Introduction

Providing an explanatory framework for numerous ‘old’ and ‘new’ archaeological issues, complex systems, and complex dynamic behaviour became increasingly prominent talking points in recent archaeological and anthropological discourse. Complexity, as a wider framework, potentially offers the capacity to structure various specified approaches under a more holistic umbrella, a direction which has been demanded by some during the last 20 years (e.g. Bentley & Maschner, 2009; Furholt, 2021; Kristiansen, 2014). Therefore, this framework may prove to be central in the undertaking of integrative efforts between an increasingly specialised and fractured discipline in the future.

Aiming for a snapshot of the most current developments in archaeological complexity studies, we hosted a session entitled ‘Networks of Interaction and Communication: Patterns of Emerging Complexity’ at the Annual Meeting of the European Association of Archaeologists in 2020. Papers in this Special Issue resulting from the session cover a wide variety of issues ranging from data aggregation to developing methods and explaining complex patterns of the past. We hope that the Special Issue will enrich the conceptual scope among readers both familiar and unfamiliar with the field of complexity research.

What is Complexity?

As human beings, we are complex systems living in a world consisting of and surrounded by other complex systems. Complexity is an ongoing story of the organisation of matter. We, as human beings, develop complex cultures and technologies. We interact with other humans as well as forming bonds with our surroundings, objects, and each other. Human lives, lifeways, societies, and ecospheres historically and presently are rooted in relationships of systemic complexity.

Connotations matter. Most commonly ‘complexity’ pertains to social complexity, such as the degrees of hierarchy, inequality, economic power, or social make-up which are discussed in the context of archaeological research (Barton, 2014; cf. Adams, 2001; Carballo et al., 2014; Feinman, 2011), although this does not mean that these two uses are mutually exclusive (e.g. Daems, 2021). However, ‘complexity’ as a term does not exclusively relate to socio-cultural structures, as it tends to go deeper than that. Specifically in complex systems research and adjacent fields, it entails a variety of perspectives on systemic interaction, scalar, causal, and explanatory issues. While the term may seem reasonably straightforward at first, it is defined with quite some variability in the literature (Ladyman et al., 2013). Definitions may range from very sparse ones such as an observance showing ‘structure with variations’ (Goldenfeld and Kadanoff, 1999) to the ones that focus more on the behaviour of systems such as sensitivity to initial conditions, a large number of interacting parts, or multiple pathways along which a system can evolve (Whitesides & Ismagilov, 1999).

Here, we follow the definition of complex systems as ‘systems that cannot be explained by reduction to their component parts’ used by Bentley and Maschner (2003b), which may be extended to one qualifying complex systems as ‘large networks of components with no central control and simple rules of operation giv[ing] rise to complex collective behaviour, sophisticated information processing, and adaptation via learning or evolution’ provided by Mitchell (2009) and cited by Kohler (2012: 93). Both of these definitions capture the essence, i.e. self-evolving behaviour resulting from the interaction of a system’s component parts, which is known for emergent properties or synergy effects (i.e. an overall effect is greater than a sum of parts). The interaction of component parts in complex systems is non-linear, which means that the output is not necessarily proportional to the input (cf. a linear relationship obligatorily presumes an output proportional to the input). The output could be disproportionately large or there could be no effect on output at all. These properties put significant limits on the predictability of complex systems’ behaviour. More specifically, an earlier state may lead to multiple later states, each of which is possible to occur. In this sense complex behaviour is unpredictable.

