical studies in high species diversity areas like in the tropics have shown that it is often difficult to obtain this stabilisation level [START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF]2002). The use of Gini-Lorenz concentration curves that provide the woody plant diversity index (or Pareto index) were therefore developed to be compared with indices of modern ecological reference. Phytosociological studies show indices around 20:80 (i.e. 20% of the species are represented in 80% of the analysed fragments) in temperate regions and between 30:70 and 25:75 in Brazilian tropical regions [START_REF] Chabal | L'anthracologie[END_REF][START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF].

The combination of both curves to verify the minimum number of analysed charcoal fragments was first applied to archaeological charcoals from Mediterranean and temperate climatic conditions [START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF]. In temperate and Mediterranean Europe, this method highlighted the identification of large enough assemblages and recommended a minimum of 400 fragments per stratigraphic unit [START_REF] Chabal | L'anthracologie[END_REF]. This approach was consequently extended to tropical [START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF][START_REF] Dotte-Sarout | Not just carbon: assessment and prospects for the application of anthracology in Oceania[END_REF][START_REF] Dotte-Sarout | Evidence of forest management and arboriculture from wood charcoal data: an anthracological case study from two New Caledonia Kanak pre-colonial sites[END_REF][START_REF] Dussol | Experimental anthracology: evaluating the role of combustion processes in the representivity of archaeological charcoal records in tropical forests, a case study from the Maya Lowlands[END_REF], as well as arid and semi-arid regions (e.g. Australia, [START_REF] Whitau | Wood charcoal analysis at Riwi cave, Gooniyandi country, Western Australia[END_REF]. For instance, [START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF] suggests that a minimum of 200 to 300 fragments per samples is necessary to give a representative image of the past vegetation in Brazilian context.

In southern Africa, the potential of archaeologically recovered charcoals as a tool to reconstruct past woody vegetation was first recognised at Boomplaas Cave in South Africa [START_REF] Deacon | Fossil charcoals as a source of palaeoecological information in the Fynbos region. Fynbos palaeoecology: a preliminary synthesis[END_REF][START_REF] Deacon | Correlation of palaeoenvironmental data from the Late Pleistocene and Holocene deposits at Boomplaas Cave, southern Cape. Late Cainozoic palaeoclimates of the southern hemisphere[END_REF][START_REF] Scholtz | Palynological and palaeobotanical studies in the southern Cape[END_REF]. Since then, other anthracological analyses undertaken at Middle Stone Age (MSA), Later Stone Age (LSA) and Iron Age sites have confirmed their reliability for palaeoenvironmental studies [START_REF] Prior | An investigation of climatic change in the Holocene epoch using archaeological charcoal from Swaziland, Southern Africa[END_REF][START_REF] Dowson | Shifting vegetation zones in the Holocene and later Pleistocene: preliminary charcoal evidence from Jubilee Shelter, Magaliesberg, southern Transvaal[END_REF][START_REF] Tusenius | Charcoal analytical studies in the north-eastern Cape, South Africa[END_REF][START_REF] February | Archaeological charcoals as indicators of vegetation change and human fuel choice in the late Holocene at Elands Bay, Western Cape Province, South Africa[END_REF][START_REF] Wadley | Vegetation changes in the eastern Orange Free State: The Holocene and later Pleistocene evidence from charcoal studies at Rose Cottage Cave[END_REF][START_REF] Esterhuysen | Palaeoenvironmental and archaeological implications of charcoal assemblages from Holocene sites in western Lesotho, southern Africa[END_REF][START_REF] Cartwright | The wood charcoal assemblages from Elands Bay Cave, Southwestern Cape: principles, procedures and preliminary interpretation[END_REF][START_REF] Cowling | Fossil wood charcoal assemblages from Elands Bay Cave, South Africa: implications for Late Quaternary vegetation and climates in the winter-rainfall fynbos biome[END_REF][START_REF] Parkington | Palaeovegetation at the last glacial maximum in the western Cape, South Africa: wood charcoal and pollen evidence from Elands Bay Cave[END_REF][START_REF] Allott | Palaeoenvironments of the Middle Stone Age at Sibudu Cave, KwaZulu-Natal, South Africa: An analysis of archaeological charcoal[END_REF][START_REF] Bamford | Macrobotanical remains from Wonderwerk Cave (Excavation 1), Oldowan to Late Pleistocene (2 Ma to 14 ka BP), South Africa[END_REF][START_REF] Bamford | Pollen, charcoal and plant macrofossil evidence of Neogene and Quaternary environments in southern Africa[END_REF][START_REF] Mvimi | Reconstruction of environments and plant use in Holocene Southern Africa: study of macrobotanical remains from Late Stone Age sites of Toteng (Botswana), Leopard Cave and Geduld (Namibia)[END_REF]. While most of these studies have highlighted the potential impact of the nature of the deposits, the wood selection bias or the sampling effect on the interpretation of the anthracological results, they were not supported by experimental investigation. The anthracological studies from Holocene sites of the Northern Namibian Desert [START_REF] Eichhorn | Anthrakologische Untersuchungen zur Vegetationsgeschichte des Kaokolandes[END_REF][START_REF] Eichhorn | Use of firewood resources in a hyperarid environment: charcoal analysis from sites in the Skeleton Coast Park, Northern Namib Desert[END_REF][START_REF] Vogelsang | Holocene human occupation and vegetation history in northern Namibia. Holocene human occupation and vegetation history in northern Namibia[END_REF][START_REF] Vogelsang | Holocene human occupation and vegetation history in northern Namibia. Holocene human occupation and vegetation history in northern Namibia[END_REF]) used a sampling strategy based on the method used in West African savannas [START_REF] Neumann | Charcoal from West African Savanna Sites[END_REF], itself derived from statistical studies from European environmental context [START_REF] Chabal | La représentativité paléo-écologique des charbons de bois archéologiques issus du bois de feu[END_REF][START_REF] Figueiral | Méthodes en anthracologie: étude de sites du Bronze final et de l'âge du Fer du nord-ouest du Portugal[END_REF].

Sample sizes of 200 to 400 fragments were considered representative for most of the sites and sometimes down to 150 fragments for semi-arid sites [START_REF] Vogelsang | Holocene human occupation and vegetation history in northern Namibia. Holocene human occupation and vegetation history in northern Namibia[END_REF].

Except for Namibian anthracology studies, the representativeness of analysed samples and the choice of sampling methods have not been statistically investigated for southern African prehistoric contexts. For instance, [START_REF] Tusenius | The study of charcoal from some southern African archaeological contexts[END_REF] analysed between 22 and 78 charcoal fragments per layers from three different sites in the North Eastern Cape. [START_REF] February | Archaeological charcoals as indicators of vegetation change and human fuel choice in the late Holocene at Elands Bay, Western Cape Province, South Africa[END_REF] analysed charcoals from 12 sites from the KwaZulu-Natal and Limpopo Provinces with sample sizes varying from 20 to 390 fragments with fragment size ranges from 3 to 15 mm. At Sibudu Cave, [START_REF] Allott | Palaeoenvironments of the Middle Stone Age at Sibudu Cave, KwaZulu-Natal, South Africa: An analysis of archaeological charcoal[END_REF] analysed sub-samples of 120 fragments each from eight layers extracted from 2m 2 deposits in five size categories from 5 to >20mm.Therefore, an intra-and inter-site variability of number and size of fragments analysed per units is generally observed. This seems to be the result of various interrelated factors such as the deposit contexts, the excavation techniques, the availability of reference materials and the challenge linked to taxa identification within the allocated time [START_REF] Cartwright | The principles, procedures and pitfalls in identifying archaeological and historical wood samples[END_REF]. The differential sampling protocols hinder the possibility to conduct meaningful statistical comparisons between sites. Furthermore, wood taxonomic identification is a time-consuming task, especially in the subtropical biomes of southern Africa, rich in plant species [START_REF] Thuiller | Predicting patterns of plant species richness in megadiverse South Africa[END_REF]. In our study area, the southern African interior plateau in central Limpopo, the species and genera richness of the native woody plants (trees and shrubs of more than 2.5 m high) are estimated to include 479 species and 242 genera for a surface of 25 000 km 2 grid cell (for details see figures 2 and 3 in O' Brien et al., 1998).

