Inequality in relational wealth within the upper societal segment: evidence from prehistoric Central Europe

Marzian, Johannes; Laabs, Julian; Müller, Johannes; Requate, Tilman Article — Published Version Inequality in relational wealth within the upper societal segment: evidence from prehistoric Central Europe Humanities and Social Sciences Communications Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Marzian, Johannes; Laabs, Julian; Müller, Johannes; Requate, Tilman (2024) : Inequality in relational wealth within the upper societal segment: evidence from prehistoric Central Europe, Humanities and Social Sciences Communications, ISSN 2662-9992, Springer Science and Business Media LLC, Berlin, Vol. 11, Iss. 1, pp. 1-12, https://doi.org/10.1057/s41599-024-03053-x This Version is available at: https://hdl.handle.net/10419/302043 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ ARTICLE Inequality in relational wealth within the upper societal segment: evidence from prehistoric Central Europe Johannes Marzian1,2,7✉, Julian Laabs3,4,7, Johannes Müller4,5,6 & Tilman Requate2 While our understanding of long-term trends in material wealth inequality in prehistoric societies has expanded in recent decades, we know little about long-term trends in other dimensions of wealth and about social developments within particular societal segments. This paper provides the first evidence of inequality in relational wealth within the upper societal segment of a supra-regional network of communities in prehistoric Central Europe over the first four millennia BCE. To this end, we compiled a novel dataset of 5000 single-funeral burial mounds and employed burial mound volume as a proxy for the buried individual’s relational wealth. Our analysis reveals a consistently high level of inequality among the buried individuals, showing a wave-like pattern with an increasing trend over time. Additionally, our findings show temporal shifts in the size of the upper societal segment. Based on a review of archeological and paleo-environmental evidence, the temporal change in inequality may be explained by technological progress, climate and population dynamics, trade and social networks, and/or sociopolitical transformations. https://doi.org/10.1057/s41599-024-03053-x OPEN 1Kiel Institute for the World Economy, Kiel 24118, Germany. 2Department of Economics, Kiel University, Kiel 24118, Germany. 3Department History, Leipzig University, Leipzig 04107, Germany. 4CRC 1266 Scales of Transformation, Kiel University, Kiel 24118, Germany. 5Department of Pre- & Protohistory, Kiel University, Kiel 24118, Germany. 6Cluster of Excellence ROOTS, Kiel University, Kiel 24118, Germany. 7 These authors contributed equally: Johannes Marzian, Julian Laabs. ✉email: [email protected] HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x 1 1234567890():,; Introduction For decades, researchers have been trying to learn about the evolution of social inequality in humanity’s deep past. Empirical advances have been made in understanding inequality in modern and preindustrial as well as ancient societies (Alfani, 2021; Milanovic, 2016; Piketty, 2014; Piketty and Saez, 2014; Scheidel, 2017; McGuire, 1983; Bogaard et al., 2019; Borgerhoff Mulder et al., 2009; Fochesato et al., 2019,2021; Kohler et al., 2017; Windler et al., 2013). Especially our knowledge about the development and drivers of ancient inequality has greatly improved in recent years. But, the literature often focusses on explaining inequality in the entire society. To gain a comprehensive understanding of (ancient) inequality, however, it is also crucial to examine inequality within specific societal segments, such as the very rich or very poor. Current research emphasizes the importance of understanding inequality dynamics within so-called “elites,”as intra-elite inequality and conflicts can potentially destabilize entire societies (Turchin, 2023). However, such conflicts and substantial societal changes typically occur only every few decades. Therefore, adopting a long-term perspective and studying social dynamics in ancient societies can provide valuable lessons for the present and future. At this point, we still lack long-run data on inequality within “elites”or, more broadly, within an “upper societal segment.”Furthermore, when studying this segment, we need to look beyond material wealth inequality and explore other types of inequality. The reason is that members of an upper societal segment exert power not only through their material wealth but also through, for example, their social ties and networks. In this paper, we take an initial step in providing long-run evidence from prehistorical Central Europe regarding the development of inequality within an upper societal segment. In particular, we focus our analyses on inequality in relational wealth and changes in the size of the upper societal segment. In this context, we consider the relational wealth of an individual as its endowment with social ties and networks (Borgerhoff Mulder et al., 2009). To study relational wealth inequality among individuals in prehistorical Central Europe, we constructed a dataset of ~5000 single-funeral burial mounds that date back to the first four millennia BCE. Central Europe is archeologically well studied, but a detailed quantitative assessment of inequality in the longue durée is still lacking. The focal point of our inequality analyses is the volumes of the burial mounds, which we employ as proxies for the relational wealth of the buried individuals. We assume that the larger