A Multilevel Spiral model of

Sociocultural Evolution:

Polities and Interpolity Systems

Hiroko Inoue and Christopher Chase-Dunn

Institute for Research on World-Systems, University of California Riverside

Image result for spiral


Draft V. 8-9-2019, 13856 words.  To be presented on the regular session on Theorizing Social Change at the annual meeting of the American Sociological Association

Tuesday, August 13, 2:30 to 4:10 PM, Sheraton New York, Third Floor, Liberty 4. This is IROWS Working Paper #126 available at http://irows.ucr.edu/papers/irows126/irows126.htm

 Abstract: The comparative world-systems theoretical research program employs anthropological and biological frameworks of comparison to comprehend the evolution of geopolitics and economic institutions.  This paper outlines a revised formulation of the iteration model proposed by Chase-Dunn and Hall (1997: Chapter 6) to explain the emergence and continued increase in sociocultural complexity in prehistoric and historical world-systems. We reformulate the iteration model as an explicitly multilevel model that shows the causal connections among processes operating within polities and those that operate between polities. For the within-polity part of the model we begin with the structural demographic theory proposed by Jack Goldstone, Peter Turchin and their colleagues. We include the role of social movements in the “secular cycle” of rise and fall within polities. For the world-system level of analysis part of our multilevel model we include the variables from the original iteration model and we add non-core development, trade relations and world revolutions in which social movements in different parts of the interpolity system cluster together in time to produce consequences for the both the polities and for the whole system.  We discuss our preliminary approach to two-level simulation modeling.

The world-system perspective emerged in the context of the world revolution of 1968 with a focus on the structural nature of global stratification – now called global north/south relations. Because it emerged mainly from sociology and radical economics it was somewhat immune to the tectonic debates between the realists and the liberals in international relations. But there has been considerable overlap with some international relations schools, especially the long cycle empirical theory developed by George Modelski and William R. Thompson (Modelski 1987; Modelski and Thompson 1988;1996). Despite different conceptual terminologies, these approaches have had much in common, and both became interested in questions of long-term sociocultural evolution.  Modelski and Thompson study “power cycles” by which they mean what world-system scholars have called the hegemonic sequence - the rise and fall of hegemonic core powers, which Modelski and Thompson call “system leaders.” One important difference is with regard to the attention paid to the non-core. Like most international relations theorists, Modelski and Thompson focused most of their attention on the “great powers” in the interstate system – what world-system scholars call the core (but see Thompson and Modelski 1998; Reuveny and Thompson 2007). The world-systems scholars see the whole system, including the periphery and semiperiphery, as an interdependent and hierarchical whole in which power differences and economic differences are reproduced by the normal operations of the system. The core/periphery hierarchy is a fundamental theoretical construct for the world-system theory.

Economic Cycles in Smaller World-Systems

Modelski and Thompson (1996) also incorporate Kontratiev waves[1] into their power cycle model, asserting that each power cycle contains two Kondratiev waves. They have claimed that something like Kondratiev waves already existed in Sung dynasty China. This raises the issue of the possible existence of economic cycles in small and middle-sized world-systems. Chase-Dunn and Mann (1998) noticed the existence of long-term cycles of the growth and decline of trade networks in precontact Northern California based on archaeological evidence.  Chase-Dunn and Hall termed these to be oscillations. Trade networks got larger and then declined and then a new trade network with somewhat different but overlapping spatial boundaries emerged. The archaeological evidence is clear about the spatial extent of these networks based on the known location of diagnostic trade items like certain kinds of shell beads. But the archaeological evidence only roughly indicates how much trade there was and how this might be growing or declining over time.  So it shows extent but not changes in intensity.

Discussions of the most recent Kondratiev wave disagree with respect to the recovery that should have begun in the 1990s. Grinen, Korotayev and Tausch (2016) contend the upturn in GDP growth was mostly due to the rise of China and India. Paul Mason (2015) contends that there was no upturn in productivity, and so no K-wave recovery. He contends that the neoliberal globalization project was able to prevent the class struggle that would have incentivized new investments in labor saving technology by capital flight from the core to the non-core. This deindustrialization of the core and industrialization of the non-core greatly expanded the global work force available to capital and reduced the incentive to invest in labor-saving technology that would have enabled a K-wave recovery. 