At Bushman Rock Shelter (BRS here after), charcoals are the most common macro-botanical remains at the site, especially for the LSA sequence. A first diagnosis after dry sieving at 3mm and sorting during excavation revealed high frequencies of charcoal fragments ranging up to > 20 mm. The sequence benefits from a high stratigraphic resolution, well-dated occupations and preserves one of the few terrestrial archives of the late Pleistocene -early Holocene transition in southern Africa. The analysis of the rich-charcoal remains from BRS offers the opportunity to address questions regarding the economic as well as the ecological context in which the LSA hunter-gatherers evolved [START_REF] Puech | Gestion du bois et paléoenvironnements à la transition Pléistocène/Holocène dans le bassin sud du Limpopo. Les chasseurs-cueilleurs du Later Stone Age du site de Bushman Rock Shelter[END_REF]. Due to the abundant charcoal material, previous observations led to the investigation of a relevant sampling strategy to answer our research questions, while keeping the high resolution of the rich charcoal deposit. The purpose is to obtain manageable sample sizes and to assess whether the richness of the sample reflects the richness of the whole assemblage in order to avoid any bias that would be added to wood selection related to human choice or post-depositional factors. In future analyses of the charcoal material, this methodological investigation would allow us to obtain a more accurate image of the entire assemblage in order to discuss its representativeness regarding palaeoecological and palaeoeconomical interpretations (Théry-Parisot et al., 2010a;2010b). To investigate which sub-sampling method is adequate and to ensure that it is reproducible, it is important to assess the influence of the fragment size-classes, the nature of sedimentary deposits and the spatial and temporal resolution on the charcoal spectra. We discuss the applicability of common European anthracological methods for sampling representativeness and their relevance to the southern African region.

Environmental and archaeological context

The archaeological site of BRS is located in the southeastern part of Limpopo Province (Ohrigstad District), near the border with Mpumalanga, about 300 km northeast of Johannesburg in South Africa [START_REF] Porraz | Bushman Rock Shelter (Limpopo, South Africa): A perspective from the edge of the Highveld[END_REF]. Situated on the northern edge of the Great Escarpment in the Drakensberg chain, this south-facing shelter is carved within the dolomitic rocks of the Malmani Subgroup of the Transvaal Supergroup, with an average altitude of 950 meters above sea level. Modern landscape around the site straddles the Grassland and Savanna Biomes of the Highveld, to the west of the dramatic Blyde River Canyon, representing the physical and ecological limit with the Lowveld to the east (Figure 1). More locally, the Molapong and the Ohrigstad Rivers, tributaries of the Blyde River, flow close to the shelter. The current local vegetation is characterised by open to closed woodland, with well-developed shrub layers along the low mountain slope -"Poung Dolomite Mountain Bushveld" vegetation-typesurrounded by a cultivated valley with higher elevation patches of woody grassland -"Ohrigstad Mountain Bushveld" and "Lydenburg Thornveld" vegetation-types [START_REF] Mucina | The vegetation of South Africa, Lesotho and Swaziland[END_REF]. Amongst the variety of plants surrounding the site, the following shrub and woody taxa are present: the marula (Sclerocarya birrea subsp. caffra), the stamvrug (Englerophytum magalismontanum), the jacket-plum (Pappea capensis), the African olive (Olea europea subsp. europea), several species of Acacia spp. (Vachellia spp. and Senegalia spp.), bushwillow (Combretum spp.), figs (Ficus spp.) and Grewia spp. [START_REF] Porraz | Bushman Rock Shelter (Limpopo, South Africa): A perspective from the edge of the Highveld[END_REF] personal field observations). The site is located at the junction of two major centres of plant endemism, Sekhukhune Centre [START_REF] Siebert | The physical environment and major vegetation types of Sekhukhuneland, South Africa[END_REF] and Wolkberg Centre [START_REF] Van Wyk | Regions of floristic endemism in Southern Africa: a review with emphasis on succulents[END_REF]. The local climate is controlled by a summer rainfall regime characterised by mild and dry winters with a mean annual precipitation of about 900 mm and a mean annual temperature of 17.7°C [START_REF] Mucina | The vegetation of South Africa, Lesotho and Swaziland[END_REF]. [START_REF] Mucina | The vegetation of South Africa, Lesotho and Swaziland[END_REF]. Bottom left: aerial view of the site with major rivers. Bottom right: view of the south-facing shelter.

Excavations during the 1960's to 1970's exposed a well-stratified sequence of ca. 7m thick deposits associated with ephemeral Iron Age occupations capping two extensive chronocultural phases attributed to the LSA and the MSA [START_REF] Eloff | Bushman Rock Shelter, Eastern Transvaal: Excavations, 1967-8[END_REF][START_REF] Louw | Bushman Rock Shelter, Ohrigstad, Eastern Transvaal: A Preliminary Investigation[END_REF][START_REF] Plug | Some research results on the Late Pleistocene and Early Holocene deposits of Bushman Rock Shelter, Eastern Transvaal[END_REF]. A new excavation was initiated in 2014 [START_REF] Porraz | Bushman Rock Shelter (Limpopo, South Africa): A perspective from the edge of the Highveld[END_REF] to investigate late Pleistocene and early Holocene cultural dynamics in the eastern part of the southern African interior plateau, a somewhat forgotten geographical area, to refine the palaeoenvironmental context at a local scale, and to place the sequence within the current southern African chrono-cultural archaeological framework [START_REF] Lombard | South African and Lesotho stone Age sequence updated (I)[END_REF]. The LSA sequence covers about 1.5 m thick deposits and benefits from a robust chronology with main two occupational phases covering the period dated to about 15.7-10.7 ka cal BP, consistent with the end of the Pleistocene and the onset of the Holocene (Figure 2). The evolution observed in the lithic and bone industries informs about the succession from the Robberg to the Oakhurst techno-complexes. The fauna comprises a majority of small to large bovids as well as abundant tortoise shell sand bones [START_REF] Plug | Some research results on the Late Pleistocene and Early Holocene deposits of Bushman Rock Shelter, Eastern Transvaal[END_REF]Feyfant, 2019). The presence of several perforated beads bearing ochre residues and made from giant snail shells (Achatina sp.), ostrich eggshells and marine shells (Nassarius kraussianus) should be noted [START_REF] Dayet | Beads, pigments and early Holocene ornamental traditions at Bushman Rock Shelter, South Africa[END_REF]. Finally, the LSA sequence is characterised by exceptionally well-preserved botanical remains such as seeds (cf. Sclerocarya birrea), phytoliths, charcoals and some remarkable fragments of unburnt wood, leaves, and grasses.

The rich organic material preserved at BRS offers the opportunity to propose multi-proxy palaeoenvironmental reconstructions for the region, where only limited past climate records are available, especially for the late Pleistocene-early Holocene transition (but see [START_REF] Scott | Vegetation history and climate in the Savanna biome South Africa since 190,000 ka: a comparison of pollen data from the Tswaing Crater (the Pretoria Saltpan) and Wonderkrater[END_REF][START_REF] Abell | The Pleistocene/Holocene transition in South Africa: evidence for the younger Dryas event[END_REF].

Stratigraphic deposits and archaeological charcoal assemblage

Initial observations identified the South profile as a preferred location for the new excavation of the LSA sequence at BRS. Stratigraphic units (SUs), referring to the smallest sedimentary event of the site formation, have been defined according to the soil description (colour, texture, and grain-size), as well as the composition and concentration in mineral and organic archaeological materials observed during the excavation (Figure 2). Each SU was excavated per décapage within the spatial grid, i.e. sub-square of 0.5 x 0.5 m (but 0.4 x 0.5 m for the LSA sequence part). A décapage represents a plane surface that is defined by the position of at least three artefacts [START_REF] Porraz | The MIS5 Pietersburg at '28'bushman rock shelter, Limpopo province, South Africa[END_REF]. A décapage is distinguished from a spit as it strictly follows the morphology and the natural slope of the deposit and since the thickness is not standardized but depends on the nature of the sediment and the density in archaeological material or in "remarkable" remains (e.g. beads). At BRS, the décapage do not exceeds 20 mm thick.

The sedimentary deposits of BRS are predominantly anthropogenic including generally thick whitish layers, alternating with usually thinner reddish layers and interspersed by brown and black lenses rich in botanical remains. The whitish-and reddish-coloured layers correspond to thin to thick sedimentary events that are loose or indurated with varying proportions of soil aggregates, ashes and scattered charred organic materials [START_REF] Porraz | Bushman Rock Shelter (Limpopo, South Africa): A perspective from the edge of the Highveld[END_REF]. Preliminary micromorphological analyses suggest that the whitish-coloured layers are mostly composed of redeposited ashes with variable quantities of carbonized and humified plant materials. They could represent a long-term deposition resulting of mixing, and repeated activities most likely through anthropogenic processes, such as dumping or hearth rake-out [START_REF] Chabal | L'anthracologie[END_REF]Théry-Parisot et al., 2010a). The reddish-coloured layers present ubiquitous aggregates of silt and clay from an allochthonous source, likely a soil, from outside of the shelter [START_REF] Miller | Preliminary report on micromorphological analyses of sediments from Bushman Rock shelter, South Africa[END_REF]pers. comm.). At the site, both are the best-represented deposits in terms of spatial distribution.