the volume of the burial mound, the greater the individual’s relational wealth. In other words, an individual who possessed a large burial mound had a higher economic and political ability to mobilize people and resources within its (social) network to accomplish specific goals than an individual with a small burial mound. It is important to note that these networks were typically confined to local communities/ societies and did not extend across the entire region of Central Europe. Nonetheless, we assume that the respective communities/societies were economically and socially highly interconnected, forming part of a supra-regional network. This perspective is supported by existing archeological evidence (Parker Pearson, 2003; Kristiansen and Larsson, 2005; Milisauskas, 2011; Kerig and Shennan, 2015; Furholt, 2021). Despite potential variations in social–cultural formations within prehistoric societies, individuals with greater access to resources and networks constitute the upper societal segment. Of course, the proportion of individuals holding higher social status in comparison to the entire population may vary due to differences in social practices. However, as burial mounds were predominantly reserved for those individuals who had a high social status, these data offer us a unique opportunity to analyze inequality between those socially distinguished individuals that formed the upper societal segment of the mentioned supraregional network (Capelle, 2000; Eggert, 1999). To analyze inequality among these individuals, we employ inequality indices such as the Gini index to the data. We interpret the resulting values as measures of inequality among buried individuals’ leverage to make use of their resources and networks. In addition to the burial mound data, we collected information on the number of individuals buried in flat and collective burials. From these data, we can estimate the share of individuals buried in burial mounds over time. This share gives us an idea about how many people were able to express their relational wealth via burial mounds. Or, to put it differently, this share tells us about the size of the upper societal segment. Ouranalysesrevealtwokeyfindings about prehistoric inequality. First, there is a wave-like trend in the share of individuals who had sufficient relational wealth for the construction of a burial mound. This finding indicates a changing size of the upper societal segment in Central Europe over time. Second, the level of inequality in relational wealth between these individuals was high throughout the entire period. However, it was not constant but steadily changed with an increasing trend over time—especially during the last 1200 years BCE. From an archeological perspective, factors that help to rationalize our results are the establishment of new technologies and their social implications (Boserup, 1981; Childe, 1957;O’Brien and Shennan, 2010), improvement or deterioration of weather and climate conditions (Roberts, 1998; Erdkamp and Manning, 2021), changes in the size and composition of the population (Johnson, 1982;Bettencourt et al., 2007; Müller, 2013a; Zimmermann, 2012), the emergence and rearrangements of trade and social networks (Furholt, 2014;Feinman,2017; Kristiansen et al. 2018), and shifts in the sociopolitical structure (Furholt et al., 2020; Kienlin and Zimmermann, 2012). Burial mound volume as a proxy for relational wealth Earth mounds are among the most well-known archeological structures in Europe (Harding, 2000;Johansenetal.,2004; Bourgeois, 2013). They represent a complex social practice involving economic, ideological, and political realities and are considered as the graves of individuals with a distinguished social status (Capelle, 2000; Assmann, 2013; Müller-Scheeßel, 2013; Endrigkeit, 2014; Osborne, 2014;Müller,2018). To assess the social status of a buried individual, we use the volume of its burial mound as a proxy for its relational wealth (Borgerhoff Mulder et al., 2009; Beck and Quinn, 2023). The relational wealth of an individual represents its economic and political ability to mobilize people and resources in its (social) network to achieve certain goals. Since the buried individual is dead at the time when the burial mound is erected, we consider the erection as a posthumous form of its relational wealth. Furthermore, studies on ethnoarcheological documented communities show that constructing a monument often involves a larger kinship group that extends beyond the individual household (Jeunesse, 2018;Miller,2021; Wunderlich et al., 2021). In this context, the construction of a burial mound can also be understood as a social signal symbolizing a long-term investment of the deceased and the associated group (Bliege Bird and Smith, 2005; Quinn, 2019). Hence, burial mounds ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x 2HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x demonstrated the economic and political ability of the individual and group to compete and collaborate with other individuals and groups in the local and regional network (Parker Pearson, 2003; Leach, 1979). In our analyses, we only use burial mounds dedicated to a single individual. Therefore, it is possible to interpret the construction of a burial mound as directly related to an individual’s relational wealth. Hence, the larger the burial mound, the wealthier, more powerful, and the better integrated the buried individual into local and regional networks. Furthermore, we use a burial mound’s volume instead of its floor area to measure