Transport Patterns as Heuristic Testing Variables for the Social Coherence of Taxonomic Units at Different Spatial Scales

Taxonomic units in archaeology strongly convey the assumption of a social connection between the people having left the sites attributed to these units. The (implicit) assumption is that people whose sites are attributed to the same unit had closer social relations among one another than they had to people whose sites are attributed to other taxonomic units, and that such social proximity is reflected in similarities in their material culture. It is often difficult to be sure about the processes behind the emergence of similarities and dissimilarities. Therefore, taxonomic units relying on this criterion require additional testing in order to be meaningful components of studies on social relations. Dynamic objects, whose location of origin is known in addition to their place of discard, provide means for such testing, because they reflect the movement or contact patterns of people, potentially providing information on social boundaries or links on different spatial scales. Social coherence—the degree of connectedness between the people having left the sites attributed to these units—is sensitive to phenomena of spatial and temporal scale. However, there is no coherent terminology that would match scale levels of taxonomic units to those of social units. This paper proposes a hierarchical systematics for taxonomic units and their social equivalents applicable to both hunter-(fisher-)gatherer and farming societies to facilitate discussions on this topic. Based on this systematics, we propose an approach to test the coherence of taxonomic units regarding different social scale levels based on transport patterns of dynamic objects. Knowledge on the mode of acquisition (direct/embedded procurement, exchange, trade) of the dynamic objects is not a prerequisite. Three case studies from the Late Upper Paleolithic in Central Europe, the Late Paleolithic in Bavaria, and the Early Neolithic in Norway will be discussed to evaluate the potential and limits of the approach.


Introduction
Taxonomic units in prehistoric archaeology are neither cast according to common standards, nor do they follow a consistent epistemological goal. They rather encompass more or less spatially and temporally coherent clusters of sites (Reynolds & Riede, 2019), pooled for different analytical purposes. The chronological and geographic scale of these units can be extremely variable and ranges from units spanning continents and lasting hundreds of thousands of years (e.g., the Acheulean) to units comprising a handful of sites and spanning some hundred years, at most (e.g., the Salpetrian). Despite this marked heterogeneity, these units usually convey ideas about the social connectedness of their members (e.g., Wiśniewski et al., 2017) and are used as basic entities in studies about social relations of prehistoric people (e.g., Schwendler, 2012;Vanhaeren & d'Errico, 2006). The use of taxonomic units in this way is not without problems, because the relation between scale levels of archaeological units and their social equivalents is rarely discussed, probably not least because a general framework for such a discussion is not available at present (for different systems see, for instance, Weniger, 1991;Eriksen, 2000;Zvelebil, 2006).
An (mostly implicit) assumption underlying taxonomic units is that members of one such unit were socially closer connected to one another than they were to members of other taxonomic units. In prehistory-or generally before the advent of telecommunication technologies-social connectedness strongly depended on direct contact between people. Measuring distances between sites could thus provide a rough estimate about the social connectedness of the people who left them. Simply equating social with spatial proximity, however, ignores potential social boundaries or bridges and their effects on interpersonal contact (Gamble, 1998), let alone potential biases introduced by settlement patterns of mobile societies. Consequently, archaeological taxonomic units essentially rely on morphological and technological similarity between artefacts to establish taxonomic membership. Indeed, it seems that interaction, be it between individuals or groups, fosters significant similarities in material culture (Boyd & Richerson, 1985), while in the case of isolation cultural drift alone will likely cause the accumulation of regional differences (Koerper & Stickel, 1980;Neiman, 1995). This process is particularly pronounced in smaller populations with smaller sets of objects in their material culture (Buchanan & Hamilton, 2009, 280). It follows that low social connectedness between groups likely increased overall dissimilarities in material culture (Henrich, 2004;Shennan, 2000Shennan, , 2001. However, similarities in material culture can also be caused by several other factors, which are entirely independent of social connectedness (Clark, 1994(Clark, , 2009, for instance, material or functional constraints (Centi & Zaidner, 2020), analogous developments under similar selective pressure (O'Brien et al., 2018), or common ancestry coupled with low innovation rates (Barton & Clark, 2021). Similarities of these kinds violate the basic assumption of close social interaction and potentially lead to including assemblages of socially distant people in the same taxonomic group. Conversely, social connectedness is not necessarily expressed through similarities in material culture (Hodder, 1982), and archaeological remains left by closely connected people can be attributed in different taxonomic units. To be a meaningful tool in studies of social proximity and distance, it is thus necessary to contrast taxonomic units with additional variables that carry dynamic spatial information, reflecting either individual movements or social interaction. Such information is provided by all objects whose place of origin is different from their place of discard. The more precisely the origin of such dynamic objects can be determined, the more valuable their contribution for taxonomic testing.
At present, prehistoric archaeology is not only painfully lacking fixed criteria as to what constitutes a taxonomic unit; there is not even a systematics that would allow for a comparison of the existing units with regard to their highly varying levels of scale, let alone an approach to test their social coherence. While a unified catalogue of criteria for the definition of taxonomic units seems currently out of reach, a hierarchical systematics for a standardized discussion of taxonomic units and their social equivalents together with a heuristic test of social coherence might be possible.
In the following, we thus propose a systematics of taxonomic scale levels which is organized hierarchically to provide a vocabulary for comparisons and allow putting taxonomic units in a meaningful relation to one another. Against this systematics, we put forward for discussion an approach for heuristically testing the social coherence and external relations of traditional taxonomic units in different archaeological contexts. In comparing the results of three case studies from different settings and scale, we evaluate the suitability of the approach under different conditions and explore its potential and limits with regard to testing implicit assumptions of social proximity and distance in traditional taxonomic units.
The idea for this joint contribution sprang from discussions at the CLIOARCH workshop on taxonomic issues in Archaeology at Aarhus University in November 2019 (Riede et al., 2020).