While high variability in terms of sedimentation processes occurred for the different SUs at BRS, we assume that these reddish-and whitish-coloured units may represent several occupational phases and we interpret them as synthetic deposits according to the anthracological terminology (see section 1). They tend to extend laterally across the entire exposed profile (i.e., 4m) and they are characterized by some degree of sedimentary homogeneity throughout. As such, they are clearly distinct from localised organic lenses that are often basin-like and with a high concentration of botanical macro-remains such as charred seeds, charcoals and occasionally slightly charred twigs. These lenses can either be associated with plant processing and consumption areas, or with combustion feature areas (i.e. primary refuse such as remains of hearth-like structures) both derived from domestic fire activities. They may be interpreted as in situ occupation phases and may represent a range of chronological tempos from single or repeated short-time activities to long and persistent activity [START_REF] Mentzer | Microarchaeological approaches to the identification and interpretation of combustion features in Prehistoric archaeological Sites[END_REF]. Nevertheless, the temporality of a given SU will be reconsidered a posteriori of the anthracological results according to the number of taxa, their diversity and their ecological coherence.

Despite the quality of Eloff's excavation and the good preservation of the botanical remains, no systematic charcoal sorting occurred during the previous excavations and no anthracological study was carried out for the site. From the 2014 to 2018 campaigns, we carefully sorted the LSA fragments of wood charcoal using 3 mm mesh dry sieving from the bulk sediment excavated by décapage per sub-square (0.4 x 0.5 m for the LSA sequence) and per SU [START_REF] Théry-Parisot | Charcoal analysis[END_REF]. A first diagnosis after sieving and sorting during excavation revealed high frequencies of charcoal fragments that could sometimes measure more than 20 mm in length.

Material and methods

1. Selection of the stratigraphic units for the representativeness test

To investigate the adequate sub-sampling approach and to verify the reproducibility of the method, it is important to assess the influence of the different types of sedimentary deposits on the charcoal spectra in terms of fragmentation, frequency and taxa richness. Two levels of analysis were conducted for this study. Firstly, we systematically counted charcoal fragments in 94 décapages from various SUs from the top of the LSA sequence (see Appendix A for detailed SUs list and data measurements). Secondly, we performed the taxonomic identifications on two SUs characteristics of the two types of synthetic deposits that are best represented at the site, i.e. the whitish and reddish layers. We excluded lenses from this study because the nature of charcoal accumulation must be known. The species diversity should be interpreted on a caseby-case basis and the accumulation process should be supported by further micromorphological analysis and archaeological studies. Therefore, the following SUs were analysed in one sub-square for each size-classes: SU Blanca and SU Cabri. Blanca is a thick, whitish, ashy-layer characterised by different concentrations and sizes of charcoal and seed fragments within the SU. It comprises few lithic and faunal artefacts associated with the Oakhurst techno-complex, dated to ca. 11 ka cal BP. Because of the exploratory nature of this study and the thickness of SU Blanca, among the six décapages that composed the unit in the selected sub-square, we analysed charcoals from décapages 2, 4 and 6 only. Cabri is the SU directly underneath Blanca and it is defined as a ca. 2 cm thin pinkish to brownish soft layer. It is rich in faunal remains and lithic fragments in quartz also attributed to the Oakhurst phase and dated to ca. 11.3 ka cal BP. From the field observation Cabri does not appear particularly rich in botanical remains including charcoals, therefore, both décapages 1 and 2 that composed the SU were analysed.

2. Estimation process of charcoal fragment count

In this study, to assess the different charcoal abundances throughout the LSA sequence, we randomly selected the charcoal fragments from 94 décapages indifferent SUs and grid subsquares to be counted (see Appendix A for detailed SUs list and data measurements). Given the large range of size and the abundance of fragments in some of the smallest excavation units, i.e. décapage by SU and by sub-square, it initially proved practical to separate them into five size-classes: [3; 5[ mm, [5; 10[ mm, [10; 15[ mm, [15; 20[ mm and ≥ 20 mm, as was applied at Sibudu Cave (Allott, 2004(Allott, , 2005[START_REF] Allott | Palaeoenvironments of the Middle Stone Age at Sibudu Cave, KwaZulu-Natal, South Africa: An analysis of archaeological charcoal[END_REF], Figure 3). We then measured the weight and the volume for all selected décapages. Due to the irregular sizes and shapes of charcoals remains and the unavoidable inclusion of air pockets in the beaker used, the volume measurement is inaccurate for larger fragments. Therefore, the weight was measured for each size-class but the volume could only be measured for the two smallest size-classes [3; 5[ mm and [5; 10[ mm. As the volume of air pockets depends mainly on type and size of the container, the same graduated beakers were used to measure the two respective size-classes. We counted manually the fragments from the three size-classes ≥ 10 mm for all the selected décapages. Since some small size-classes were abundant and the counting of each of them was time-consuming, we used an estimation count method based on the volume and weight for fragments < 10 mm (Figure 3). Firstly, we manually counted the fragments with size-range of

3. Anthracological analysis

For the identification analysis of SUs Blanca and Cabri, each charcoal fragment was either manually broken or split with the help of a blade according to the required three planes for anatomical studies of wood: transverse, longitudinal tangential and longitudinal radial [START_REF] Leney | Simplified procedure for examining charcoal specimens for identification[END_REF]. Anatomical characters were observed using a reflected light microscope with bright and dark fields at magnifications of 50x, 100x, 200x, 500x and occasionally 1000x for particular tiny anatomical wood features. The anatomical characters were recorded following the description of the IAWA Committee [START_REF] Wheeler | IAWA list of microscopic features for hardwood identification: with an appendix on non-anatomical information[END_REF]. For taxonomic identifications, they were compared with published anatomical wood atlases (Kromhout, 1975;[START_REF] Tusenius | The study of charcoal from some southern African archaeological contexts[END_REF][START_REF] Neumann | Woods of the Sahara and the Sahel: an anatomical atlas = Bois du Sahara et du Sahel = Hölzer der Sahara und des Sahel[END_REF][START_REF] Eichhorn | Anthrakologische Untersuchungen zur Vegetationsgeschichte des Kaokolandes[END_REF], the online database InsideWood (InsideWood, 2004-onwards;[START_REF] Wheeler | Inside Wood -A Web resource for hardwood anatomy[END_REF], as well as with the modern reference collections available at the University of the Witwatersrand. These collections were started by Wadley and collaborators currently include more than 500 different taxa from diverse vegetation-types and climatic regimes of southern Africa (e.g. [START_REF] Wadley | Vegetation changes in the eastern Orange Free State: The Holocene and later Pleistocene evidence from charcoal studies at Rose Cottage Cave[END_REF][START_REF] Esterhuysen | Palaeoenvironmental reconstruction from Pleistocene to present: an analysis of charcoal from sites in the eastern Free State and Lesotho[END_REF][START_REF] Allott | Palaeoenvironments of the Middle Stone Age at Sibudu Cave, KwaZulu-Natal, South Africa: An analysis of archaeological charcoal[END_REF][START_REF] Chikumbirike | Archaeological and palaeoecological implications of charcoal assemblages dated to the Holocene from Great Zimbabwe and its hinterland[END_REF][START_REF] Lennox | Woody taxa from charcoal in Sibudu's Middle Stone Age hearths[END_REF][START_REF] Lennox | Identifying Asteraceae, particularly Tarchonanthus parvicapitulatus, in archaeological charcoal from the Middle Stone Age[END_REF], and unpublished collections including new modern specimens recently collected by the authors in the vicinity of BRS).