relational wealth. The reasoning is as follows: If we assume that the effort required to build a burial mound is proportional to its floor area, this will mean that a burial mound with a large floor area would have the same height as one with a small floor area. Given the observed shapes of burial mounds, this relationship does not seem reasonable. Since we cannot observe the volume of each burial mound in the dataset, we make archeologically reasonable assumptions about a burial mound’s shape to compute the respective volumes. We explain the computation procedure in the methods section in more detail. Measuring prehistoric inequality with burial mound data To construct our dataset, we collected information on the size of burial mounds from extensive archeological catalogs. Our dataset provides information on 4986 burial mounds in Central Europe. It covers the first four millennia BCE and includes burial mounds from the Neolithic up until the appearance of the Romans in Central Europe. Additionally, we collected data on the prevalence of individuals buried in flat and collective burials. In our analysis, we measure inequality in relational wealth between individuals in the entire geographic area of Central Europe, which yields the most time-granular perspective. Although our dataset’s spatial granularity allows for subregional analyses, we leave them for future research. Such analyses require a thorough discussion of the regional archeological background, which is beyond the scope of this article. SI, Sections 1 and 2 display all variables included in our dataset and the additional data, along with a concise description of their meaning. The references of the primary archeological catalogs from which we compiled the data are available in SI, Section 8. Given that the dating intervals of the burial mounds vary between 10 and 4700 years, we decided to limit our analysis to burial mounds with a maximum dating interval of 600 years. This restriction reduces the size of our dataset, but it ensures more precise results. Nonetheless, it is worth noting that limits beyond 600 years do not significantly alter our findings (see SI, Section 7). Hence, our results are mainly driven by the welldated burial mounds. Finally, we split our observation period into intervals of 200 years and assign each burial mound to one of the intervals according to the average of the initial and final value of its dating interval. The choice of 250and 300-year intervals, again, does not substantially alter the results (see SI, Sections 5 and 6). Figure 1displays maps with the spatial location of the burial mound sites in each 200-year interval. To avoid confusion about small sample sizes, we note that some sites consist of multiple burial mounds. However, for the intervals 0–200 BCE, 2800–3000 BCE, and 3000–3200 BCE, the number of burial mounds is too low for a credible analysis (see SI, Section 4). Although the burial mound sites are spatially dispersed within the 200 intervals, we consider the entire study region to be characterized by high economic and social connectivity (Parker Pearson, 2003; Kristiansen and Larsson, 2005; Milisauskas, 2011; Kerig and Shennan, 2015; Furholt, 2021). Furthermore, we view the communities within this region as parts of a supra-regional network that spans across Central Europe. To assess the degree of inequality in relational wealth between the individuals of the upper societal segment of the supraregional network, we use the Gini index and indices from the class of Generalized Entropy Measures (Kohler et al., 2017; Windler et al., 2013; Cowell, 2000). 1 It is important to emphasize that the estimates obtained for the indices are subject to statistical uncertainty. A typical method to calculate the standard error of an index is the use of asymptotic theory, notably bootstrapping. In the present dataset, however, the summary statistics in SI, Section 4 show that we face “heavy-tailed”distributions, a reason why bootstrapping is not sufficient (Davidson and Flachaire, 2007; Cowell and Flachaire, 2015; Dufour et al., 2019). We, therefore, apply permutation tests to assess the statistical significance of differences between two inequality estimates (Dufour et al., 2019). Methods Computation of a Burial Mound’s Volume from its Ground Area. As argued in the section “Burial Mound Volume as a Proxy for Relational Wealth,”we use a burial mound’s volume instead of its floor area as a proxy for the buried individual’s wealth. Since we cannot observe the volume of each burial mound, we employ a non-linear transformation of its floor area and information about its shape to reconstruct the volume. It is important to mention that the dataset contains burial mounds of five different geometric shapes (viewed from a bird’s eye view): round, round-oval, oval, rectangular, and trapezoid. For the transformation, we summarize the shapes round, round-oval, and oval as “round”and the shapes rectangular and trapezoid as “rectangular.” Starting with round-shaped burial mounds, the procedure is as follows: Let rbe the radius of a circle and a sphere, Abe the area of the circle, and Vbe the volume of the sphere. Then A¼πr2 and V¼4 3πr3 : Supposing that the volume of a round-shaped burial mound can be approximated by the formula of a hemisphere Vround ¼2 3πr3 and that the height of the burial mound is proportional to its radius, then reformulating V round yields: Vround ¼2 3πr3¼2 3 π0:5 π0:5πr3¼2 3π0:5π1:5r3¼2 3π0:5πr2  1:5¼2 3π0:5A 1:5 : Multiplying the volume by an arbitrary constant would not influence