Axioms
The following reflections rest on two axioms: A) To be a meaningful tool for research about social groups and their relations, taxonomic units should only include assemblages that show a closer connectedness among one another than with assemblages of other taxonomic units.
Besides similarities in the material culture (i.e., all objects and artistic expressions with their morphological and technological properties), this connectedness should be archaeologically visible by either a joint exploitation of raw material sources, such as outcrops of siliceous rocks or fossil mollusks, and/or participation in the same exchange or trade networks. A mutual exclusive use of raw material 8 Page 4 of 26 sources or participating in mutually exclusive exchange networks, in contrast, indicates lower connectedness or even avoidance of contact.
B) The social scale, for which transport patterns of objects are indicative, varies. It thus cannot be assigned on general terms or a priori, but must be checked for each case individually.
Different classes of dynamic objects, such as lithic raw materials or mollusk shells, often show class-specific ranges of transport distances in certain periods and areas, obtained via specific modes of acquisition, such as direct procurement, exchange, or trade, thus reflecting contact on different spatial and social scales (Eriksen, 2000;Maier, 2015;Nyland, 2016;Olsen & Alsaker, 1984). However, there is no fixed relation between an object class and the social scale for which it is indicative, nor are all dynamic objects in same period and area necessarily circulated according to the same rules. Transport distances of lithic raw materials during the Upper Paleolithic in Western Europe, for instance, rarely exceeded 300 km (Féblot-Augustins, 1997). Mollusk shells, in contrast, were regularly transported over much greater distances (Álvarez-Fernández, 2011). During the Upper Paleolithic in eastern Central Europe, however, mollusk shells are transported only over rather short distances, indicating a mode of acquisition fundamentally different from what can be observed in Western Europe (Hladilová, 1999). Consequently, mollusk shells in Western Europe are indicative of contacts on a larger social scale than mollusk shells in Eastern Europe. An example for chronologically different modes of acquisition for a single class of objects are lithic raw materials. Their acquisition by hunter-gatherers during the Paleolithic probably took place as direct or embedded procurement (Binford, 1979: 259;Floss, 1994: 325), while during the Neolithic the transport regime seems to be rather exchange or trade (e.g., Roth, 2008;Zimmermann, 1982). It is often difficult to recognize the social mechanisms behind the transport patterns in the archaeological record and modes of acquisition can take place on different spatial scales. Direct acquisition can take place over 100 km or more, while items can be traded over just a few kilometers. Therefore, the proposed protocol does not require an a priori assumption about specific modes of acquisition. Instead, it interprets the spatial relation between the taxonomic unit on the one hand and the transported objects on the other. The only requirement is to meaningfully match the scale level of the taxonomic unit under study with the scale level of the dynamic object class used for testing, depending on the question at hand.