As can be seen by these various understandings, ‘complexity’ is not quite as straightforward as one would surmise. However, what most understandings and definitions have in common is an epistemological component relating to predictability, contingency, and a full understanding of causal as well as constitutional trajectories (regarding constitutional trajectories, see Sartenaer, 2015). A good way to approach what complexity means in a more general sense is to confront it with complication (cf. Garnsey & McGlade, 2006). A complicated system for example can be defined as a system that has many interacting component parts but is generally understandable through full but also partial knowledge of the entities involved in its function. An illustrative example could be an aeroplane (without pilots), which is conceptually easy to define—a thing that flies—as well as systemically closed, as it consists of specific parts that enable it to function. In Arthur’s (2009) terms, an aeroplane is a complex technology because its component parts are also technologies. However, it represents a complicated system because the output may be derived from the input. Despite consisting of thousands of components, even a layperson could explain how it works, merely through knowledge gained from high-school physics class, namely the effect of aerodynamic lift, facilitated by the shape of its wings in combination with forward propulsion in air. Of course, aeroplane experts can trace every single interaction of every single component part within the system ‘aeroplane’ and can consequently provide a much more elaborate explanation, yet even partial knowledge of structure is enough to grasp the general function of an aeroplane.

On the other side, a complex system harbours certain characteristics which escape full epistemological access. An example of such a system—to stay within the realm of aviation—could be seen, not in the plane itself, but in the engineering department(s) which are involved in designing it. The reason for that lies within at least two aspects. These are as follows: First, an engineering department involves humans as interacting agents. Humans, through their capacity to make choices, which for example are informed by certain aesthetic, economic, or scientific demands, tend to introduce contingency to the systems they are embedded in, particularly social systems. While certain processes can show some regularities within these systems, for example, design decisions dictated by official regulations or simply physics, others are informed by influences from outside of the observed department. Things such as aesthetics, the placement of windows and seats, or the design of reading lamps—while not necessarily important for the functioning of the plane itself—are influenced by larger societal features such as aesthetic conventions at the time of design, the location of the department or even popular culture, and cannot be fully known through the observation of the outcome. We simply lack the epistemological access to the individual trajectories that caused these decisions, as we are most likely dealing with a team of different engineers interacting, producing a variety of possible outcomes, and we also cannot look into the minds of individuals.

Second, processes important to engineering an aeroplane that involve technological invention and innovation show certain characteristics of path dependency as well as emergence (Arthur, 2009; Roux, 2013; Solée et al., 2013). This means that such processes are on the one hand dependent on their historical trajectories, and on the other cannot be predicted from a current state (Shanahan, 2005).

As has been mentioned before, a key characteristic of complex systems is emergence. Originally, the term was coined conceptually by philosophers like John Stuart Mill and rose to new importance among the so-called British Emergentists of the early twentieth century before phasing out of discourse for a while (McLaughlin, 2008; Parravicini, 2019). Eventually, it reappeared in the context of complexity research. While the philosophical discussion of what it entails exactly is still ongoing and far from settled (cf. Parravicini, 2019), a pragmatic choice would be to adopt an epistemological variant that entails the production of system states which are unpredictable through the observation of prior states, yet are causally determined (at least in part) by processes rooted in these prior states. Emergence, therefore, represents precisely the element of limited epistemological access that renders systems complex rather than just complicated. In that sense, the concept of ‘aeroplane’ represents a stage in the evolution of a complex technology (Arthur, 2009), emerging from countless systemic interactions between engineers, the economy, material sciences, or even popular culture instilling ideas. All these interactions are enmeshed within complex systemic relationships, while the actual ‘aeroplane’ that gets built and used remains merely complicated. Of course, this does not mean that complex processes are completely unknowable as, even though they may not be predictable from one level of observation, they may show regularities and patterns on a higher one.

In consequence, the challenge that presents itself to the observer of a complex system is one of causality: when and why are regularities reached? The point of this example is to demonstrate the epistemological limitations introduced through complexity, which manifest in the hard-to-answer question of coeval explicability of individual behaviours, large-scale patterns, and historical trajectories within complex systems, as it will not be possible to locate singular drivers providing clear causal explanations.

Complexity in Archaeology: Applications

Bentley and Maschner (2003b, 2009) and Kohler (2012) describe the introduction of complexity to archaeology and an intensively growing interest in it in the 1990–2000s. Although their papers are worth reading in full, we offer some brief comments on their observations below.