the outcomes of the inequality indices in this paper since they all satisfy the scale invariance axiom (Cowell, 2000). Hence, if all round-shaped burial mounds have a hemisphere shape, transforming the floor area of each burial mound by an exponent of 1.5 yields its volume. Concerning rectangular-shaped burial mounds, the procedure is very similar. Let lbe the length of a rectangular, wits width, A its area, and let Vbe the volume of a corresponding cuboid with length l, width w, and height h. Then A¼lw HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x 3 and V¼lwh: Furthermore, suppose that the volume of a cuboid V rec — which corresponds to an area A rec —approximates the volume of a rectangular-shaped burial mound. Also, assuming that the length of this cuboid is proportional to its width l:¼c1w  ,and that the height of the cuboid is proportional to its width (h:=c 2 w), then Arec ¼c1w |{z} l w¼c1w2 and Arec ¼c1w |{z} l wc2w |{z} h Reformulating Vrec yields Vrec ¼c0:5 1 |{z} c0:5 1 c1w |{z} l wc2w |{z} h ¼c1:5 1w3c2 c0:5 1 ¼ðc1w2Þ1:5c2 c0:5 1 ¼A1:5 rec c2 c0:5 1 : Again, multiplying the volume by an arbitrary would not matter for the computation of the inequality indices. Hence, if all rectangular-shaped burial mounds have a cuboid shape, with their length and height proportional to their width, transforming the floor area of each burial mound by an exponent of 1.5 yields its volume as well. Mathematical formulas for the inequality indices and their asymptotic standard errors. The following three expressions present formulas for computing the indices from the class of generalized entropy measures Ic;I0;I1  the Gini index (G), and the normalized Gini index (G*) Cowell (2000). Ic¼1 n 1 cc1ðÞ ∑ n i¼1 xi  x  c1  8c≠0;1 I0¼1 n∑ n i¼1log  x xi  for c¼0 I1¼1 n∑ n i¼1 xi  x  log xi  x  for c¼1 G¼1 2n2 x∑ n i¼1 ∑ n j¼1xixj  G¼n n1G The notation is as follows: ndenotes the number of burial mounds in the sample, iand jspecific burial mounds, x i and x j the volume of burial mounds i,j, xthe arithmetic mean of x, and ca sensitivity parameter. The following expression states the formula for the asymptotic standard error (ASE) that is valid for all indices from the GEM Fig. 1 Spatial distribution of the burial mound sites in each of the 200-year intervals of the analysis. A green dot shows the geographical position of a burial mound site. ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x 4HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x class (Cowell and Flachaire, 2015). ASE Ic ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n2∑ n i¼1Zi Z  2 r Z i denotes a term that differs for particular values of the sensitivity parameter c, and  Zis the average of all Z i . Using the same notations as in the previous formulas, the following three expressions give the respective Z i for different values of c. Zi¼1 c2c xi  x  ccxi  x Icþ1 c2c  8c≠0;1 Zi¼xi  x  log xi  for c¼0 Zi¼xi  x log xi  x  I11  for c¼1 Regarding the normalized Gini index, the subsequent expression displays a formula for its asymptotic standard error (ASE) with the notation being as before (Cowell and Flachaire, 2015). ASE G ðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 n xðÞ 2∑ n i¼1Zi Z  2 s Correspondingly, the next expression defines the formula of the Z i , where xiðÞ denotes the ith element of the ordered sample. The observations in the ordered sample are ranked by ascending magnitude of their burial mound volume. Zi¼Gþ1ðÞxiðÞþ2i1 n  xiðÞ2 n∑ i j¼1xj ðÞ Procedure of performing permutation tests. A primary methodological objective of this paper is to present a suitable tool for testing the statistical significance of a difference in two values of an inequality. In the presence of heavy-tailed distributions, the most appropriate tool for this exercise is permutation tests (Dufour et al., 2019). The theoretical foundations of the permutation test date back to the early 20th century (Pitman, 1937), but the recent work of Dufour et al. (2019) demonstrates their superiority in testing differences in inequality. Therefore, this section aims to provide a step-by-step procedure for conducting permutation tests based on their work. Concerning more detail on the method’s technical foundations, we refer to the respective paper. Suppose there are two populations, Aand B. For example, population Acould be the population of all burial mounds in the Neolithic in Central Europe, while population Bcould be the population of all burial mounds in the Bronze Age in Central Europe. The primary purpose lies in determining if the degree of inequality differs between these two periods. To measure the degree of inequality, we can use an inequality index θ. Hence, the “true”population degree of inequality in the Neolithic is θ A and in the Bronze Age θ B . However, since it is impossible to observe the entire population of burial mounds in each period, we cannot determine θAand θB. Thus, both values are unknown. Therefore, relying on observable sample data, we need to estimate them to get an idea about their values. The vector XA¼xA 1;xA 2; :::; xA m  contains the sample data from the Neolithic, and the vector XB¼ xB 1;xB 2; :::; xB n  the sample data from the Bronze Age. There are m burial mounds in the sample XAand nburial mounds in the sample XB. The elements xA 1;xA 2; :::; xA mare the corresponding volumes of observed burial mounds in the Neolithic, and the elements xB 1;xB 2; :::; xB nare the corresponding volumes of observed burial mounds in the Bronze Age. Ideally, these samples are representative of their respective