Spatial, social, and taxonomic scale levels
The scale at which questions are addressed is of great significance because many properties of observable phenomena, such as size, extent, magnitude, or frequency, but also feedback processes, timing of system responses to external factors, and the occurrence of so-called emergent properties (i.e., characteristics of a system only observable at certain scale levels, but not at others), are dependent on the scale of observation (Zhang et al., 2004). It follows that not all questions can be addressed meaningfully at all scales and that it is necessary to match the process scale of interest with the scale of observation. Social connectedness prior to the advent of longdistance communication techniques and long-term storage of information strongly depended on spatial and temporal proximity. The latter, including the problem of non-contemporaneity, will not be addressed in this paper. It therefore must suffice to say that contemporaneous individuals are-as a matter of necessity-more closely connected than non-contemporaneous ones, particularly prior to the invention of writing. The following reflections thus focus on spatial aspect of taxonomic units and their social equivalents.
Many terms used to describe social and taxonomic units, such as "local community" (Johnson, 1982) or "regional group" (Romano et al., 2020) carry a strong notion of spatial scale. Moreover, the spatial extent of a taxonomic unit already gives an idea about the social connectedness of their members, usually in an inversely proportional relation (i.e., the larger the unit, the weaker the ties between two randomly selected members of that unit). Where individuals have to move to interact, space is a main obstacle in connecting with others, and there seem to be clear patterns in human mobility decaying with distance (Simini et al., 2012). It therefore seems advisable to use space as a reference for the definition of scale levels to which taxonomic and social scale can be compared.
As spatial scale hinges on distance, the social scale hinges on connectedness. Since distance between individuals influences their abilities to communicate, spatial and social scales are related, but not identical. Besides distance, connectedness also depends on other factors such as number and densities of people, land use (sedentary or mobile), subsistence, or social organization. With regard to the ethnographic record on hunter-(fisher-)gatherers, social scale levels are likewise not coherently defined and often restricted to a local and regional scale (Binford, 2001;Johnson, 1982;Uthmeier, 2021). Moreover, it is debated whether these societies exhibit a nested and hierarchical (Whallon, 2006), or a fluid and overlapping structure (Damm, 2022). In our view, these stances are not mutually exclusive. Generally, human social systems seem to self-organize in hierarchical, self-similar structures over successive scale levels, probably as the result of an evolutionary process optimizing acquisition and redistribution of energy and information (Zhou et al., 2005;Hamilton et al., 2007;Fernández-López de Pablo et al. 2022). This process results in a sequence of ever-larger social units, which are both discrete and flexible with regard to group membership (Hamilton et al., 2007). Primarily, social connectedness is a property of individuals (Codding et al., 2022;Damm, 2022). In prehistoric contexts, however, individuals are often invisible, and the remains left for analyses are often palimpsests representing the actions of several people who were not necessarily living contemporarily (Maier et al., 2022). And not only do individuals become increasingly invisible with higher scale levels, the importance of individual decision making also becomes just one factor among many others. In the following, social connectedness therefore refers to groups rather than individuals, particularly at scale levels larger than the regional scale. These groups-or networks (Fernández-López de Pablo et al., 2022)-are understood as having different spatial extents and their organizational structure, or contact pattern, probably likewise varies with scale.
On a local and regional scale, such networks are probably structured in several task-dependent "circuits," i.e., specific sub-networks, where different sub-sets of the same group of people regularly interact with one another (Damm, 2012). These subnetworks therefore show a wide overlap with regard to the people involved. Consequently, social connectedness at this scale does not hinge on individuals but rests robustly on numerous broadly redundant circuits.
Particularly for societies lacking the means of communicating over larger distances without moving people, networks probably change on supra-regional and continental scales, where distances between individuals cannot be traveled within a few days and take a more dispersed structure. Generally, the social connectedness between individuals thus decreases as the spatial extent of network increases. Within these networks of supra-regional or larger scale, the problem of decreasing social connectedness with distance can be mitigated by a few far-travelling individuals who provide long-distance contacts between otherwise mainly regionally centered groups. In this case, the network will probably resemble so-called small-word networks (Milgram 1967;Watts & Strogatz, 1998;Bentley & Maschner, 2008), where most individuals live in a regional social context and few far-travelling individuals provide long-distance contacts and thus controlling the flow of information throughout the entire network. Depending on size, such small-world networks will probably range from a close-meshed structure, where adjacent clusters are connected to one another, to a more extended form, where some clusters distant from one another have no direct contact but are connected via intermediate clusters (Fernández-López de Pablo et al., 2022). It can be assumed, that such indirect contacts become more numerous with increasing levels of scale. Relying on few individuals to connect many, such networks are probably more prone to disturbances than those with redundant circuits.
To date, there is no standardized procedure with which taxonomic units in archaeology are fitted to spatial and socials scale levels. Terms such as "facies," "culture," or "techno-complex" are frequently used, but their application is inconsistent. These inconsistencies together with a lack of hierarchies of the applied terms prevent comparisons among them. As a consequence, they tend to obscure past social relations rather than to illuminate them (e.g., Shea, 2014).
Leaving aside the discussions of whether the term "culture" is a fortunate choice for a taxonomic category in archaeology (see, for instance, Wotzka, 1993), it can be stripped of its problematic semantic implications and simply be taken as a taxonomic unit of a certain spatial scale. As such, it can be hierarchically nested into a three-step sequence of facies, culture, and techno-complex. Traditional taxonomic levels-facies, archaeological culture, techno-complex-can be integrated as follows. In most instances, the term facies seem to refer to sub-units of archaeological cultures or techno-complexes at regional or smaller scales. Given that archaeological cultures in comparison to techno-complex carry a stronger notion of social connectedness, we connect the former to supra-regional and sub-continental scale levels and the latter to continental and larger scales. In the archaeological record, these taxonomic units are represented by sites unevenly spaced in the landscape forming clusters and voids. For sake of clarity, it seems useful to distinguish between a taxonomic unit and its real-world correlate in the archaeological record.
The systematics proposed below (Table 1) involves, of course, some arbitrary decisions, but it is spatially consistent, hierarchically organized to allow for the assessment of relations between units, corresponds to geographical, archaeological, and ethnographic observations, and accounts for the fact that human mobility decays with distance.
With a circumference of roughly 40,000 km, the equator is taken as a starting point. Multiplied by a scaling factor of 0.5, a distance of 20,000 km is set as lower limit for the global scale. To account for the growing costs of long-distance travels, we decrease the scaling factor in each step by 0.1, i.e., one order of magnitude, eventually, arrive at seven scale levels. With 20,000 km * 0.4, the lower limit of the trans-continental and upper limit of the continental scale is set to 8000 km, a distance value rarely exceeded among the seven continents. Further down the line, the boundary between the continental and the sub-continental/supra-regional scale is set to (8,000*0.3) 2,400 km. Archaeological correlates at the continental scale level are observable during the Paleolithic, for instance, in the distribution of artistic conventions (e.g., for female representations between 30 and 15 ka, e.g., Gaudzinski-Windheuser & Jöris, 2015). For the Neolithic/Bronze Age, traded oxhide ingots (Sabatini & Lo Schiavo, 2020) as well as lapis lazuli (Massa & Palmisano, 2018) and tin objects (Berger et al., 2019) are good examples. There are no reported ethnographic units at this scale level if the square root of the group territories is taken as an indicator of maximum distances (Binford, 2001) and the archaeologically observable transports probably reflect an extended small-world network, where far-travelled individuals establish and maintain contact between two or more small-world networks. For archaeological correlates at the sub-continental/supra-regional scale, transport patterns of fossil and sub-recent mollusk shells are frequent examples for the Paleolithic (e.g., Maier, 2015), while transport patterns of Spondylus objects (Windler, 2018) or Amphibolite adzes (Nowak, 2008) are examples from the Neolithic. In the ethnographic record, there are eleven cases of groups where the square root of the territory shows distances between 480 and 812 km. We therefore link this scale with periodically aggregating groups (Group 3 according to Binford, 2001). Socially, these groups probably constitute small-world networks. On the regional scale (480-48 km), the acquisition of raw materials for expedient tools, often siliceous rocks, can serve as archaeological correlate for both the Paleolithic (Féblot-Augustins, 1997) and the Neolithic (Roth, 2008;Schyle, 2011;Zimmermann, 1995). In the ethnographic record this scale level can be linked to aggregated groups (Group 2 according to Binford, 2001) which probably have networks of overlapping circuits. This also accounts for dispersed groups (Group 1 according to Binford, 2001), which are then linked to the extra-local scale between 48 and 4 km. Trips of more than 48 km, the upper limit of the extra-local scale, usually cannot be travelled by foot within 1 day. And even if boats are used, the foraging radius usually does not surpass this distance (e.g., Ames, 2002). A catchment area of 4 km is frequently exploited around a site and is set as upper limit for the local scale.
There are other terms which may gain in analytical power when linked to a scheme of scales by specifying, e.g., direct procurement on extra-local scale, exchange on supra-regional scale, largest unit acting jointly on a regional scale, or identity-conscious interaction unit of regional scale. Having established such a systematics, it is now possible to describe and compare taxonomic units in these terms (Table 2). It can be stated, for instance, that the Acheulean is an archaeological unit at a trans-continental scale and with the taxonomic hierarchy of a techno-complex. The Mousterian, Micoquian, Aurignacian, Gravettian (sensu lato), and Magdalenian, in contrast, are archaeological units at a continental scale with the taxonomic hierarchy of a techno-complex. In the western and central European part of the Aurignacian, lithic raw material procurement suggests a subdivision into five regional groups (Schmidt & Zimmermann, 2019) of regional to supra-regional scale. Findings on personal ornaments suggest three independent social units, two of which show a mutual exclusive pattern, potentially reflecting an extended small-world network. Examples for archaeological units at a sub-continental or supra-regional scale are the Solutrean, Pavlovian, or Badegoulian, with a social structure likely resembling a small-world network. The Salpetrian, on the other hand, is a unit of regional scale at the taxonomic level of a facies with a social structure likely showing overlapping circuits, while the Gorodtsovian and Spitsynean are facies of extra-local scale.