            International relations theory is about the logic of power that exists in networks of competing and allying polities. It has been developed mostly by observing, and trying to explain, what happened in the European state system since the treaty of Westphalia in 1648, but a similar logic was probably operating in earlier interpolity systems (Wohlforth et al 2007). The comparative world-systems theoretical research program has been developed to comprehend and explain sociocultural evolution as it has occurred in an anthropological comparative framework – by considering prehistoric small-scale foraging human polities and interacting systems of those polities since the Stone Age (Chase-Dunn and Mann 1998).  We review some of the basic concepts of the world-systems empirical theory and briefly report some of the research that has been done to test some of the propositions that stem from it.

Image result for leafcutter ants            Territoriality is a feature of interaction among microorganisms, insects, plants and animals. A complete grasp of the roots of human imperialism would need to take this larger biogeographical context into account. Organized warfare and competition for territory first emerged about 50 million years ago among social insects, especially ants. In an early version of imperialism some ants kill the queen in an invaded colony and substitute their queen for the dispatched old queen and thus harness the labor of the invaded colony for raising and feeding the offspring of the invaders. The ant/human comparison reveals a fascinating case of parallel evolution in which rather similar behaviours and social structures emerged by very different processes of selection--Darwinian in the case of insects, cultural in the case of humans (Gowdy and Krall 2015; Turner and Machalek 2017: Chapter 15). Ants forge strong cooperation based on so-called genetic eusociality.  Most of the workers in a colony are closely genetically related because they are the offspring of a single queen. This produces a superorganism at the level of the colony and so it is colonies rather than individuals or small groups that compete with one another for territory and resources. The social insects prove that even Darwinian natural selection operating in the absence of culture and in the presence of only simple communication techniques and relatively simple nervous systems in individuals can produce complex social structures when group selection is operating. This is the important thing about the emergence of warfare among colonies of social insects. Gowdy and Krall (2015) stress the importance of collective food gathering, but it is the interaction of resource acquisition and competition for territory that drives the emergence of complex social structures among insects. These same mechanisms turn-out to be important for driving the emergence of complex social structures among humans, though the process is speeded up by the rise of culture and complex cognition.

Leafcutter Ants

Human cooperation beyond the level of the family is based on shared ideology and institutional mechanisms that facilitate integrated action.  It is the evolution of institutional mechanisms such as states and markets that have made it possible for large groups of humans to cooperate with one another. Competition for resources occurs simultaneously at several different levels –between individuals, families, organizations and polities. Warfare among polities has been an important selection mechanism driving sociocultural and human biological evolution since the Stone Age. And geographical variation has been, and still is, an important context and cause of geopolitical evolution (Bergesen 2018).

Regarding theory construction we follow the cumulative theory and testing approach embodied in Imre Lakatos’s (1978) schema of theoretical research programs. Theories should be explicitly and clearly formulated regarding the meanings of concepts and interrelated causal propositions. Formalization can be axiomatic or can be simulation models. We favor the latter (see Fletcher et al 2011).  Different formalized models can be compared regarding their simulation outcomes and parts of these can be empirically tested. Our theoretical research program is still under construction, but we can report some of the results so far.


The World-System Perspective

The world-system approach is less functionalist and more critical of power than most international relations theories. This is due to its origins during the world revolution of 1968 and the anti-Vietnam war movement, but it may also stem from greater attention to those who live at the bottom of the system (the non-core).  World-systemists describe and analyze the rising predominance of capitalism. They employ ideas from Karl Marx and Max Weber to produce a critical prehension of world historical social change.  The main builders of the world-system approach in the 1970s were Immanuel Wallerstein, Terence Hopkins, Samir Amin, Andre Gunder Frank and Giovanni Arrighi.   