populations. Using the volumes in each sample, we can compute ^ θAand ^ θB;where ^ θAis the degree of inequality in the sample XAand ^ θBthe degree in sample XB. Both ^ θAand ^ θBare estimates of the true but unknown population degree of inequality. From this perspective, it is evident why statistical uncertainty surrounds the estimates ^ θAand ^ θBand why computing the difference between ^ θAand ^ θBdoes not answer the question if the degree of inequality between the population differs. A more appropriate answer to this question is to perform hypothesis testing using, for example, permutation tests. The most appropriate permutation test for testing differences in inequality proceeds as follows: 1. Set up a pair of hypotheses: H0:θA¼θBvs. H1:θA≠θB. The null hypothesis H0states that employing inequality index θto assess the degree of inequality in population A and B, inequality does not differ between them. In contrast, the alternative hypothesis H 1 states the degree of inequality differs. 2. To test this pair of hypotheses, the permutation test uses the sample data from XAand XB. To guarantee the asympotitc validity of the permutation test, it is necessary to scale the samples XAand XBusing their respective sample means  xA and  xB. Hence, the scaled samples are XA¼xA 1  xA; xA 2  xA; :::; xA m  xA  and XB¼xB 1  xB; xB 2  xB; :::; xB m  xB  . 3. Under H0, it does not matter from which sample the data for computing ^ θAand ^ θBstems. Therefore, the permutation test merges XAand XBto obtain a combined sample XC¼xA 1  xA; xA 2  xA; :::; xA m  xA; xB 1  xB; xB 2  xB; :::; xB m  xB  .XCcontains mþnburial mound volumes. 4. The next exercise is to permute XC:In total, there exist mþn ðÞ !different permutations. 5. The problem is that the larger the sample sizes mand n, the larger the number of possible permutations. Therefore, the permutation test randomly draws Kof these mþnðÞ! permutations without replacement. Hence, including the initially combined data XC, there are Kþ1 permutations available for the analysis. 6. Subsequently, we need to choose a suitable test statistic for testing the difference in the degree of inequality between the two populations. In this case, S¼^ θA^ θB ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ VθA ðÞ þ^ VθB ðÞ pis an appropriate test statistic. ^ VθA and ^ VθB are estimates (asymptotic/bootstrap) of the variance of ^ θAand ^ θB. If the samples are dependent, it is necessary to adjust the denominator by including the covariance of the samples. 7. Using the formula for the test statistic from 6., as well as the data from the original samples XAand XB, the permutation test computes the observed test statistic Sobs. 8. The next step splits each of the Kpermutations into two samples of size mand n. For example, the first mburial mound volumes form the elements for the sample of population A, whereas the remaining nburial mound volumes form the elements for the sample of population B. 9. The computation of the test statistic from 6—using the data from the split samples of the Kpermutations—yields K values of the test statistic. 10. Finally, comparing the values of the Ktest statistics with the initially observed test statistic Sobs yields the permutation test’sp-value. The formula for the p-value is the following: pvalue ¼2 min ∑ K j¼1IS j≤Sobs ðÞ þ1 Kþ1; ∑ K j¼1IS j≥Sobs ðÞ þ1 Kþ1 8 < :9 = ; .Sjis the HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x 5 test statistic’s value corresponding to permutation Kand IðÞ is an indicator function taking on the value 0 if the condition within the brackets is not true and 1 if the condition is true. In addition to the importance of rescaling the samples, there is another condition under which permutation tests are asymptotically valid. This condition holds when the sample sizes are equal, or the underlying distributions have the same asymptotic variance. However, it has been shown that even for very unequal sample sizes and heavy-tailed distributions, permutations tests outperform bootstrap and asymptotic testing procedures (Dufour et al., 2019). It has also been shown that permutation tests are superior to other testing procedures from a size and power perspective (Dufour et al., 2019). Therefore, they are the best option for testing differences in inequality in our dataset. A time-granular perspective on social inequality Figure 2shows the results of the temporally fine-grained analysis of inequality in relational wealth between individuals of the upper societal segment, the sum of buried individuals (individuals buried in burial mounds, flat burials, and collective burial), and the share of individuals buried in burial mounds. Since the results are very similar across the four inequality indices (see SI, Section 4), we discuss our findings considering the Gini index. We use the share of individuals buried in burial mounds to get an idea about the size of the upper societal segment. To calculate this share, we divide the number of single-funeral burial mounds by the sum of individuals buried in collective and flat burials and burial mounds. Studying our results and accompanied archeological evidence, we recognize a repeating, wave-like pattern in the share of individuals buried in burial mounds over time. The pattern consists of two phases. In the initial phase, only a few individuals were buried in burial mounds, whereas in the second phase, many more were buried in burial mounds. In each of the two phases, we observe fluctuations in inequality in relational wealth between the individuals of an upper