Material
Against the background of this systematics, we explore the social coherence of taxonomic units in hunter-gatherer or hunter-fisher-gatherer societies on different spatial scales, exemplified in three case studies from the Late Upper Paleolithic to the Early Neolithic.

The Late Upper Paleolithic in Central Europe
With a southeast-northwest extent of about 3000 km, the taxonomic unit Magdalenian is of sub-continental scale, and even if only the central European part is considered, an extent of about 1400 km clearly exceeds supra-regional dimensions. There are over 650 assemblages from more than 540 sites in Central Europe attributed to the taxonomic unit Magdalenian. Based on 744 individual lithic raw material transports ≥ 15 km from 151 assemblages (Maier, 2015) and 198 transport patterns of mollusk shells from 62 assemblages, one of us has proposed a subdivision of the Magdalenian in Central Europe into 5 sub-units of regional scale aggregated into 2 sub-units of supra-regional scale, socially connected by a small-world network (Maier, 2015). We will review these results with regard to the proposed method.
Special attention will be given to a unit located along the courses of the Vltava and Saale River, for which, in contrast to the 4 other regional sub-units, preference has been given to arguments of territorial size in its spatial delimitation. This unit comprises 73 assemblages in Bohemia and eastern Germany. Information on raw material transports is available for 22 assemblages (Maier, 2015).

The Late Paleolithic in Bavarian
The dataset for the Bavarian Late Paleolithic comprises 24 sites, most of which are surface finds. On a larger taxonomic scale, they are attributed to the arch-backed point techno-complex. On a regional scale, they have been described as a distinct variation of the "Federmesser-groups" and pooled in an independent taxonomic sub-unit, the so-called "Atzenhofen-Group" (Sauer, 2018;Schönweiß, 1974Schönweiß, , 1992, which is the only singled-out entity of the Late Paleolithic in Bavaria. Defining characteristics for the attribution of a site to the Atzenhofen Group is the location on sandy ridges above the valley floor and the use of tabular chert, lydite, and erratic flint (Schönweiß, 1974(Schönweiß, , 1992. Note that lithic raw materials are a defining element of the Atzenhofen group, which might signal circular reasoning in testing. However, only the presence of three specific materials is considered indicative of taxonomic membership. Other materials, let alone their transportation patterns, are not considered. Information on raw material transport is available for all 24 sites (Sauer, 2016).