Early forays into the behaviour of complex systems in archaeology are associated with the studies of processual archaeologists in the 1960–1970s, including the work of Clarke (1972), Flannery (1968, 1972), and Renfrew (1978). However, applications often dealing with complex, non-equilibrium systems should be demarcated from the system approaches of many other ‘new’ archaeologists, which were grounded on the general systems theory favouring equilibrium models (Bentley & Maschner, 2003a, 2009; Kohler, 2012). It is worth mentioning that several remarkable studies of the 1970–1980s gained the interest they deserved with a significant delay from publication. These may be exemplified by Justeson’s (1973) introduction of Shannon’s (1948) information-theoretic approach (for recent consideration, see Nolan, 2020; Paige & Perreault, 2023) or Zubrow’s (1985) introduction of fractals to archaeology (see Brown et al., 2005). The same holds for explicit forays into complexity research—specifically in nonlinear dynamics applied to archaeological data (e.g. McGlade & Allen, 1986; Van der Leeuw, 1982). Perhaps, the discipline was not yet ‘prepared enough’ for implementing a complexity framework.

‘Being prepared’ is, in a sense, fitting the Goldilocks principle presuming that out of the great range of possible conditions, the actual conditions are all ‘just right’ (Rees, 2000; and this principle is also something to be considered when dealing with the emergent phenomena). By the early 1990s, postprocessual critiques revealed significant issues in the system thinking of the 1960–1970s (e.g. Hodder, 1985). Chaos, a ‘predecessor’ of complex systems in terms of research history, and complex dynamic systems are being intensively studied in other fields and explained to a wide audience by non-fiction books (e.g. Bak, 1996; Gleick, 1987; Strogatz, 2003). It is notable that Chaos. Making a New Science by Gleick (1987) became a national bestseller in the USA and achieved several awards. Archaeology was increasingly equipped with the necessary tools due to the increasing availability and speed of computers, the development of object-oriented programming languages and platforms for agent-based modelling (Kohler, 2012), and many datasets comprising categorised and chronologically sequenced evidence were available.

Lorenz’s (1963) work on weather forecasts, iterations of a discrete version of the logistic population growth model by May (1976), and studies of turbulence by Feigenbaum (1978, 1979) revealed chaos as a sensitive dependence on initial conditions. The latter definition describes the significant effect of small changes in an earlier state on the behaviour of deterministic systems in their later state. The aforementioned and other studies have shown that complex behaviour may partially arise in systems described by simple equations. Also, such systems are not necessarily characterised by a significant diversity or number of components, while random events matter. To bring this to archaeology, let us take the example of Neiman’s (1995) neutral model of cultural evolution presuming that cultural traits are copied relatively proportional to their frequencies in assemblages. Cultural drift and neutral innovation are considered drivers of evolution. Even given the values of population size and innovation rate being equal, realisations of the assemblage composition over time differ as the result of random events (Neiman, 1995: 12–14, Fig. 2).

Chaotic behaviour generally arises from one or a few variables. Complex systems possess many degrees of freedom including the variables whose values are hard to estimate. Intensive conceptualization of complexity and the analysis of archaeological data in this framework were manifested by edited volumes and chapters contributing to the general reviews of archaeological method and theory with complex systems behaviour since the 1990s (e.g. Beekman & Baden, 2005; Bentley & Maschner, 2003a, 2009; Kohler, 2012). It is worth mentioning the volume edited by Bentley and Maschner (2003a) which collects a variety of empirical and theoretical approaches to complex systems in archaeological contexts. The studies in this volume range from mathematically informed modelling of social inequality (Bentley, 2003), applications in chronological sequencing (Bronk Ramsey, 2003), and the assessment of wide-spanning eco-cultural landscapes (Bogucki, 2003) to practise-based theory (Layton, 2003) and general methodology (McGlade, 2003).

Even though the term ‘complexity’ often does not appear in evolutionary (Darwinian) archaeology, various aspects of cultural evolution (in its wide sense) are the primary topics being explored within the complexity framework (e.g. Boyd & Richerson, 1985, 2005; Cavalli-Sforza & Feldman, 1981; Creanza et al., 2017; O’Brien & Shennan, 2010; Prentiss, 2019; Richerson & Christiansen, 2013; Roberts & Vander Linden, 2011; Shennan, 2002, Shennan, 2009). The evolution of human beings at its broadest scale represents a complex interplay between genetic, cultural, and ecological factors (for a review, see O’Brien & Lala, 2023). Among the most recent examples, this may be illustrated by the evolution of milk consumption as a mutual influence between spatio-chronologically varied spread of dairying impacting Neolithic lifeways, the evolution of lactose persistence, and an increased pathogen exposure (Evershed et al., 2022).