Charcoal-type identification process follows the methodology described by Höhn and colleagues for the woody species-rich environment in Cameroon [START_REF] Höhn | Analysis of Charcoal Finds[END_REF][START_REF] Höhn | Charcoal identification in a species-rich environment: The example of Dibamba, Cameroon[END_REF]. The taxonomic level attribution is mostly determined to the family and genus level followed by "sp.". Species attribution is only possible for monospecific genera or when a single species is present in the modern local vegetation and is generally preceded by "cf." meaning it is close to a given species. Charcoal-type concept is defined for current indeterminate taxa and a type may represent one or several species. Finally, fragments with poor preservation and/or with anatomical characters not discernible enough are classified as unidentifiable. The identification level is closely dependant on taphonomical preservation, the size of the fragment and the taxa available in reference collections. In the framework of the study of BRS charcoals, the identification process is still in progress, and taxa level identification could evolve as the work progresses. For this reason, the analysis of each sample proceeds from the largest fragments to the smaller ones. Large fragments provide a better image of the complete anatomical wood features, sometimes from heartwood to sapwood when preserved, and can later help to identify the small fragments. Nonetheless, we systematically analysed fragments from each size-classes to avoid any sample bias. The ecological meaning of identified charcoal-types is not the purpose of the present work and will be discussed in a future paper with more samples and SUs analysed.

We plotted the saturation curves alongside the taxonomic charcoal-type identifications for each décapage in order to discuss the richness and the representativeness of the total assemblage. These curves were obtained by plotting the taxa frequency against the number of analysed fragments in a given sample. We also produced Gini-Lorenz concentration curves to provide the woody plant diversity index of the sample [START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF][START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF] by plotting the cumulative relative frequencies against the species rank percentages. The anthracology diagrams were plotted in relative frequency and in concentration (frequency related to the same percentage of volume of sediment) for each décapages in SUs Blanca and Cabri with the proportion of represented size-classes. Finally, we calculated the beta diversity β -number of taxa that differ between samples or difference in taxa richness [START_REF] Whittaker | Evolution and measurement of species diversity[END_REF] between décapages to estimate the homogeneity pattern of a given SU.

Results

Figure 5 presents the differential abundance of charcoal fragments of the selected 94 décapages with the size-classes [3; 5[ and [5; 10[ mm estimated with the polynomial functions based on weight. These two smallest size-classes are the best represented portions but fragments ≥ 10 mm are not preserved in all décapages (Figure 5). A large variability in total charcoal frequencies is observed between décapages within a given SU from a minimum of 13 fragments (Betty P3A 6) to a maximum of 1794 fragments (Blanca P3D 7, Figure 5a, Appendix A). However, once the abundance is express in percentage, a lower amplitude of the variability is observed in a given size-class between décapages and size fragments seem to be spread according to a Poisson distribution (Figure 5b). Except for three décapages (i.e. Canta P3D 3, Canta N3D 2 and Cabu N3D 2), the smaller the size-classes are, the higher the charcoal abundance is. For the analysis of SU Blanca, 169, 134 and 176 charcoal fragments were identified and 13, 14 and 12 different charcoal-types were respectively recognised in the décapages 2, 4 and 6. Once grouped as a single assemblage, the total increases to 479 identified charcoal fragments distributed in 20 different charcoal-types whose percentage of relative frequencies are illustrated as an anthracology diagram in Figure 6a. A first observation is that in terms of frequencies the same six dominant charcoal-types are recognised in the three décapages of Blanca. A second observation is that the same dominant charcoal-types are distributed in at least three different size-classes from the smallest. Brachylaena sp. and Acacia sp. are the only charcoal-types that are distributed from < 5 to ≥ 20 mm ranges. Since the fragment identification proceeded from the largest to the smallest fragments (see 4.3 section), the number of analysed fragments from [3; 5[ mm is limited and may misrepresent the real proportion of the charcoal-types in this size range. Therefore, when excluding the smallest sizeclass, the higher the relative frequencies of charcoal-types are, (1) the better represented the fragments into the five size-classes are, and (2) the higher the probability that they follow a Poisson distribution is. The 14 other charcoal-types have relative frequencies less than 10% and are never identified in the all three décapages. Indeed, these "rare" charcoal-types are more scattered between the three décapages and are never larger than 10 mm. The identified "rare" charcoal-types are spread along the different analysed décapages and lead to a high beta diversity (> 55% of difference in taxa richness between décapages). This induce taxa heterogeneity along the SU Blanca (Table 1). However, in terms of relative frequencies, around 90% of the total identified fragments are represented by the same six charcoal-types, which reflects a certain homogeneity that is summarised in the Blanca total grouping where the three décapages were analysed as a single sample. Finally, while the total concentration of charcoal fragments is higher in décapage 2 of Blanca (84,5/l), larger fragments are present in the underlying décapages with much lower concentration (respectively 44,7/l and 14,7/l, Figure 6a).

Table 1: Beta diversity between all analysed décapages from SUs Blanca and Cabri and between Blanca total and Cabri total. The ratio of taxa differences per total taxa is followed by the beta diversity in percentage.

SU Cabri is composed of two décapages and 44 and 68 charcoal fragments were identified with 7 and 11 different charcoal-types recognised in the décapages 1 and 2, respectively. We analysed all the charcoal pieces in décapage 1 and two thirds of the sample in décapage 2, both from the largest to the smallest fragments (see 4.3 section). Once grouped as a single assemblage, the total increases to 112 identified charcoal fragments distributed in 13 different charcoal-types. The anthracology diagram in Figure 6b illustrates the percentages of relative frequencies. The charcoal-type Acacia sp. is abundant in décapage 1 with ca. 80% of the total identified fragments. Acacia sp.is still the dominant charcoal-type recognised in décapage 2 to a lesser extent (ca. 40%) and, with four other dominant charcoal-types, they reach ca. 80% of the total identified fragments. However, at this stage of the study caution should be exercised as charcoal-types could represent more than one species, particularly for Acacia sp. where more than 70 species occur in southern Africa and at least 19 species occur around BRS [START_REF] Smit | Field guide to the acacias of South Africa[END_REF]. No fragments are larger than 10 mm and only Acacia sp. and cf. Colophospermum mopane have fragments in the [5; 10[ mm size-class. Based on the small sample size of analysed fragments, we could not observe any fragment distribution pattern and the high beta diversity (62% of difference in taxa richness) between décapage 1 and 2 explains the apparent heterogeneity in charcoal-types represented along the SU Cabri (Table 1). The total charcoal fragment concentrations are likely the same between the two décapages and thus do not distort the proportions of charcoal-types (Figure 6b). Décapages from SUs Blanca and Cabri present different patterns of fragmentation and of distribution (Figure 6). The total charcoal fragment concentration of Blanca décapages vary from very low (14,7/l in décapage 6) to high (84,5/l in décapage 2). Nonetheless, once grouped as a single sample, the total charcoal concentration is diluted in Blanca total (28,2/l) and becomes quite similar to the concentration of Cabri total (32/l). The beta diversity is about 52% between Blanca total and Cabri total based on the 23 different charcoal-types recognised but should be higher if only respective dominant charcoal-types are considered (Table 1).

Discussion

1. Charcoal fragment frequency, concentration and distribution

The use of interpolated function based on volume or weight to count efficiency and quickly samples with abundant charcoal fragments is sometimes used for botanical and microfaunal remains in archaeological and environmental studies [START_REF] Chrzavzez | Approche expérimentale de la conservation des charbons de bois dans les gisements paléolithiques : processus post-dépositionnels, fragmentation et représentativité des assemblages anthracologiques[END_REF]Théry-Parisot, pers. comm.). The polynomial functions reveal robust coefficients of correlation R 2 for both volume and weight methods. For the anthracological analysis of BRS, weighing of samples in the laboratory was deemed the most convenient method in terms of time investment and protocol.

Nonetheless, the weight method requires an electronic scale and processing in the laboratory after excavation. The volume method needs only a graduated glass and is therefore suitable for a quick abundance estimation directly at the site during excavation. If the bucket volume/weight of excavated sediment is measured before sieving at the site, the measurement or estimation of charcoal volume, weight or frequency is also useful to estimate the concentration of charcoal fragments in a given sample. The taxa (or charcoal-type) concentration could provide further information regarding their relative spatial and temporal accumulation. It also allows inter-and intra-site comparisons and it could potentially provide information about the occupation patterns in terms of spatial management and site function.

At BRS, the volume of sediments for each excavated décapage is systematically recorded, which allows us to estimate densities of archaeological material.