The Early Neolithic in Norway
The sites of the Norwegian Early Neolithic (4000-3300 cal BC) data set are attributed to hunter-fisher-gatherer (HFG) and taxonomically assigned to the Central Norwegian HFG populations (previously termed the slate culture) (n = 6), the West Norwegian HFG populations (n = 34), and the East Norwegian HFG populations (related to the Funnelbeaker culture, but with agriculture playing a minor role, e.g., Solheim, 2021) (n = 18). Raw material information is available from 5 sites. The attribution to these taxonomic units (which are also subdivided) follows Bergsvik (2006) and Solheim (2009Solheim ( , 2012 and is mainly based on distinctive differences in core technologies between them. The dataset from Norway comprises three contemporary taxonomic units. However, while the West Norwegian HFG is represented in its entirety, the sites attributed to the Central Norwegian HFG and East Norwegian HFG are only partly located in the area of investigation and are stretching further northwards and eastwards, respectively. For the inland/mountain East Norwegian sites, shores at the coast in eastern Norway are most relevant. Even if the measured distance might be shorter to the outer western coast, a procurement from these shores seems less likely given that they lie within the distribution area of the eastern Norwegian HFG sites.

Method
The proposed method to test the social coherence of a taxonomic unit by means of transport patterns of dynamic objects rests the comparison of two areas, namely, the area of the taxonomic unit and the maximum procurement polygon of dynamic objects. It needs to be stressed that this is a heuristic approach rather than an objective measure. When interpreting the results, other observations should thus also be considered. All calculations are done in QGIS Version 3.10 (QGIS.org, 2021) using a metric projection and LibreOffice.

Area of taxonomic unit (ATU)
The first aspect to be considered is the area of the taxonomic unit (ATU) which shall be put to the test. Initially, all sites attributed to a specific taxonomic unit are plotted on a map. Subsequently, a convex hull is constructed around all sites and the area of the resulting area is extracted. The largest extent of the ATU defines its scale level. To test the social coherence of a taxonomic unit on its own spatial scale, the dynamic object class used for testing must match this scale. If dynamic objects with transport patterns on smaller scales are chosen, the result will inform about the number and relation of units of smaller social scales nested within the taxonomic unit. If dynamic objects with transport patterns on larger scales are chosen, the result will inform about external relations of the taxonomic unit.
If more than one taxonomic unit is considered, the ATUs should be spatially exclusive. Overlapping ATUs of different taxonomic units would indicate the joint exploitation of resources by members of otherwise different social units and thus would violate axiom A.

Maximum procurement polygon (MPP)
The second aspect is the area of the maximum procurement polygon of dynamic objects (MPP) selected to test the coherence of the taxonomic unit. In a first step, a dynamic object class of matching scale is chosen, and all available information on transport distances are collected and evaluated as to their reliability and precision. The reliability depends on the method used to determine the location of origin, Page 12 of 26 such as macroscopic inspection, microscopic inspection, and chemical fingerprinting. Only those transport distances deemed reliable are taken into consideration. The precision depends on the extent of the identified source location, which can vary from specific outcrops with only small extents to very large areas such as the Atlantic shore or the northern European moraine deposits. If the extent of such an area is large and the specific location of the outcrop can thus not be determined precisely, the closest point to the site potentially yielding the dynamic object's origin is chosen, unless other archaeological arguments speak in favor of another location. In a second step, the dynamic object acquisition polygons are mapped for each individual site of the taxonomic unit. To this end, the site itself and all related outcrops (or their closest points) are mapped, and a convex hull is constructed. This is repeated for each individual archaeological location. To allow sites with information of only one dynamic object source to be included in the study, each site may receive a buffer whose value is chosen with regard to the dynamic object class. In our study, each site receives a 5-km radius buffer, since an exploitation of local lithic raw materials is generally assumed. Raw material outcrops receive no such catchment buffer.
In a third step, all overlapping raw material polygons for the respective taxonomic unit are merged into one polygon, the maximum procurement polygon of dynamic objects (MPP), and its areal value is extracted. If the raw material polygons form more than one overlapping cluster, each cluster is merged individually, resulting in several MPPs. Again, the largest extent of a MPP defines it scale level.