societal segment that follow an increasing, overarching trend. The pattern emerges first from about 3800 BCE to 3300 BCE and second from 3300 BCE to 2200 BCE. Then, the third and fourth time, it emerged from roughly between 2200 BCE and 1200 BCE and from 1200 to 200 BCE. We rationalize the context of the pattern and its two phases based on the rich corpus of literature on the emergence of (ancient) inequality and social stratification (Borgerhoff Mulder et al., 2009;Kohleretal.,2017; Kienlin and Zimmermann, 2012;Lenski,1966; Price and Feinman, 1995,2010;Stanish,2017;ThomasandMark,2013): The pattern’sfirst phase (1) is characterized by the occurrence of innovations, such as new production techniques and technologies in the form of new tools, metals, or crops. This occurrence often goes along with the emergence of new or shifting overregional trade and exchange networks. Goods being exchanged over such networks are not only commodities and resources but also knowledge. Initially, only a few people take pivotal positions in these networks and make use of the incoming innovations. The management of the flow of information and resources in their network also helps these few people consolidate their social position over time. This setup can then be used to further gain economic and political power. As a result, the relational (and material) wealth of those individuals steadily increases and makes them part of the upper societal segment. Those who have nodal positions in regional and inter-community exchange networks are likely part of a local managerial elite (Stanish, 2017). At the end of phase (1) and during the transition process to phase (2), the innovation becomes established and is more widely used in society; but key network positions are still held by a few individuals. At the start of the pattern’s second phase (2), disruptive events such as migration, cultural transformation, or environmental change trigger a rearrangement of large-scale trade and exchange networks established in phase (1). This rearrangement offers Fig. 2 Development of inequality in relational wealth between the members of the upper societal segment using time intervals of 200 years. The red and black lines connecting inequality estimates and the shares of individuals buried in burial mounds for consecutive time slices are linear interpolations and not actual observations. A “x”on top of each line connecting the inequality estimates indicates if the difference in the estimates between two periods is statistically significant (p-value < 0.1). In contrast, a “o”indicates a statistically insignificant difference (p-value ≥0.1). The numbers on top of the inequality estimates show the sample size. The green bars represent the sum of buried individuals (burial mounds, flat graves, and collective graves) in the respective time intervals captured by our data. The black line displays the share of individuals buried in burial mounds, which gives us an idea about the relative size of the population’s upper societal segment and social mobility and structures. SI, Sections 4 and 7 contain the numerical results for this figure. ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x 6HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x more individuals the opportunity to install their own and more localized networks. These networks are large enough for individuals to accumulate sufficient relational wealth that separates them from individuals from other parts of society. However, there are still individuals who can take pivotal positions in aggregated localized networks. These positions allow them to accumulate a high level of relational wealth. This two-phase pattern repeats with the occurrence of another set of innovations and can be accelerated due to advances in transportation and infrastructure. Over time, the spread of certain innovations raises agricultural productivity, which can increase overall prosperity and might induce changes in population size (Turchin et al., 2022). Throughout these two phases, changes in technology, prosperity, and population size might result in competition between the individuals of the upper societal segment to aspire to more influence. All these changes may alter the pace of interaction within and the density of networks, which lead to increasing, but fluctuating levels of inequality in relational wealth. A comprehensive overview of our proposed patterns is described in the following paragraphs and summarized in Table 1. The trends in network structures shown in Table 1are derived from the modeled size of collectively acting groups (Zimmermann, 2012), the influences of the innovations and transformation triggers listed in Table 1, and the findings of the cited works. The first occurrence of the pattern (P1, 3800–3300 BCE) started with the emergence of new agricultural technologies such as animal traction and the ard around 3800–3400 BCE (Bakker et al., 1999; Whitehouse and Kirleis, 2014). The first phase (Ph 1.1, 3800–3500 BCE) is connected to long and round burial mounds with considerable size differences, which explain the high values of the Gini index. However, the large inequality estimates in the North and Central region of our research area partly contradict our views on the character of these Neolithic societies (Müller, 2001). Instead, they correspond to a higher degree of social stratification and are consistent with the unexpected extent of regional cooperating networks (Sørensen, 2014). In addition to changes in the subsistence economy, there were advances in copper