            Terence Hopkins and Immanuel Wallerstein (1979) described the cyclical rhythms and secular trends of the capitalist world-economy as a stable systemic logic that expanded and deepened from its start to its end, but that did not much change its basic nature over time. Giovanni Arrighi (1994) described overlapping systemic cycles of accumulation in which rising and falling hegemons expanded and deepened the commodification of the whole system. His modern world-system oscillated between more corporatist and more market-organized forms of political structure, while the extent of commodification deepened in each round (Arrighi 2006). He built on Wallerstein’s focus on hegemony as based on comparative advantages in profitable types of production (Wallerstein 1984, 2004). And he utilized Wallerstein’s idea that each hegemon goes through stages in which its comparative advantage is first based on the production of consumer goods, and then capital goods and then finance capital (see also Arrighi and Silver 1999; Arrighi 2008).  Arrighi was also inspired by the work of Fernand Braudel to focus special attention on the changes in the relationships between finance capital and state power that occurred as the modern world-system evolved.  For both Wallerstein and Arrighi the hegemon occupies the top end of a global hierarchy that constitutes the modern core/periphery division of labor. Hegemonies have been unstable and have devolved into hegemonic rivalry as comparative advantages diffused and the hegemon failed to stay ahead in the development and implementation of new lead technologies. Arrighi’s formulation allowed for greater evolutionary changes as the modern system expanded and deepened while the Wallerstein/Hopkins formulation depicts a single continuous underlying logic that does not change much except at the beginning and at the end of the historical system.

As we have mentioned above, the world-system scholars study the dialectical and dynamic interaction between the core, the semiperiphery and the periphery and how these interactions are important for the reproduction of the core/periphery hierarchy and how they affect the outcomes of struggles for hegemony (Boswell and Chase-Dunn 2000). The hegemon and the other great powers are the top end of a global stratification system in which resources are competitively extracted from the non-core and resistance from the non-core plays an important role in the evolution of the system. This approach focusses on both institutions and on social movements that challenge the powers that be. It is noted that rebellions, labor unrest and anti-colonial and anti-imperial movements tend to cluster together in certain periods. Often in the past the rebels were unaware of each other’s efforts, but those in charge of keeping global order knew when rebellions broke out on several continents within the same years or decades. These periods in which collective unrest clustered in time are called “world revolutions” by the world-system scholars (Arrighi, Hopkins and Wallerstein 1989).  These semi-synchronized waves of resistance have been labeled by pointing to the symbolic years that connote the general nature of the movements – 1789 (the American, French. Bolivarian and Haitian revolutions); 1848—(the “Springtime of Nations” plus the Taiping Rebellion in China; 1917 – (the Mexican, Irish, Chinese and Russian revolutions and the first Arab Spring); 1955 – (the anti-colonial revolts and the non-aligned movement at the Bandung Conference); 1968—(the student rebellions) 1989—(the demise of communist regimes); and 20xx, the period of global unrest that emerged in the first decade of the 21st century (Chase-Dunn and Niemeyer 2009).  These complex events had important consequences for both reproducing and restructuring the modern world-system. Arrighi, Hopkins and Wallerstein (1989) notice a pattern in which enlightened conservatives try to coopt powerful challenges from below by granting some of the demands of earlier world-revolutions. This has been an important driving force toward democracy and equality over the past several centuries.

The modern system is multicultural in the sense that important political and economic interaction networks connect people who have very different languages and religions.  Most earlier world-systems have also been multicultural. There is, however, an emerging global culture that is produced by the interaction among and convergence of the subcultures and civilizations. It is a contentious mix that tends to be dominated by the national and civilizational cultures of the core states, but it is also an outcome of global communications and contentious resistance (Almeida and Chase-Dunn 2020). It includes the predominant ontologies of the universe and of life, the nature of time and beliefs about human nature. Science, humanism and formal rationality are the key tropes (Meyer 2009).

Immanuel Wallerstein (2011b) uses the term “geoculture” for the predominant political tendencies of global culture. There is a tripartite ideological structure that emerged after the French revolution in which the ideology of centrist liberalism is flanked by an evolving and interacting Global Right and Global Left (Almeida and Chase-Dunn 2020).