The particular conditions of accumulation of the archaeological deposits at BRS has enhanced the preservation of numerous macro charcoal remains with remarkable sizes, sometimes larger than 20 mm. The abundance and range of sizes of charcoal fragments mean that they can easily be sorted into size-classes. We tested the relevance of using the five size-classes with an analysis of the abundance estimation, size-class distribution and fragmentation process of 94 décapages. [START_REF] Chabal | L'Homme et l'évolution de la végétation méditerranéenne des âges des métaux à la période romaine; recherches anthracologiques théoriques[END_REF][START_REF] Chabal | Forêts et sociétés en Languedoc (néolithique final, antiquité tardive): l'anthracologie, méthode et paléoécologie[END_REF] demonstrated a Poisson distribution of the taxa fragmentations that has been formulated by the "single fragmentation law" hypothesis. This trend seems to be observed at the level of décapages' samples, independently of their relative charcoal fragment concentration or their taxa-type attribution (Figure 5). If some fragments did reach more than 20 mm, the distribution pattern shows that only fragments from the two smallest size-classes [3; 5[ and [5; 10[ mm are statistically representative at BRS. Considering the time required for the sieving and analysis, it appears more convenient for the study of the entire sequence to group fragments ≥ 10 mm as a single size-class. Therefore, the recommended size-classes are [3; 5[, [5; 10[ and ≥ 10 mm. This initial estimation of total frequencies of charcoal fragments from various décapages throughout the sequence provides an overview of the fragmentation patterns.

2. Sample representativeness

The saturation curves (cumulated frequencies of analysed fragments against the frequencies of the cumulative identified charcoal-types) were plotted alongside the analysis for the three décapages of SU Blanca (Figure 7a, c ande). The saturation point was not reached for any of them, which likely results from the low number of identified fragments in each décapage (less than 200). When the three décapages are grouped as a single sample with a total of 479 charcoal fragments and a minimum of 20 different taxa, the saturation point is still not attained despite the larger sample size (Figure 7g). The number of identified fragments in the two décapages of Cabri is very low (respectively 57 and 111), which explains why no saturation points were reached (Figure 8a andb). Even when grouped, the total sample Cabri total remains too small (112 fragments analysed) to be interpreted (Figure 8e). The unstabilised curves in Blanca and Cabri décapages were mainly inferred from the limited number of fragments that have been observed. Once the décapages of Blanca were grouped as a single sample, the unstabilised curve was less reliant on the sample size (479 fragments analysed) but better reflective of the charcoal-type richness in woody species-rich environments characterised by grassy and savanna woodland of southern Africa. It is often expected in species-rich environments that stabilisation of the frequency saturation curves is difficult to reach, for instance in tropical regions [START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF]2002, Figure 9a). For this reason, we propose to visualise the saturation curves from Blanca total and Cabri total with cumulated charcoal-type frequencies (ordinate axis) in a logarithm scale (Figure 10). Indeed, the logarithm scale allows spacing of the abundant charcoal-types and bringing closer together the numerous "rare" charcoal-types. More importance is then placed on the dominant taxa and less importance on the "rare" taxa that disturb the quantitative interpretation (Figure 9b and10b). The saturation curve from Blanca total is less steep and a threshold plateau is almost attained, showing that Blanca total presents a good sample size. This model of saturation curve plotting is useful to highlight trends that are hidden by the presence of many taxa with low frequencies. However, the Cabri total sample remains too small in frequency to reveal any threshold plateau. For thin SUs (ca. < 5 cm thick) with low concentration of charcoals (32/l analysed out of 48/l from total excavated sediment) such as Cabri, the spatial unit of a subsquare (40 x 50 cm) is too small. We therefore recommend the analysis of two sub-squares to increase both the surface and sample size in order to obtain reliable quantitative (frequency) and qualitative (taxa richness) results. to 24:76 for the three décapages. These indices are considered as "normal" for rich and diverse taxa environments and are in accordance with reasonably well distributed taxa as observed in Figure 6a. The grouped décapages sample of Blanca total has an index of which is close to an index for temperate environments and results from an increase of the "rare" charcoaltype richness identified with a lower distribution of these charcoal-types (Figure 8h).In contrast, the Gini-Lorenz concentration curves from Cabri décapages show a high index of 21:79 in décapage 1 resulting from a low taxa diversity due to a strong dominance of the charcoal-type Acacia spp. (80%) (Figure 8b). The Gini-Lorenz index of 27:73 in décapage 2 is considered as "normal" for species-rich environments with a higher range of frequency (Figure 8d). The Cabri total assemblage presents a relatively high diversity with an index of 23:77 (Figure 8f).

Nevertheless, these results should be regarded with caution due to the small total sample of 112.

The use of Gini-Lorenz concentrations has enabled the assessment of a reliable sample size in tropical region based on phytological studies of Brazilian vegetation-types [START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF]2002). However, no Gini-Lorenz indices currently exist for modern southern African vegetation, which is characterized by a mix of vegetation-types with high species richness of woody plants (fynbos, forest, grassy and savanna woodland) and lower ones (semi-arid and desert where herbs and succulents dominate). The Gini-Lorenz concentration curves, which are visual and easy to use, could offer an interesting complementary approach, but the application of Gini-Lorenz indices based on Brazilian values must be used with extreme caution for southern African anthracology studies. More in-depth studies need to be carried out, in particular regarding the verification of whether there are ranges of values of this index that are more characteristic of southern African vegetal formations. The abundance of charcoal fragments should allow their analysis per décapage -i.e. the smallest excavation unit at the site. The analysis of two SUs resulting from different sedimentary processes reveals the need for a large size of identified charcoal fragments. An increase of identified fragments per décapage might allow (i) a better representation of the charcoal-type diversity; (ii) testing the Gini-Lorenz index reliability of the SU; and (iii) potentially stabilising the saturation curve. If it is possible to increase the number of identified fragments for Blanca décapages, a thin SU such as Cabri yields no statistically significant analysis per décapage. In addition, considering that a décapage follows the archaeological and geomorphological constraints imposed by the SU deposit, defining a décapage in terms of time resolution is complex.

Among the 23 different charcoal-types that we identified in SUs Blanca and Cabri, the dominant charcoal-types show different patterns in frequencies between the two SUs. In addition, while it is not significant for SU Cabri, the percentage frequencies of the dominant charcoal-types in the three décapages of SU Blanca are relatively homogeneous between the different décapages. Together, charcoal-type frequencies and the preliminary micromorphological observations ensure the relevance to analyse the LSA sequence of BRS using the SU as the level of resolution. However, in the case of thick SUs with high charcoal abundance like Blanca, the SU should be split into two samples, a top SU sample and a bottom SU sample to keep any potential information of resolution.

4. 2. Size classes versus randomised analysis

The analyses of the décapages of SUs Blanca and Cabri show that the fragmentation patterns are not homogeneous between charcoal-types and between décapages of any given SU and even between both SUs. For this reason, the analysis of a single size-class necessarily introduces a bias. One the one hand, the analysis of the largest fragments only decreases the taxa richness and diversity of the unit. On the other hand, the analysis of only the smallest fragments does not allow for the study of the fragmentation pattern of taxa throughout the sequence. To avoid any sampling bias during the analysis, randomised sampling has to be done in each size-class of a given SU. If the total sample size of the SU is less than 500 charcoal fragments, we recommend analysing all the pieces, in order to be representative of the SU. In the other cases, we suggest analysing a minimum of 500 fragments, in proportion of each size-class available for the given SU. The saturation curves (with logarithm scale of the cumulated taxa frequencies) and Gini-Lorenz curves should be plotted alongside the charcoal identification. If a saturation point is recognised, the analysis can stop; if not, it should not exceed the identification of 800 fragments.

Conclusion

This article proposes a review of the main anthracological principles and methods regarding their application to southern African contexts. Since the 1980's, archaeological projects in the region have increasingly integrated studies of charcoal recovered from the sites because they provide valuable palaeoecological and palaeoethnobotanical information. However, the question of the adequate sample size and of its representativeness of both the deposit and the environment have not been deeply explored and no normalized method has been developed for the whole region unlike what has been proposed for other regions [START_REF] Chabal | La représentativité paléo-écologique des charbons de bois archéologiques issus du bois de feu[END_REF], 1994[START_REF] Scheel-Ybert | Stabilité de l'écosysteme sur le littoral Sud-Est du Brésil à l'Holocène Supérieur[END_REF][START_REF] Dotte-Sarout | Not just carbon: assessment and prospects for the application of anthracology in Oceania[END_REF][START_REF] Höhn | Charcoal identification in a species-rich environment: The example of Dibamba, Cameroon[END_REF]. We tested these methodological questions using the charcoal assemblage from two LSA stratigraphic units, which are characteristic of the main sedimentary processes at BRS. We recommend the following methodological points for the specific anthracological study of the synthetic layers of the LSA sequence of BRS:

 Charcoal fragments from décapages should be sorted according to three size-classes: [3; 5[, [5; 10[ and ≥ 10 mm Rockshelter, Limpopo). We thank May Murungi for helping the authors with wood collection, as well as René Reddy and Kevin Balkwill for the identification of voucher specimens at the Moss Herbarium of the University of the Witwatersrand. We would like to thank Vanna Lisa Coli for her comments on data processing. This work was presented at the 7 th International Anthracological Meeting in Liverpool in September 2019. We want to thank Eleni Asouti for her invitation to contribute to the current special issue.