metallurgy, and early copper items became valuable prestige goods (Brozio et al., 2023). The second phase (Ph 1.2) dates between 3500 and 3300 BCE, and due to the low numbers of burial mounds and their decreased differentiation, a low Gini index is measured. A climatic cold event (Bond −5.9 ka climate event), dating around 3500 BCE, probably affected Central European societies as decreases in indicators of human activity show (Kolářet al., 2022; Bond et al., 2001; Heitz et al., 2021; Parkinson et al., 2021). Furthermore, it is reasonable to assume that the technology of the wheel and the increasing use of animal traction in transport and agriculture became established around 3500–3400 BCE (Klimscha, 2017; Table 1 Overview of the occurrences of the proposed patterns with 2 phases and the corresponding size of the upper societal segment (given by the share of individuals buried in burial mounds; black line in Fig. 2), inequality in relational wealth between the individuals of the upper societal segment, network structure, and innovations/triggers that led to transformations in social structures and networks (see the text for more details). Pattern Phase Dating BCE Size in upper societal segment Inequality in upper societal segment Network structure Innovation/triggers P1 Ph 1.1 3800–3500 Medium High More centralized •Animal traction and the ard •Horticulture •Copper metallurgy Ph 1.2 3500–3300 Small Low More localized •Bond −5.9 ka climate event •Agriculture •Wheel and the increasing use of animal traction in transport and agriculture P2 Ph 2.1 3300–2800 No dataaNo dataaMore centralized •Cattle: draft animal, dairy production •Long distance trade peak jade (west)/ copper tools (east) Ph 2.2 2800–2200 Large Medium More localized •New communication networks •Influx of steppe individuals •Gender differentiation P3 Ph 3.1 2200–1600 Small High Centralized •Bond −4.2 ka climate event •Tin bronze technology Ph 3.2 1600–1200 Large Medium More localized •Tin bronze technology generally established •Societal transformation in the EastMediterranean •Changes in long-distance trade networks P4 Ph 4.1 1200–800 Small High More centralized •Collapse of Mediterranean societies •Changes in long-distance trade networks •Millet •Horse and chariot •Ideological changes (cremation as burial rite, bird symbolism) Ph 4.2 800–400 Medium Very high Localized with central hubs •Iron metallurgy •Division of land •Mediterranean networks P5? Ph 5.1? 400–? Small Very high Localized with central hubs •Early monetary economy •Oppida aDue to collective burial tradition, our proxy is not valid here. Based on the increased size differentiation of collective burials, we expect more inequality between burial communities (Müller, 2019; Wunderlich et al., 2019). HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x 7 Mischka, 2022). In contrast to other phases, a collective burial tradition emerged in our research area (northern parts) or burials in general became less visible (central part). Relational wealth, in this phase, was less attached to single individuals as labor investments were mostly assigned to structures of communal character, such as collective megalithic graves. However, it is reasonable to expect communication of economic and relational wealth between communities or extended sociopolitical groups through the erection of collective building endeavors (Gebauer, 2014; Wunderlich, 2019). The megalithic graves between 3500 and 3300 BCE show differentiation in size, respectively, in labor investment, but lower compared to earlier long barrows. Furthermore, there was an increase in the number of burial monuments (Müller, 2019; Wunderlich, 2019). The size of collective acting groups, compared to the preceding phase (Ph 1.1), decreased (Zimmermann, 2012). Especially between 3600 and 3000 BCE, megalithic tombs were built in Northern Central Europe, which were used for collective burials of lineages or other sociopolitical groups (Schulz Paulsson, 2016). This raises the question of whether ideology played a role in the adoption or subsequent abandonment of collective burial practices (Müller, 2010; Brozio et al., 2019). To compute the sum of buried individuals, we assume in average 25–50 burials in one collective burial (Schiesberg, 2012), which led to the high numbers visible in Fig. 2. Given the predominant practice of collective burials in our study area, the initial phase (Ph 2.1, 3300–2800 BCE) of the second instance of the pattern (P2, 3300–2200 BCE) proves difficult to capture with our proxy. In the time intervals from 3200 to 2800 BCE, we only observe 7 burial mounds in our data, which is the reason why we do not compute any inequality index. In phase Ph 2.1, there are mostly collective megalithic graves, but the types of monuments altered from dolmen variations to architectural elaborate passage or gallery graves. The latter ones show higher differentiation in size and labor investment. Also, fewer such monuments were built, and there was an increase in individual flat graves (Müller, 2019; Wunderlich et al., 2019; Wunderlich, 2019). This demonstrates the ability of some communities to acquire more relational wealth than their contemporaries and is similar to the first phase of our pattern. Ph 2.1 is associated with a resurgence of human activity observed in many regions around 3300–3000 BCE (Parkinson et al., 2021; Kolářet al., 2022). During this phase, two contemporary transregional trade networks of prestige goods played a major role in connecting major parts of our research area–jade axes in the Western