Empirical Studies of Upsweeps in World-Systems

Upsweeps are development events in which the size of polities or settlements increase dramatically. Our research on upsweeps[2] in the territorial sizes of largest polities[3] and the population sizes of largest cities[4] since the Bronze Age is germane to testing competing hypotheses about the causes of long-run trends in the formation of complexity and hierarchy (Chase-Dunn et al. 2006).[5] The unit of analysis is a systemic network of polities based on political/military interaction (PMN). We study changes in the sizes of the largest polities and the largest cities using these as attributes of the PMN. We have conducted a series of quantitative studies that have identified those instances in which the scale of polities and cities significantly changed (upsweeps and downsweeps) in five PMNs[6] (Inoue et al 2012; Inoue et al 2015) and we have begun testing the hypothesis that these scale changes were caused by semiperipheral marcher states (Inoue et al 2016). We contend that polities in semipeipheral positions have been in fertile locations for the implementation of organizational and technological innovations that have transformed the scale, and sometimes the developmental logic, of world-systems (Inoue et al. 2016).  Semiperipheral polities enjoy geopolitical advantages (the marcher state advantage of not having to defend the rear) and “advantages of backwardness” such as less sunk investment in older organizational forms; less subjection to core power relative to peripheral polities; and greater incentives to take risks on innovative technologies and institutions. Upsweeps in the territorial size of the largest polity in an interpolity system can occur when one of the polities conquers the others to form a larger polity. We try to determine whether the conquering state had previously been in a semiperipheral or peripheral location within the regional interpolity system.[7]

In our studies of upsweeps and non-core marcher states we examined four regional world-systems (Mesopotamia, Egypt, East Asia, and South Asia) as well as the expanding Central political/military network that is designated by David Wilkinson’s (1987) temporal and spatial bounding of state systems since the Bronze Age. This produced a list of twenty-one territorial upsweeps.

The results of our studies show that ten of the twenty-one instances of territorial upsweeps were produced by conquests by semiperipheral marcher states, and three were due to conquests by peripheral marcher states (Inoue et al. 2016).  So more than half of the examined instances of territorial upsweeps were caused by conquests by noncore marcher states and the other eight were not. This means that the hypothesis of noncore development explains a lot of upsweeps but does not explain about half of them. The phenomenon of noncore development cannot be ignored in any explanation of the long-term rise of polity sizes, but it is not the only explanation. We characterized the events that led to the territorial expansion of the largest state as follows:

1.       Semiperipheral Marcher State conquest (SMS)

2.       Peripheral Marcher State conquest (PMS)

 3. Mirror-Empires -- a core state that was under pressure from a non-core polity carried out a territorial expansion;

4. An Internal Revolt -- a new regime was formed by an internal ethnic or class rebellion; and

5.  Internal Dynastic Change -- a coup carried out by a rising faction within the ruling class of a state led to a territorial expansion (Inoue et al. 2016).  These were instances in which processes internal to existing core states were important causes of territorial expansion.


Semiperipheral Marcher State (SMS)

Probably an SMS (Shang, Mauryan)

SMS and Internal Revolt (IR)

Peripheral Marcher State (PMS)



Internal Revolt











6 1/3*

Table 1: Count of the 21 upsweep cases with regard Type of Territorial Upsweep(Inoue et al. 2016: Table 2) [8]

*Combined upsweeps that involved polities using different upsweep types are counted as portions of an upsweep. Thus, in the East Asian PMN the Qin/Western Zhou/Xiongnu upsweep that peaked in 176 BCE was a composite upsweep produced by three polities composed of three different types of upsweep. Each of these is counted as 1/3 in Table 1. 


We also found that nine of the eighteen urban upsweeps we identified in these same PMNs were produced by noncore marcher state conquests (SMSs and PMSs) and eight directly followed, and were caused by, upsweeps in the territorial sizes of polities (Inoue et al 2015).  Whereas about half of the upsweep events were caused by one or another form of non-core development, there were a significant number of upsweep events in which the causes seem to be substantially internal (Inoue et al. 2016).  Thus what is needed is a multilevel model in which processes that occur within polities are linked with processes occurring between polities. Such a model would have important implications for debates in international relations theory as well as for interdisciplinary approaches to explaining sociocultural evolution.

Levels of Sociocultural Structural Analysis

Macrostructural analyses in social science implicitly or explicitly contain subunits of nested levels of analysis. In our earlier iteration model of world-systemic evolution we specified variables that were alleged to be operating at the level of whole world-systems, but this was not always clear to readers who critiqued this model (e.g. Aldecoa 2018). They asked about the levels at which these variables were operating and whether some variables operated at more than one level of analysis? We use polities rather than societies as subunits of world-systems, but we also acknowledge that world-systems contain smaller actors that constitute important units of analysis and that these are often nested within one another in ways that facilitate the construction of dynamical models.  A complete multilevel model would contain:

·         human individuals,

·          households,

·         organizations,

·         settlements,

·         autonomous polities, and

·          whole world-systems.