Mesoudi (2011, 2-3) defines culture as "information that is acquired from other individuals via social transmission mechanisms such as imitation, teaching, or language". This broad definition reveals the key similarities and differences between biological and cultural evolution. Unlike biological species, cultural traits do not reproduce themselves but are replicated by people. Different transmission modes and biases account for various choices and behavioural differences occurring in interactions between individuals and their groups. As an example, cultural evolution involving both gradual and punctuated change may be modelled from individual choices. These choices range in the continuum between rational (informed) decision-making, learning from experts, random or biased copying from others, and uninformed individual decision-making (e.g. O’Brien et al., 2019 and references therein; Vidiella et al., 2022).

In contrast to living organisms, innovation within cultural traits, especially traits of a sophisticated structure, often results from the recombination of component parts. The idea of recombination as a source of innovation is well-developed in technology science and widely used in archaeological research (Arthur, 2009; see the references in Diachenko et al., 2023; O’Brien & Lala, 2023). Technological solutions resulting in complex technologies require further solutions, which frame the self-evolving nature of technology in its broad sense (Arthur, 2009).

The cumulative outcome of cultural transmission results in assemblage diversities, which are often investigated with the application of information-theoretic approaches (however, in this case, the meaning of ‘information’ significantly differs from Mesoudi’s definition provided above: for the extended details, see Gheorghiade et al., 2023). Major trends in studying archaeological diversity are captured by the volumes edited by Leonard & Jones (1989) and Eren & Buchanan (2022). Information-theoretic approaches are capable of simultaneously identifying patterns occurring at different scales and, therefore, questioning complex behaviours behind these patterns.

Recent observations on the demographic trends in prehistory revealed rise-and-falls (or booms and busts) in population size and density. The ‘mechanics’ producing these patterns remain debated (see the references in Kondor et al., 2023). In some cases, including the LBK in West-Central Europe, social dynamics approximated with the application of Shannon (1948) entropy to pottery decoration motives nearly correspond to the boom and bust in population size (Gronenborn et al., 2014, 2017, 2020). Along with the outcomes of other studies, these observations reveal that population size and structure should not be seen as a ‘box’ containing socio-cultural patterns but as an ‘environment’ framing those (e.g. Deffner et al., 2022; Henrich, 2004; Lipo et al., 2021; Powell et al., 2009; Premo, 2016). For instance, we could observe the emergence of complex behaviour from the interaction of small hunter-gatherer groups (e.g. Boyd & Richerson, 2022) or pre-Hispanic Mesoamerican households (e.g. Feinman et al., 2022). An inverse effect is also notable. Cultural innovations may result in population increase (Richerson et al., 2009).

The effect of population size and structure is also well illustrated by the phenomenon of the ‘innovativeness’ of modern towns/cities. A city represents an open system, which cannot be explained in isolation: it is dependent on goods, information, people, etc. flowing into and out of it, as well as policy-making like zoning decisions, so it is hard to grasp factors outside of the observed window. Simultaneously, it is organised in multiple layers and composed of other, often complex, sub-systems, the most well-known to us being ourselves—human beings (e.g. Ortman et al., 2020). Human social systems are always complex. They form intricate connections on multiple levels of organisation, which are hard to predict through the isolated observation of singular-acting subjects. Individuals take action based on a vast set of capabilities, constraints, and motivations which in the big picture introduce contingency to the system ‘city’ at large. As shown by Bettencourt et al. (2007), a metropolis with a population 50 times exceeding the population of a town is 130 times more innovative than the latter. ‘Innovativeness’ is, therefore, an emergent outcome of interactions described with super-linear scaling (Johnson, 2010). The higher population size and density generally presume a higher number of interactions. The outcomes of interactions are not predictable or at least limitedly predictable in the sense of possible system states as emergent patterns (e.g. Sindbæk, 2022). Therefore, the increase in population size and density presumes an increase in the variability of social organisation (e.g. Feinman, 2013). Comparative analysis of archaeological and modern city/town scaling may be, among the other studies, addressed via the papers resulting from the Social Reactor Project (see the project’s bibliography and related papers at: https://www.colorado.edu/socialreactors/publications).