Figure 1 :

 1 Figure 1: Location of Bushman Rock Shelter (BRS). Top left: map of South Africa with seasonal rainfall regimes and the Great escarpment. Top right: zoom on the Limpopo area with vegetation biomes (adapted from Mucina and Rutherford, 2006). Bottom left: aerial view of the site with major rivers. Bottom right: view of the south-facing shelter.

Figure 2 :

 2 Figure 2: Upper South Profile of Bushman Rock Shelter (before excavation in 2014) with details on the SUs Blanca and Cabri. Ortho-photography by M. Haaland.

Figure 3 :

 3 Figure 3: Flowchart of charcoal counting estimation for < 10 mm size-ranges with the use of function of correlation. R 2 = coefficient of correlation.

  [5; 10[ mm from 91 décapages and with size-range of [3; 5[ mm from 46 décapages in diverse SUs with variable abundance and various sedimentary nature of deposit (Appendix A). The choice of a lower number of counted décapages from the [3; 5[ mm range can be explained by the higher number of fragments for which the manual counting was particularly timeconsuming (up to 921 fragments for the most abundant, Appendix A). Secondly, the number of charcoals fragments per volume and per weight of these décapages was plotted for each sizeclass. Finally, the best approximate linear trend curves were drawn to build predictor functions and their respective coefficients of correlation R 2 were compared. The function of correlation between the frequencies of charcoal fragments per décapage and both weight and volume is close to a polynomial function of type: 𝑦 = 𝑎𝑥² + 𝑏𝑥. We observed a highly significant correlation between the number of fragments and the weight of a given décapage sample with coefficients of correlation R 2 of 0.9945 for the[3; 5[ mm range and of 0.9584 for the [5; 10[ mm range (Figure 4a). A slightly lower correlation, but still with very high significance, was observed between the number of fragments and the volume of a given sample with coefficients of correlation R 2 of 0.9901 for the [3; 5[ mm range and of 0.9574 for the [5; 10[ mm range (Figure4b). A greater difference in wood density and proportion of air pockets included in the beaker can explain the slightly lower correlation of the [5; 10[ mm range. The predictor function based on volume or weight can be used to quickly estimate the number of small fragments with accuracy in order to assess the abundance of charcoal fragments of the two small portions from the remaining décapages.

Figure 4 :

 4 Figure 4: Frequencies of charcoal fragments manually counted against weight in grams (a) and against volume in millilitres (b). Polynomial predictor function and coefficient of correlation are mentioned above the trend curves in solid and dashed line.

Figure 5 :

 5 Figure 5: Charcoal abundance per SU per sub-square and per décapage (e.g. BlancaN3A: SU Blanca, sub-square N3A) and their distribution per size-classes. Fragment numbers from sizeclasses [3; 5[ and [5; 10[ mm are estimated with respective polynomial predictor function based

Figure 6 :

 6 Figure 6: Anthracological diagrams of charcoal fragment frequencies in percentage and the charcoal concentration of the analysed samples in identified fragments per sediment litre (Nid/L). a) Frequencies of the analysed décapages of SU Blanca and of Blanca total as the sum of the analysed décapages. b) Frequencies of the analysed décapages of SU Cabri and of Cabri total as the sum of the analysed décapages. "T-number" refers to an identified charcoal-type and is followed by taxonomical attribution when determined. All histograms have the same scale percentage.

Figure 7

 7 Figure 7

  Figure 8

  Figure 9

o

  length; The analysis of the archaeological sequence should be performed at the stratigraphic unit level of resolution with some specificities: o Thick SUs (ca. >10 cm thick that are composed of at least 6 décapages and with high charcoal concentration) should be analyzed as two distinct samples, a top one grouping the upper décapages and a bottom one grouping the lower décapages; The analysis of at least two subsquares is recommended for thin SUs (ca.<5 cm thick) with low charcoals concentration (<20 fragments / l), to increase sample size and taxa richness;  To avoid any sampling bias during the analysis, randomized sampling has to be done in each size-class; The analysis of a minimum of 500 fragments per stratigraphic unit is recommended;  The plot of the saturation curves with cumulated taxa in logarithm scale and Gini-Lorenz curves with caution of the indices interpretation is recommended alongside the identification to ensure the representativeness of the analysed sample regarding the total assemblage of the deposit. The saturation point cannot be reached systematically depending on the type of but the use of the curves allows observing a trend in the taxonomic diversity.Our work highlights the importance of systematic integration of the excavation techniques and the nature of the deposits based on both field observations and micromorphological analyses in order to elaborate a strict and adequate sampling strategy, from the field to the laboratory. Any sampling strategy should be adapted on a case-by-case basis and according to the specificities of the study site. We encourage further methodological studies to test and adapt the main principles of the discipline for the specific requirements of southern Africa. reference collections of the University of the Witwatersrand. The missions were financially supported by some Crédits Scientifiques Incitatifs from University Côte d'Azur lead by I. Théry-Parisot (PRehistOire et BioarchEologie : Gestion des ressources végétales et paléoenvironnements des sociétés de chasseurs-cueilleurs d'Afrique du Sud, Bushman

Acknowledgments

The Bushman Rock Shelter project is funded by the French Ministry of Foreign affairs (excavation permit #2475). We acknowledge the South African Heritage Resources Agency for providing the temporary export permit for the charcoal analysis conducted at the CEPAM at the University Côte d'Azur (permit ID2983). This article is part of a PhD project co-funded by the Martine Aublet Foundation of the Musée du Quai Branly Jacques Chirac. The support of the DST-NRF Centre of Excellence in Palaeosciences (CoE-Pal) towards this research is hereby acknowledged. Opinions expressed, and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the CoE-Pal. We would like to acknowledge the Institut français en Afrique du Sud (IfAS -Recherche) for the mobility grant that allowed three of us (EP, MB and ITP) to sample modern woods for the reference collection and to visit the charcoal


Tat Loon Chng

Nikita Lepikhin

Inna Orel

Nikolay A Popov

Svetlana Starikovskaia

Atomic Nitrogen Density Measurements in a Nanosecond Capillary Discharge

This paper forms part of a larger study geared towards examining the atomic nitrogen production as a function of reduced electric fields, particularly in nanosecond type discharges. In this study, the atomic nitrogen density in a pure molecular nitrogen capillary discharge at 27 mbar is measured using two-photon absorption laser induced fluorescence (TALIF). Due to its small volume, the capillary provides an ideal geometry for achieving high levels of specific deposited energy into the plasma (> 1 eV per molecule) as well as high peak reduced electric fields (> 500 Td). Under these conditions, our results show that unusually high densities of atomic nitrogen are recorded, with the time evolution measurements indicating a peak dissociation fraction of slightly more than 10%. Further validation of these results with numerical simulations are ongoing, but on the current basis, support the notion that the capillary discharge is an extremely efficient configuration for the generation of nitrogen atoms.

I. Introduction

ver the past two decades, the use of high voltage pulses occurring on the nanosecond timescale for plasma initiation has found broad applicability in diverse fields such as medicine, aerodynamics, combustion and even agriculture. Also commonly known as nanosecond discharges, the attractiveness of this enabling technology lies in its ability to generate higher than usual electric fields (or reduced electric fields) which can in turn alter the chemical reactivity of a particular system. This change in reactivity is expedited by the opportunity to couple energy into internal degrees of freedom of atoms or molecules, thereby leading to an extraneous production of reactive species such as electrons, ions, radicals and excited state particles, through processes such as electronic excitation, dissociation and ionization. As a consequence, much of recent research has provided insight into the transient chemical pathways made available by this infusion of reactive species. However, even under these conditions of high electric fields, an important distinction which should be made is the specific delivered energy to the discharge, i.e. energy normalized by the number of particles. When this number is low (nominally defined in terms of eV per molecule and abbreviated as eV/mol), the plasma kinetics involve mainly chemical reactions between the reactive species and the background/bath gas. At increased specific delivered energies (on the order of 1 eV/mol), which is the focus of this study, the probability of interaction between reactive species becomes much likelier.