Interpretative scheme
The above-described procedure is followed by a visual inspection of the ATU and MPP polygons to check for plausibility of the results. If, for instance, the test aimed at coherence of ATU and MPP at the same scale level, a gross mismatch in their extents might either indicate a mismatch in the selection of the dynamic object class with regard to the target scale or the inadequacy of the taxonomic unit for the social scale in question. In both cases, the selection should be reconsidered.
If the visual inspection seems plausible, the following relations may be interpreted meaningfully: a) A single MPP largely overlaps with the ATU. b) More than one MPP largely overlap with the ATU. c) A single MPP hardly overlaps with the ATU. d) More than one MPP hardly overlap with the ATU.
In case a), the ratio between the ATU and MPP is calculated (ATU/MPP), and the resulting value is interpreted as follows. Values around 1 show a taxonomic unit which is well represented by the transport pattern of the selected mobile object class, corroborating its social coherence on the analyzed scale. The closer the values are towards 0, the more the MPP surpasses the ATU, indicating that the social network, in which the mobile object class used for testing circulates, is larger than the taxonomic unit in question. The more the values exceed 1, the more the ATU surpasses the MPP, indicating that the social network, in which the mobile object class used for testing circulates, is smaller than the taxonomic unit in question. While values smaller than 1 thus might indicate the need to enlarge the taxonomic unit, values larger than 1 suggest further subdivisions (Fig. 1).
Case b) is similar to case a) with values larger than 1. In the logic of the proposed method, more than one MPP per taxonomic unit strongly indicates that the latter comprises more than one distinguishable social unit of its corresponding scale.
Cases c) and d), with MPP(s) hardly overlapping with the ATU and thus oriented outward of the taxonomic unit in question can indicate a false attribution of sites at the fringe of the ATU. If that is not the case, they can be interpreted in terms of external relations on a matching social scale.

Results
The Magdalenian is a taxonomic unit at the level of an archaeological culture of sub-continental scale. In its western part, it comprises at least one unit of supra-regional scale, indicated by a far-flung MPP of mollusk shells. This MPP, however, has no matching equivalent in the eastern part, where transport distances of mollusk shells are generally much shorter.
With regard to lithic raw materials, five non-overlapping MPPs of regional and supra-regional extent can be identified between the Rhône River in the west and the Bug river in the east (Fig. 2). In Central Europe, the taxonomic unit Magdalenian thus comprises likely four sub-units of regional scale and one of Fig. 1 Interpretative scheme. Squares, raw material sources; solid line, maximum procurement polygon (MPP). Crosses, sites; dashed line, area of taxonomic unit (ATU) supra-regional scale. Based on these observations, one of us has proposed five taxonomic sub-units (Maier, 2015), which now can likewise be evaluated using the same method. Since in four cases the raw material transport patterns were used to delimit these units against one another and to determine their extent, it is not surprising that a calculation results in values close to 1 (Table 3). Mapping the gathered information on the sub-unit along the rivers of Vltava and Saale, however, results in a single ATU with one large and two very small MPPs, all strongly overlapping with the ATU. It can thus be concluded that the derived information is indicative of the internal structure of the taxonomic unit, rather than for external relations. The ATU/MPP ratio of 3.4 strongly exceeds the value of 1, indicating that it potentially harbors more than one social unit of regional scale and thus should be further subdivided.
The Atzenhofen Group (Fig. 3) can be described as a taxonomic unit at the level of a facies of regional scale. With a value of only 0.2, however, the ATU sits rather centered within a much larger MPP, likewise of regional scale. This finding  GADM, 2021;NEAD, 2021) indicates that the taxonomic unit in its current state is likely too small to represent a social unit of regional scale und thus should probably be enlarged.
For the Norwegian case study, only the area of the West Norwegian HFG is represented in its entirety, while the sites attributed to the Central Norwegian HFG and East Norwegian HFG are only partly located in the area of investigation and are stretching further northwards and eastwards respectively. The East Norwegian HFG also stretches westwards along the eastern coast, but sites from this area have not been included in the analysis (Fig. 4). The Central and East Norwegian HFG are therefore mapped for discussion but cannot be subject to the presented approach. The area of the West Norwegian HFG is a taxonomic unit on the level of an archaeological culture of supra-regional scale. With regard to the other case studies, it is thus best comparable with the supra-regional unit in the easternmost part of the Magdalenian, i.e., sub-unit 5, rather than with the Magdalenian itself. The ATU/ MPP ratio of 1.7 indicates the potential for a further subdivision.

Discussion
Since the results provided by the presented approach are a heuristic measure for the social coherence of taxonomic units, they need to be discussed in light of further evidence.

The Late Upper Paleolithic in Central Europe
One of us has proposed the subdivision of the Magdalenian in Central Europe in two supra-regional units of three (west) and two (east) regional units, respectively (Maier, 2015). In light of the above-stated reflections, this proposal can be further refined.
The mollusk shell MPP of supra-regional scale in the western part of the Magdalenian represents the largest regularly observable transport distances of the taxonomic unit Magdalenian. It thus constitutes its largest observable substructure. With regard to its extent, it is unparalleled in the eastern part, where mollusk shells are transported only over much shorter distances. The largest substructure in the eastern