Scaling relationships also characterise fractals, irregular forms resulting from complex processes. The fractal dimension may be used as a direct measure of complexity. Mathematically defined as the ‘set[s] for which the Hausdorff dimension strictly exceeds the topological dimension’ (Mandelbrot, 1983: 15), fractals are usually introduced to archaeology via their properties. These are scale-invariance and self-similarity in case of identical replication at any scale or self-affinity in case of invariance in changes in size or invariance in more than one scaling factor (Mandelbrot, 1983). Case studies and potential applications may be found in the review by Brown and co-authors (2005) and Bruvoll’s (2023) paper in this Special Issue.

Intensively developing approaches to archaeological complex systems include, but are not limited to, network analysis and agent-based modelling which are only briefly brushed upon in our introduction. Network analysis is an obvious approach to the underlying structure of complex systems (for the statistical properties of complex networks, see Albert & Barabasi, 2002). A network (a graph) is composed of a set of nodes (vertices) connected with edges (links). Nodes may represent archaeological sites or features within sites. Interactions (i.e. edges) may be simulated (for instance, by applying a random graph) or approximated from evidence, such as imports and imitations etc. (e.g. Brughmans, 2010, 2013; Knappet, 2011). Agent-based modelling comprises the simulation of interactions between autonomous entities (e.g. Costopoulos & Lake, 2010; Kohler & Vander Leeuw, 2007; Wurzer et al., 2015). Results may be interpreted as a possibility to gauge behavioural patterns under different controlled circumstances.

Two decades ago, Bentley and Maschner pointed out that ‘complexity theory’ is ‘not a theory so much as an approach to systems’ (2003b: 1). ‘Complexity’ in archaeology remains rather ‘complexity-thinking’ in the present day. The very short list of applications discussed above identifies extremely fruitful results and significant explanatory potential of complex systems analysis applied to various topics within our discipline. But what about challenges? The major questions are as follows: (1) To what extent may the often sophisticated mathematical approaches be applied to the archaeological record, which is statistically weak in the majority of cases? (2) What chronological data resolutions should be considered? (3) And how do we statistically ‘filter’ our evidence? These questions are not new to the discipline, and they were recently raised again by Perreault (2019) in close relationship to the topics discussed above. Perreault suggests refocusing from a micro- to a macro-archaeological perspective, accumulation and analysis of big data, and matching complexity to data dimensionality through the analysis of long-term patterns (Perreault, 2019: 39, 191–193).

Contributions to this Special Issue

The papers in this Special Issue comprise a set of diverse approaches to archaeological complexity. Let us briefly introduce the contributions.

O’Brien and Lala (2023) address the concept of evolvability from an archaeological perspective. They define evolvability as the ability of an organism to evolve not only based on genetic but also all other heritable variations, including cultural traits. By exploring multiple different aspects of evolvability within the cultural and generally extragenetic realm such as niche construction, modularity, plasticity, and developmental bias, the authors argue for the importance of culture as a mechanism underpinning the evolvability of humans in particular. Through their elaborate discussion of the concept of evolvability, O’Brien and Lala demonstrate the inherently complex and emergent nature of the processes involved, occurring at different rates at different levels of strength, depending on what particular cultural expression is observed. They conclude by emphasising that not only organisms but also their ability and capacity to evolve are evolving.