The primary objective of this work is to experimentally measure the atomic nitrogen (N) production in a low pressure, molecular nitrogen (N2) capillary discharge using two-photon laser induced fluorescence (TALIF). Due to its unique geometry (small diameter and volume), a cylindrical capillary tube provides an ideal configuration for producing nanosecond discharges with high values of specific delivered energy. The natural idea is to make use of these measurements to aid in the modeling efforts of such discharges. The current study complements previous work, in which important aspects of this discharge such as the delivered energy, electric field and temperature have been quantified [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF]. In addition, similar measurements of atomic oxygen (O) have also been performed using an identical geometry [START_REF] Klochko | TALIF measurements of oxygen atom density in the afterglow of a capillary nanosecond discharge[END_REF].

II. Experimental Setup

A schematic of the discharge cell geometry used in this work is presented in Fig. 1. This configuration is very similar to that used in Ref. [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF]. A cylindrical quartz capillary with a nominal length of 67 mm and an internal and external diameter of 1.7 mm and 3.0 mm respectively is placed between two pin-shaped electrodes and encapsulated by a rectangular 48 mm by 67 mm metallic screen. Pure N2 gas enters and exits the capillary via two glass side arms at a flow rate of 5 sccm by means of a Brooks Instruments 5850TR mass flow controller. This flow rate was chosen with a view to ensuring gas renewal before each successive high voltage pulse. The static pressure in the capillary was kept constant at 27 mbar based on previous work which indicated this as a reasonable pressure for initiating a reproducible and homogeneous plasma. Pressure measurements are made using a pair of CMR 362 capacitive pressure sensors (from Pfeiffer Vacuum SAS), each positioned at an approximately equidistant location upstream and downstream of the capillary. The operating pressure was determined by taking the average of both these sensor readings. This approach for pressure quantification was chosen due to difficulties associated with mounting a pressure transducer directly onto the capillary and was validated numerically using a Navier-Stokes solver [START_REF] Klochko | Excited species chemistry in homogeneous nanosecond discharges with high specific energy deposition[END_REF].

High voltage nanosecond pulses are delivered by means of a FPG 12-1NM high-voltage generator (HVG) manufactured by FID GmbH. Positive polarity, 9.3 kV amplitude voltage waveforms with a rise time of 4 ns and a full width at half maximum (FWHM) of 30 ns are produced by this high voltage source at a repetition rate of 10 Hz. The output of this high-voltage generator is connected to one of the electrodes (henceforth termed highvoltage electrode) via a 50 ohm impedance RG213 coaxial cable. A second such coaxial cable of identical length is connected to the remaining electrode (low-voltage electrode) but is kept ungrounded at a floating potential. The shielding of both these coaxial cables is connected to the rectangular metallic screen. Due to an impedance mismatch between the high voltage pulses and the discharge (viz. electrical load), each pulse delivered by the HVG is reflected twice, once from the high-voltage electrode and a second time from the HVG itself. This leads to a sequence of 3 incident pulses with gradually diminishing voltage seen by the discharge, each separated by about 250 ns. Custom-made, calibrated back current shunts are installed at mid-length of both coaxial cables for the purpose of measuring the specific energy coupled to the plasma. The laser system used for the TALIF experiments consists of a Sirah Lasertechnik Cobra Stretch dual-grating dye laser driven by a frequency-doubled Quanta Ray Nd:YAG laser. A dye-mix of Rhodamine B and Rhodamine 101 (supplied by Sirah Lasertechnik) is employed as the lasing medium, and when pumped with the required 532 nm light, produces output within the desired visible range of 621 nm at a repetition rate of 10 Hz. This light is then frequency-tripled via two successive alpha-BBO non-linear crystals so as to yield 3 mJ, 207 nm pulses (at the same repetition rate) with a pulse duration of about 6.5 ns. This UV light is focused with a 500 mm planoconvex lens, propagating along an axis orthogonal to the longitudinal axis of the capillary. As illustrated in Fig. 1a), care was taken to ensure that the laser beam probed a region corresponding to the center of the capillary. To avoid damaging the capillary, the laser intensity was attenuated by locating the beam focus slightly downstream of the capillary tube.

The N TALIF scheme used for these experiments is shown in Fig. 1b)(i). The two-photon 3p 4 S3/2 N resonance is accessed via a pair of 206.7 nm photons and subsequently fluoresces to three different fine structure levels, emitting light respectively at 742.6 nm, 744.4 nm and 747.0 nm [START_REF] Kramida | NIST Atomic Spectra Database (version 5.5[END_REF]. For the majority of the experiments, this resulting fluorescence is captured by a Hamamatsu photomultiplier (Photo Sensor Module H7422P) with an attached Thorlabs FB750-10 bandpass filter (center wavelength 750 nm, 10 nm FWHM). Signals are obtained by averaging over 400 laser shots within a laser intensity fluctuation of ±3%. An IR-sensitive Andor Technology SR-500i-B1 spectrometer with an attached ICCD camera was used to resolve and observe the fluorescence spectra.

In order to obtain quantitative N densities, signal calibration against an inert, reference gas -in this case krypton -was performed. This procedure -first described in seminal work by [START_REF] Niemi | Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation[END_REF] -has since been widely adopted in the literature and essentially makes use of the fluorescence from a gas of known density (in this case Kr) to calibrate the signal obtained from a gas of unknown density (N). This approach circumvents the need for producing a known amount of N which can often be a less than straightforward task. The corresponding Kr TALIF scheme involves pumping the 5p'[3/2]2 resonance with two photons at 204.1 nm, followed by fluorescence to the 5s'[1/2]1 state at 826 nm (see Fig. 1b)(ii)).

One advantage of the above approach which is relevant to this study is that the non-uniform laser intensity distribution produced by locating the beam focus away from the measurement volume (i.e. capillary) is identically replicated, and thus accounted for, in the Kr calibration experiment.

Based on [START_REF] Niemi | Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation[END_REF], the number density of atomic nitrogen may be written as:

𝑛𝑛 𝑁𝑁 = � 𝜎𝜎 𝐾𝐾𝐾𝐾 𝜎𝜎 𝑁𝑁 � � 𝜈𝜈 𝑁𝑁 𝜈𝜈 𝐾𝐾𝐾𝐾 � 2 � 𝑃𝑃𝑃𝑃𝑃𝑃 𝐾𝐾𝐾𝐾 𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁 � � 𝐴𝐴 𝐾𝐾𝐾𝐾 𝐴𝐴 𝑁𝑁 � � 𝐹𝐹 𝐾𝐾𝐾𝐾 𝐹𝐹 𝑁𝑁 � � 𝐴𝐴 𝑁𝑁 + 𝑄𝑄 𝑁𝑁 𝐴𝐴 𝐾𝐾𝐾𝐾 + 𝑄𝑄 𝐾𝐾𝐾𝐾 � � 𝐼𝐼 𝐾𝐾𝐾𝐾 𝐼𝐼 𝑁𝑁 � 2 � 𝑆𝑆 𝑁𝑁 𝑆𝑆 𝐾𝐾𝐾𝐾 � 𝑛𝑛 𝐾𝐾𝐾𝐾
where n is the number density, σ is the two-photon absorption cross-section, ν is the resonance frequency, PMT is the photomultiplier sensitivity at the resonant wavelength(s), A is the natural radiative rate, F is the filter transmission, Q is the quenching rate of the two-photon excited state, I is the laser intensity and S is the spectrally and temporally integrated fluorescence measured by the photomultiplier. Subscripts N and Kr refer to atomic nitrogen and krypton respectively. The ratio of two-photon cross-sections (value of 0.67) is obtained from [START_REF] Niemi | Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation[END_REF]; PMT sensitivities and filter transmission curves are obtained or extrapolated from their respective manuals. The natural radiative rate of N (value of 29.6 ns) is obtained from [START_REF] Niemi | Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation[END_REF], while the Kr number density of 6.7 x 10 16 cm -3 is obtained by flowing Kr gas at room temperature through the capillary at a pressure of 2.7 mbar.

In order to ensure operation within the 'linear' regime, defined as when the fluorescence signal S observes a quadratic dependence on the laser intensity (see eqn. (1)), the laser energy was varied over a range of 10-300 µJ in order to establish the optimum laser intensity. The energy used for the N and Kr experiments were 85 µJ and 30 µJ respectively.