Fig. 3
The Late Paleolithic in Bavaria, area of taxonomic units, and maximum procurement polygon (projection: EPSG 3035; GADM, 2021;NEAD, 2021) part is also of supra-regional scale but represented by lithic raw materials. It is thus the largest unit identified by the lithic MPP, while the four others are of regional scale. It is assumed that lithic raw materials are acquired by embedded procurement.
Overlapping procurement patterns are thus thought to be indicative of individuals jointly exploiting the resources of the same region and thus interacting closely with one another. The MPPs of lithic raw materials should thus represent a social organization probably structured in overlapping circuits. The impression of self-contained networks with redundant circuits becomes evident most prominently in areas, where spatially neighboring sites show mutually exclusive raw material acquisition patterns. This is the case, for instance, in the area north of Lake Constance, between site clusters 1 and 2 (Fig. 2). Sites west of the Rhine River often get their raw material from the high-quality outcrops around Lausen and Olten. The sites east of the Rhine, however, do not use these outcrops, despite their relative spatial proximity of about 70 km. Instead, raw materials from the Regensburg basin at a distance of approximately 250 km is regularly exploited. The mollusk MPP, in contrast, differs in its spatial structure inasmuch as it links several regional units of independent lithic MPPs, thus rather reflecting a small-world network. A test of the regional sub-units suggests to further subdivide the regional unit along the Vltava and Saale River. Following this suggestion results in a unit of regional scale, stretching over Bohemian and adjacent areas with a good agreement of the MPP and the sites of a regional cluster located here. It also results in another, yet much smaller regional unit in eastern Germany that covers but a part of the regional site cluster there. In this condition, it does not make for a convincing self-contained sub-unit. A problem here is the-at the moment-insufficient resolution of the source area of Baltic erratic flint. North of the Middle Range Mountains, it can be gathered at many locations. For the moment, it is thus impossible to say whether or not the Baltic flint in the Bohemian assemblages come from the area of the site cluster in eastern Germany and whether it should be included in a joint unit with the Bohemian cluster. Another conspicuous element of the eastern German cluster is that it contains the two easternmost sites which yielded mollusk shells from the western mollusk MPP. The Bohemian cluster, in contrast, does not show any connection to the west. Eventually, it can be concluded that the proposed regional sub-unit along the courses of the Vltava and Saale is probably the most debatable in terms of social coherence and that it very well might contain two separate units of regional scale.

The Late Paleolithic in Bavaria
Late Paleolithic assemblages in Bavaria have traditionally been summarized under the taxonomic term of Atzenhofen group, thought to represent a socially coherent unit of regional scale nested within the larger framework of the Federmesser Groups (Sauer & Riede, 2018). The raw material spectrum shows the exploitation of both local and exogenous raw materials (Sauer, 2016). Locally, lithic materials of strongly varying quality were exploited, such as lydite or Triassic keuper-chert, Jurassic chert, and chalcedony. Exogenous raw materials were represented by tabular chert from the Danube valley, quartzite from north-western Bohemia, and erratic flints from the North-German Lowlands. Typically, the sites show a diverse spread of both local and non-local raw materials. Assuming similar acquisition patterns as for the Magdalenian (embedded procurement), the procurement pattern of lithic raw materials should be a good variable to test whether this taxonomic unit has an archaeologically visible social equivalent of matching scale.
A first inspection shows that both the ATU and MPP are of regional scale. The ATU/MPP ratio of 0.2 strongly suggests that the area covered by the taxonomic unit is significantly smaller than the area jointly exploited by the people who produced the corresponding sites. Interestingly, the convex hull of the taxonomic unit appears well-centered within the convex hull of the MPP (Fig. 3), indicating that no edge effects or specific exogenous raw materials from a single distant source is distorting the picture. This suggests that the taxonomic unit in its current state is too small to meaningfully match the extent of the social unit indicated by the lithic raw material MPP. This is even more the case, as there are no observable transport patterns vindicating the small extent. For future taxonomic refinement, it is thus advisable to re-evaluate the sites located within the area of the MPP and to look for further arguments for including or excluding them from this taxonomic unit.

The Early Neolithic in Norway
The MPP of the West Norwegian HFG overlaps largely with the ATU, indicating that it is informative of conditions within the ATU. The ATU/MPP ratio of 1.7 for the West Norwegian HFG suggests that it might contain further regional units. However, because of the dominant location of sites along the rugged shoreline, the ATU comprises large empty areas and-in comparison to the two other examples-represents the spatial distribution of the associated sites rather poorly (Fig. 4). If these empty areas were excluded, the MPP would match the ATU rather well. Also, the single MPP has a peculiar morphology, because of a single dominant raw material source, the Siggjo rhyolite quarry (Alsaker, 1987), located in the lower third of the ATU in Sunnhordland. In contrast to the Upper and Late Paleolithic case studies, the West Norwegian HFG likely followed a sedentary lifestyle, influencing long-distance logistical mobility involving travelling by boat (Olsen, 1992;Bergsvik, 2001Bergsvik, , 2006. Exchange, in addition to direct access via embedded procurement, was probably an important mode of raw material acquisition. This is in accordance with a single dominant extraction site. Another complicating factor is that flint is difficult to connect to specific sources other than the outer coast in general. In light of these reflections, a subdivision appears inappropriate. However, when looking at the individual raw material polygons, there appears to be a difference between those located to the south and to the north of the main raw material extraction site, with the latter being larger and containing more different raw materials. Also, the location of the large settlement site Kotedalen in Nordhordland marks a boundary beyond which raw materials show marked and sudden fall-offs. For slate, quarried in the north, the fall-off is sudden, from 20 to 2% (of the total amount of raw materials found at the site), towards the south, and for rhyolite, quarried in the south, the fall-off is from 40 to 5% in the other direction (Olsen, 1992). Such fall-off is also supported by the distribution of other raw materials (Bergsvik, 2006;Olsen & Alsaker, 1984). So, despite commonly exploited sources, there seem to be two raw material circulation circuits, distinguishable by quantitative differences and sudden fall-offs, and with a boundary zone in Nordhordland, where Kotedalen is located. This indicates that the site Kotedalen was a hub in a small-world network extending northwards as well as southwards along the coast (see also Bergsvik, 2002).
The Central Norwegian HFG are only represented in their southern part. Interestingly, the MPP is directed outside the (only partly represented) ATU, being thus indicative of external relation rather than internal ones. It shows a broad overlap with the northern part of the MPP of the West Norwegian HFG. It is quite possible that this is the result of cross-boundary exchange of raw materials. It could nevertheless be interesting to re-examine the taxonomic affiliation of the sites at the southern fringe of the Central Norwegian HFG.
The East Norwegian HFG are only represented in their western part. The spatial pattern differs markedly, inasmuch as sites are often located inland. Again the ATU encircles a lot of empty space. The flint documented amongst these groups have probably been acquired at the coast of eastern Norway, although the western shores would have been considerably closer for certain sites. A similar phenomenon has been observed for the regional units within the Magdalenian in the area of Lake Constance (see above). While the Western and Central Norwegian HFG thus show overlapping MPPs indicating interaction of some sort, the East Norwegian HFG are set apart, indicating reduced or even the avoidance of contact.