region of our study area and copper tools in the Eastern region (Klassen, 2004; Pétrequin et al., 2012). In the subsistence economy cattle became important as draft animals as well as for dairy products (Weber et al., 2020; Evershed et al., 2022). In this respect, livestock may have acted as mobile capital. The pattern (P2) continued into the second phase (Ph 2.2., 2800–2200 BCE). The shift from Ph 2.1 to Ph 2.2 is profound, as the building of collective burials was abandoned, and a single burial mound tradition became established (Brozio et al., 2019). In principle, the increase in the size of the upper societal segment could result from the low number of total burials. However, comparing the absolute number of burial mounds between 3800 and 2800 BCE and 2800 to 2200 BCE, the increase in the size of the upper societal segment seems reliable. The period from 2800 BCE onward is closely associated with the subcontinental cultural phenomenon of Corded Ware. The 3rd millennium BCE in Eastern and Central Europe is characterized by the creation of new and changing communication networks, including an influx of individuals from the Central Eurasian steppe (Furholt, 2021; Kristiansen et al., 2017; Papac et al., 2021). The level of inequality between the individuals of the upper societal segment is high but also changed during that period. An interesting observation is the significant decline in the Gini index in 2600–2400 BCE which cannot be directly linked to any major external event (e.g., climate, migration, disease). Nevertheless, the change could relate to the onset of the Bell Beaker phenomena in Central Europe from 2600 BCE onward (Heyd, 2007; Olalde et al., 2018) and a decline in population numbers beginning around 2500 BCE (Müller, 2013b). A further possible indicator for high social differentiation over the considered time frame is the establishment of clear gender differentiation from the beginning of the Final Neolithic (about 2800 BCE), which consolidated during the Bronze Age (Robb and Harris, 2018). The pattern (P3) occurred a third time from 2200 to 1200 BCE, with its first phase (Ph 3.1) from 2200 to 1600 BCE. The Bond −4.2 ka climate event lasting from about 2350–1900 BCE—which is argued to have triggered the collapse of the Akkadian empire (Cookson et al., 2019; Bradley and Bakke, 2019)—did not have a uniform or strongly visible effect in our study area (Kleijne et al., 2020). With the later Early Bronze Age (2000–1600 BCE), tin bronze metallurgy became available in nearly all regions of our study area. However, access to metals, such as copper, tin, and gold, as well as other prestigious objects, was limited (MetznerNebelsick, 2021; Mittnik et al., 2019; Radivojevićet al., 2019). Most of the burial mounds from 2000 to 1800 BCE belong to the so-called “princely”burials of the Únětice groups (2200–1600 BCE) in today’s Eastern Germany (e.g., Helmsdorf) and SouthWest Poland (e.g., Łeki Małe) showing high differentiation between each other. The size of the upper societal segment was small. The world-famous “Sky Disc of Nebra”as well as circular ditch enclosures connected to astronomical observation, hint at the control of knowledge (Meller, 2019). Differentiated house sizes in densely populated but not fortified settlements and fortification features at some settlements support the interpretation of a socially stronger differentiation on community and regional scale (Meller, 2019). The inequality between the individuals of the upper societal segment is substantially higher than in the previous periods. The overall increase of inequality from 2400–2200 BCE to 2000–1800 BCE is significant (p-value =0.002). Moreover, the literature points to a growth in community sizes and population in general (Zimmermann, 2012). In addition to the increasing long-distance trade, which was dominated by the exchange of metals, the amber trade from the Baltic South shaped transregional networks in our research area (Ernée, 2016; Ling et al., 2013). Between 2000 and 1200 BCE, tin bronze became increasingly available, and improvements in bronze metallurgy emerged (Radivojevićet al., 2019; Krause, 2003). These developments led to the establishment and increased use of bronze tools (e.g., sickles) or weapons (e.g., swords) from the Middle Bronze Age onward (Horn and Kristiansen, 2018; Arnoldussen and Steegstra, 2015). With the significant drop in inequality from 2000–1800 BCE to 1800–1600 BCE, the size of the upper societal segment grew larger as the increased number of burial mounds indicated. The second phase (Ph 3.2, 1600–1200 BCE) started with a surge in burial mounds in our dataset that can be connected to the phenomenon of the so-called “Tumulus Culture”(ca. 1600–1300 BCE) and the early Older Nordic Bronze Age (ca. 1750–1500 BCE). This time frame is also characterized by major reorganizations in long-distance trade networks as well as economic and social changes often associated with the end of the Minoan society in the Mediterranean (Harding, 2000; Meller et al., 2013). Furthermore, from 1600 to 1200 BCE, the size of collectively acting groups shrunk, but we generally expect an increasing population size for this phase (Zimmermann, 2012; Müller, 2013b; Nikulka, 2016). Compared to the previous subphase (2200–1800 BCE), inequality between the individuals of the upper societal segment stayed constantly high throughout the ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-024-03053-x 8HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2024) 11:557 | https://doi.org/10.1057/s41599-024-03053-x