But here we follow Peter Turchin’s (2017) advice about simplicity in the construction of dynamical models, and so the multilevel model we propose in this paper will contain only two levels of analysis: autonomous polities and whole world-systems composed of interacting polities. The variables we propose for each of these levels will be composed of variable characteristics within polities and within world-systems.[9]

A Multilevel Model of World-Systems Evolution

The world-system perspective tends to focus on the network and relational dynamics that are external to single polities despite occasional holistic claims (above) that the contemporary system is composed of all the individuals on Earth and is more than international relations.  The findings of our studies of upsweeps suggest that we need to examine within-polity, between-polity and whole system variable characteristics simultaneously in a multilevel model. In searching for models of processes occurring within polities we are inclined to turn to the structural demographic approach developed by Jack Goldstone (1991) and elaborated and tested by Peter Turchin and Sergey Nefadov (2009). We are also encouraged by Jack Goldstone’s (2014) studies of social movements and revolutions to include these in our multilevel model of sociocultural evolution. Additionally, our overall scheme for integrating both within-polity, between-polity and system-level dynamics is inspired by the ecological models of the multilevel panarchy theory (Green et al 2015; Gotts 2007; Gunderson and Holling 2002; Holling 1973).   Peter Turchin’s (2003) modified model of Ibn Khaldun’s explanation of dynastic cycles and the long cycle approach of Modelski and Thompson (1996) are also inspirations for our new (revised) model.  We will also incorporate insights from Victor Lieberman’s (2003, 2009) studies of state formation in South East Asia and his comparisons with similar processes in other regions. And we incorporate the model of ecological degradation and collapse developed by Jared Diamond (2005).  The theoretical roots of our multilevel model are shown in Table 2.




Level of Analysis

Wallerstein (1984);
Chase-Dunn (1998);
The Iteration Model
(Chase-Dunn and Hall (1997)

Cycles of polities;
Hegemonic sequence


Long Cycle Theory
(Modelski and Thompson (1996)

Cycles of political and
economic power

Inter-polity relations

Structural demographic theory
(Goldstone (1991)
Turchin (2003, 2009)

Dynastic cycles
(One-time social change (Goldstone);
Cycles of social change (Turchin)

Individuals, groups (farmers and elites), and State

(Gunderson and Hollings (2002)

Cycles among multi-level dimensions and resulting changes

Any level
(micro, meso, and macro)

Table 2: Types of Cycles and Levels of Analysis


The panarchy approach has come to be well-known as a conceptual framework that seeks to bridge ecological and social science explanations since the 1970s (Simon 1962; Hollings 1973).  The framework has often been used to produce analogies from ecology to explain complex social systems in social science.  Research inspired by the panarchy model is similar in many respects to the world-systems approach. It employs a nested multilevel analytical framework with cyclical processes to study the emergence and transformation of complex systems (Gotts 2007; Gunderson and Hollings 2002; Odom Green et al 2015). The panarchy model employs a holistic structure that can represent and integrate ecological, social, and economic processes of stability and change. 

The panarchists assert that a whole system is more than the sum of its parts and that whole systems are often complex, hierarchical and dynamic.  Herbert Simon’s (1962) classical formulation of adaptive hierarchical multilevel organizations laid the foundation for the development of the panarchy tradition. Panarchy involves partially autonomous and distinct nested levels that are formed from the interactions among sets of variables operating at each level.  Unlike the hierarchical structure of a top-down authoritative control structure, Simon asserted that each level has its own speed of change—smaller local levels change faster; larger and global levels change more slowly and transformations can occur at each level without affecting the integrity of the whole system.  Such adaptive hierarchical systems with partial autonomy of subsystems are claimed to evolve faster than systems that have a single vertical hierarchical structure (Simon 1962). 

The panarchy paradigm posits an adaptive cycle formed by a set of stages that both larger systems and subsystems go through: (1) “exploitation” (r); (2) “conservation” (K); (3) “release” (W) or “creative destruction,” and (4) “reorganization” (a).  It is proposed that these cycles influence one another, with system-wide transformations occurring when subsystems come into synchrony and produce conditions that make transformational change more likely.