Comparison
Comparing the results of the case studies (Table 4), it seems that siliceous raw materials are a good tool for analyzing social coherence at the regional scale both for mobile and sedentary communities. However, generalization of that kind are dangerous, as can be seen in the examples of shell transports during the Magdalenian. Even within this techno-complex of continental scale, the same object class can be subject to very different transportation mechanisms within the nested sub-units. In areas where source tracing of siliceous raw materials is not possible, it might be difficult to find a suitable substitute for testing social coherence at the regional scale. In these cases, the distribution of objects other than those used to assign an assemblage to a unit might provide insights. The existence of a single dominant source of siliceous raw material located in one ATU but repeatedly used in two other non-overlapping ATUs is observable in the Norwegian case study, but not in the others.
Most of the units discussed in the case studies are facies of regional scale probably resulting from a social group with strongly overlapping circuits. Even if the "Atzenhofen group" would be enlarged to about the area of the raw material polygon, it still would be within this scale and category. Exceptions are the Magdalenian in Central Europe, which is a culture of supra-regional scale probably socially supported by a small-world network, and the Magdalenian sub-unit 6. Given its nested position within the Central European Magdalenian, it should be considered a facies of supra-regional scale. The West Norwegian hunter-fisher-gatherers, in contrast, are of regional scale, but there are arguments indicating a small-world network as a likely social equivalent of this unit, in contrast to the other cases at this scale level. Nested social scales are thus not a rigid structure, but are an emergent property of interaction between individuals, who-as a matter of necessity-have a higher statistical chance to interact more often with socially close people than with socially distant ones. It follows that the scale-related categories (Table 1) can be a bit flexible at their boundaries, while the spatial scale has to be kept rigid as the reference scale for comparisons.  Scale Supra-regional Regional Regional Regional Regional Supra-regional

Conclusion
The discussion in this article highlights that taxonomic units in archaeologydespite their strong connotation of social connectedness-cannot be readily equated with social units of the same extent but require testing. However, before such tests can be performed, a common vocabulary is needed that allow for comparisons between different scale levels of taxonomic units and their social equivalents. We find that the proposed systematics facilitates comparisons between and across taxonomic units, also between mobile and sedentary communities and is helpful to match taxonomic and social scales.
Using this systematics, a number of questions and hypotheses for future testing can be put forward, such as: -Are there structural changes in taxonomic and social scale levels with regard to time? -How do demographic parameters affect social and taxonomic scale levels? -Are there generalizable rules connected to the transition from networks organized in overlapping circuits to small-world networks?
Tests for social coherence of taxonomic units should be easily feasible, meaning that they should work without requiring elaborate software or sophisticated math. Also, they should work with a variety of object classes, ideally those whose data is regularly recorded and widely available. The proposed approach for testing taxonomic units for social coherence meets these requirements and with regard to the case studies performs reasonably well. It also has the virtue of being independent from land use strategies (mobile or sedentary) or a priori assumptions about the modes of acquisition (direct/embedded procurement, exchange, trade). The derived results must, however, be treated as heuristic suggestions which need to be further evaluated against other available data relevant for social relations. Future studies will help refining this approach and addressing its weak spots. For instance, it turns out that the approach is sensitive to site distribution. Topographic features strongly affecting the distribution of sites, such as rugged shore lines, thus seem to reduce the performance significantly. However, this problem could be addressed by adjusting the convex hull of the ATU based on the given topographic situation. Generally, the method is less suited for areas where the sources of dynamic objects cannot be determined with sufficient precision. In these cases, other dynamic object classes should be sought for substitution.
A clear advantage of such a testing procedure is that it forces researchers to make explicit statements about the relevant scale level of the taxonomic units under study. In the future, this might help to gain a better understanding of the relations and hierarchies of archaeological taxonomic units.