III. Results and Discussion

The evolution of the N atom density at various time instants with respect to the discharge initiation is shown in Fig. 2. These measurements are obtained by integrating the resonant fluorescence signals captured by the photomultiplier (PMT) for both Kr and N, followed by application into equation [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF]. The laser was tuned off resonance in order to subtract the undesired fluorescence from the quartz capillary as well as overlapping fluorescence from the background plasma emission. This background emission, which was observed to last for about 1 µs, meant that measurements made during or before this time were plagued by a much poorer signal to noise ratio. Where possible, the data shown in Fig. 2 are corrected for excited state quenching; quenching rates are determined by fitting an exponential function to the decaying section of the PMT signal. Two distinctive features of this temporal behavior are worthy of mention. Firstly, the N atom density is observed to be relatively long-lived (especially in comparison with the timescale of the nanosecond excitation) -measurable N TALIF signals are evident even up to 10 ms after the discharge is initiated. At these longer timescales, it is believed that the main loss mechanisms for atomic nitrogen are wall recombination and atom-atom recombination. For an N density of about 10 17 cm -3 , based on rate coefficients obtained in [START_REF] Evenson | Atomic-nitrogen recombination[END_REF] and [START_REF] Kim | recombination of O, N, and H atoms as Silica: Kinetics and mechanism[END_REF], the atom-atom recombination time is estimated to be about 10 ms (for a relevant rate coefficient of k ≈ 10 -33 cm 6 s -1 ) while the wall recombination time is estimated to be between 1-10 ms for a temperature range of 300 to 2000 K. The characteristic wall recombination time is estimated based on τwr = D/(vavγ) where D is the pressure-dependent diffusion coefficient, vav is the mean kinetic velocity of particles and γ is the recombination probability for atomic nitrogen with quartz.

Previous measurements have found that the gas temperature rises from 300 K to about 2100 K from the point of [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF] initiation till around 1.5 µs in the near afterglow. Both these estimates of the limiting recombination times seem reasonable when compared with the data. A direct consequence of this finding is that attempts to model nanosecond discharges with repetition rates faster than 10 ms (e.g. kHz or 1 ms) should take into account the residual atomic species production from previous pulses.

At earlier times, the other timescales of interest are the acoustic timescale and the heat diffusion time to the wall. The acoustic timescale may be simplistically defined as half the length of the capillary divided by the temperature-dependent speed of sound. Based on an earlier study using a similar discharge geometry, this figure was estimated to be about 40 µs. The acoustic time essentially dictates when the pressure within the capillary equilibrates and returns to its initial value of 27 mbar. Prior to this time, an isochoric or constant density approximation may be assumed. In addition, it is found that the heat conduction time to the wall is estimated to be on the order of about 5 µs. The heat diffusion timescale is defined as τdiff = (r/2.4) 2 /D where r is the radius of the capillary and the value of 2.4 may be treated as a shape factor for a cylindrical geometry. Since the heat diffusion timescale is faster than the acoustic timescale, this provides one of the possible reasons why there is no significant change in the N density (due to the gas-dynamic rarefaction of the hot channel) after the discharge.

Fig. 2 Temporal evolution of N atom density.

The second feature of note is the fact that the TALIF signals recorded within the first few microseconds after the discharge exhibit symptoms of strong quenching, as evidenced by the fast decay rates of the attendant PMT signals similar to an example displayed in Fig. 3.

Fig. 3 Raw PMT resonant time trace (400 shot averaged) versus temporal profile of laser intensity acquired from a 1 ns response Thorlabs DET10A photodiode.

Quenching corrections cannot be applied in this regime since the decay rates are limited by the duration of the laser pulse and therefore renders the actual quenching rate unknown. This point becomes clearer in the context of Fig. 4, which plots the measured TALIF signal decay rates (in inverse ns) as the same function of time shown in Fig. 2. The exact origin of this quenching remains unclear, but could be due to either electrons, self-quenching from N, or hot N2 molecules produced by fast gas heating [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF]. Evidence of self-quenching -due to the large density of atomic nitrogen produced -may be seen from the fact that even at the millisecond timescale (when the temperature may be assumed to be close to that of the ambient and N2 is expected to be the main quenching partner), the decay rates still slightly exceed that predicted by considering room temperature N2 quenching rates [START_REF] Niemi | Absolute calibration of atomic density measurements by laser-induced fluorescence spectroscopy with two-photon excitation[END_REF]. Due to non-uniform transmission of the bandpass filter within the wavelength vicinity of the N fluorescence (742 nm to 747 nm), there was a need to verify the linestrengths of the three respective transitions (see Fig. 1b)). Spectrally resolved emission spectra displayed in Fig. 5 shows excellent agreement with the linestrengths provided in [START_REF] Kramida | NIST Atomic Spectra Database (version 5.5[END_REF]. The peak value of the measured N density in Fig. 2 of about 1.5 x 10 17 cm -3 represents a dissociation degree of about 11%. Here the dissociation degree is defined as nN/2nN2 and provides an estimate of the fraction of the total number of N2 molecules which have been converted into their atomic constituents. As a sanity check of this unusually large number, a simple specific energy calculation based on various dominant processes is carried out using known conditions of the discharge at 1.5 µs. These dominant processes include N atom dissociation, N and N2 gas heating, as well as N2 vibrational mode heating. The idea is to compare the energy required for these processes against the measured specific energy deposited into the plasma. The latter was computed based on the back current shunt (BCS) data for the 3 HV pulses following a well-established procedure [START_REF] Lepikhin | Fast gas heating and radial distribution of active species in nanosecond capillary discharge in pure nitrogen and N2: O2 mixtures[END_REF]. This value for the total specific energy is about 1.8 eV per molecule. As one might expect, most of the energy is deposited in the first pulse when the plasma is formed together with the passage of the fast ionization wave and the discharge gap is 'closed'. As an example, the specific deposited energy in the first pulse is shown in Fig. 6.

For a dissociation fraction of 11%, Fig. 7 indicates that the total energy required for the processes of dissociation and heating described above is about 1.7 eV. This value is relatively close but still less than the measured value of 1.8 eV which suggests that the data from the N density experiments lies within physical limits. Nonetheless, it is acknowledged that these measurements do appear unusually large and warrant further examination. If indeed valid, this could signify the existence of an extremely efficient N atom dissociation mechanism related to electron impact dissociation from the A, B and C electronically excited states of N2. Estimates of these cross-sections have been provided in [START_REF] Bacri | Electron diatomic molecule weighted total cross section calculation: II. Application to the nitrogen molecule[END_REF].

IV. Conclusions and Future Work

The N atom production in a pure N2 nanosecond capillary discharge at 27 mbar has been successfully measured using TALIF. The results reveal N atom densities on the order of about 10 17 cm-3, representative of a peak dissociation fraction of about 11%. While these values may seem unusually high, estimates of the characteristic timescales of the problem as well as the specific deposited energy appear to support these large N atom densities as well as its consequent temporal evolution. Further work is ongoing, particular with regards to marrying the experimental data with a well-established plasma kinetic model. The axial distribution of N atom density as well as different gas compositions is also a subject of future research.

Fig. 1 a

 1 Fig. 1 a) Schematic of the discharge cell setup used in this study. (The region probed by the TALIF measurements is marked with a blue asterisk.) b) (i) N and (ii) Kr TALIF scheme.

Fig. 4

 4 Fig. 4 Temporal evolution of the TALIF signal decay rates. Signal lifetime is laser-pulse limited up to about 3 µs and therefore quenching corrections are only applicable beyond that time.

Fig. 5 N

 5 Fig. 5 N atom fluorescence spectra recorded by averaging over 1000 laser shots. Experimental linestrengths are computed by taking the spectral integral of each line normalized by the total spectral integral.

Fig. 6 Fig. 7

 67 Fig. 6 Specific deposited energy during the first high voltage pulse (≈1.2 eV/molecule) computed from the BCS data following a similar procedure as in [1].

Postdoctoral researcher, Laboratory of Plasma Physics.

Postdoctoral researcher (former), Laboratory of Plasma Physics.

Graduate student, Laboratory of Plasma Physics.

Leading scientific researcher, Skobeltsyn Institute of Nuclear Physics.

Senior researcher, Laboratory of Plasma Physics.O

Acknowledgments

This work is partially supported by the French National Research Agency, ANR (ASPEN Project), LabEx Plas@Par and the French-Russian international laboratory LIA KaPPA "Kinetics and physics of pulsed plasmas and their afterglow (including RFBR project 17-52-16001 and CNRS financial and organization support)".