Gheorghiade et al. (2023) discuss an information-theoretic approach to archaeological data that they label as ‘entropology’ (combining ‘anthropology’ and ‘entropy’, a measure of a system’s uncertainty). ‘Entropology’ circumscribes a research framework involving the analysis of samples with statistically questionable representativeness and non-self-explanatory patterns as outcomes. This is exemplified by a case study on pottery shapes from Bronze Age Crete. The paper primarily focuses on the issues of data aggregation and diversity estimations. In respect of the latter, the authors build upon recent advances in ecological diversity studies, shifting the estimations from diversity indexes to diversity (e.g. Jost, 2006, 2007; Chao et al., 2012, 2014). Methodological solutions and questions regarding the understanding of diversity studies in archaeology are in line with the papers comprising a volume edited by Eren &  Buchanan, 2022).

Bruvoll (2023) takes on another aspect touching complexity in archaeology that situates itself in the realm of fractal analysis. Based on the premise that fractal patterns, and in Bruvoll’s case fractal patterns in settlement plans, rarely are the result of a top-down planning process and show a rather emergent character. The author proposes the application of fractal analysis involving lacunarity (patterns in the distribution of gaps between component parts) to approach the question of construction autonomy, which in turn could indicate certain structural aspects of social life. As exemplary cases, a set of sampled settlement plans from two prehistoric regions of central and eastern Europe are investigated: Linear-Pottery settlements in the Žitava valley in southwestern Slovakia as well as Trypillia (Tripolye) settlements in central Ukraine. Bruvoll’s novel approach shows how variables of settlement layout, size, density, and house-size distribution as well as random spatial noise influence the estimation of fractal dimension and lacunarity. This study represents an exciting and important step towards the development of a new area of quantitative applications in archaeology.

One of the USSR-time jokes states that whatever you are trying to make by bringing together components and following the instructions from a Soviet factory, the result will be a ‘Kalashnikov’ anyway. Independently achieved similar or identical traits are identified in the evolution of technologies, especially when dealing with more simple devices (Roux, 2010; Shennan, 2013). The limited availability of component parts in a culture (in its narrow sense) and the limited possibility to connect various variations of component parts result in convergence (Charbonneau, 2016, O’Brien et al., 2018). Diachenko et al. (2023) link the likelihood of independent inventions to technological complexity estimated with the application of an information-theoretic approach (for the review of alternative approaches to technological complexity, see Paige & Perreault, 2022). The authors also introduce a ‘technological significance’ factor, explaining why particular modifications of technologies are more likely to occur independently and how the connectivity of parts contributes to the technology’s internal diversity. Outcomes of a case study on pottery kilns lead to a broader conclusion regarding a significant underestimation of convergent evolution in current research on prehistory.

Lastly, Jiménez-Puerto & Bernabeu Aubán (2023) bring together social network analysis and the adaptive cycles concept from resilience theory (Holling & Gunderson, 2002). Adaptive cycles are widely applicable to describe patterns of change in complex systems. Each cycle is composed of four phases: rapid growth, conservation, release, and renewal (e.g. Zimmermann, 2012). In their case study, Jiménez-Puerto and Bernabeu-Aubán use pottery styles as a proxy for interactions between the Bell Beaker groups in the Iberian Peninsula. Their analysis found that phases of an adaptive cycle correlate with the transformation in networks of interactions. These transformations are discussed in a wider framework of demographic change and socio-climate relationships.

Concluding Remarks

The papers in this Special Issue demonstrate wide horizons of complexity research in archaeology interlinking small-scale individual actions and large-scale system behaviour. The exploration of complex systems advances the discipline by incorporating and developing new analytical tools and approaches to data management. It is worth mentioning that the complexity framework largely involves quantitative approaches which derive at least some qualitative properties of systems from mathematical functions and numerical values describing these systems. However, archaeological perspectives from the humanities have been largely overlooked so far. In that regard, complexity-informed archaeological theory may aid in the development of qualitative approaches as well (e.g. Schlicht, 2023). A few decades ago, our discipline learned a lesson from chaos theory which emphasises the importance of random events. Current conceptualisations of archaeological perspectives on the past would benefit from a more intensive consideration of self-development, emergence, scale-dependent, or scale-free patterning, as well as other properties of complex systems. We hope to encourage readers of this Special Issue to engage with and consider working towards complexity-informed research.