In the panarchy model, the smaller levels have an impact on the larger level in the form of "revolts" in which local events overwhelm larger level dynamics.  Larger level dynamics set conditions for the smaller level events by means of “remember” in which the accumulated structure at the larger level impacts the reorganization of lower level events (Gunderson and Hollings 2002).  Resilience, or the capacity of a system to tolerate disturbances, allows the system to avoid collapse (Gunderson and Hollings 2002).  When the system goes beyond its resilience point, its capacity to absorb change is exceeded.  Then the system is likely to cross a threshold and to become reorganized into a regime with a new set of processes, feedbacks, and structures (Odom et al. 2015).[10]

Figure 1: Panarchy model of adaptive cycles, Adapted from Davoudi, 2012.

The panarchy approach is relevant for comprehending world-systems because it proposes a general model of the evolution of subsystems that are nested within a larger system. The obvious world-system application is to polities that have internal processes, but that are interacting within the context of a larger interpolity system.[11] The panarchy model is also suggestive regarding its description of transformational changes that occur when resilience points are exceeded. These issues are related to theories of the asymptotes that a mode of accumulation may reach, which require systemic transformational reorganization to resolve. Chase-Dunn and Hall (1997: Chapter 6) also distinguish between explanations that designate transhistorical continuities (which they call continuationism) and those that designate qualitative transformations of systemic developmental logic (which they call transformationism). The iteration model of world-system processes discussed below is an effort to specify those processes which are transhistorical, but Chase-Dunn and Hall also contend that qualitative transformations have occurred in the logic of world-systemic development. They are both continuationists and transformationist. The panarchy approach suggests how the relationships between systemic reproduction and systemic transformation could be specified.

Structural Demographic Theory

Jack Goldstone (1991) formulated the first version of what has become known as the structural demographic theory of state collapse. Demographic growth causes population pressure on resources and this results in mass poverty, heightened competition among elites, and a fiscal crisis of the state and state collapse. Structural demographic cycles [also called “secular cycles” by Turchin and Nefadov (2009)] are processes of demographic growth and increasing population pressure within polities that cause class conflict and state break-down. Turchin and Nefedov explicated Jack Goldstone’s (1991) model of the secular cycle, an approximately 200-year demographic cycle, in which population grows and then decreases. Population pressures emerge because the number of mouths to be fed and the size of the group of elites get too large for the resource base, causing conflict and the disruption of the polity. Strong empirical patterns indicate that instability dynamics in agrarian polities are governed by general mechanisms. Population growth that is greater than productivity gains in agriculture has several effects on social institutions. It leads to persistent price inflation, falling real wages, rural misery, migration from the countryside to cities and increased frequency of food riots and wage protests. Rapid expansion of population also results in elite overproduction – an increased number of aspirants for the limited supply of elite positions. Increased intraelite competition leads to the formation of rival patronage networks that vie with one another for state rewards. Elites become riven by increasing rivalry and factionalism. Population growth leads to expansion of the army and the bureaucracy and rising real costs to the state. States have no choice but to seek to expand taxation, despite resistance from the elites and the general populace. Yet, attempts to increase revenues cannot keep up with spiraling state expenses. Thus, even if the state succeeds in raising taxes, it is still headed for fiscal crisis. As all these trends intensify, the result is state bankruptcy and consequent loss of the military control because of elite movements of regional and national rebellion and a combination of elite-mobilized and popular uprisings that manifest the breakdown of central authority. This is an explanation of state collapse, which is an important part of the rise and fall of dynasties within states.

Turchin and Nefedov (2009) tested their formulation on several agrarian empires, confirming the principle that cycles of population growth and elite overproduction lead to sociopolitical instability and regime collapses within states.  And Peter Turchin (2017) has extended the theory and operationalized the model to explain cycles of political instability in the United States since 1790.

Figure 2:  Causal form of the structural-demographic model of the within-polity secular cycle


Figure 2 is a revised diagram of the structural demographic model presented by Peter Turchin (http://peterturchin.com/structural-demographic-theory/) as the main logical components of the structural-demographic theory.[12] The right side is the main focus of the secular cycle model of state collapse. “Inequality overshoot” includes increasing overall inequality (landless peasants, wage stagnation, unemployment) and the expansion of the size of the elite. Political instability and economic contraction include elite competition and conflict, mass rebellions and social movements from below, banditry, peasant revolts, civil wars, coups and revolutions.  State collapse involves the decline in state legitimacy, fiscal crises, failure of military power and the failure of state-managed welfare institutions. The negative effect of state collapse on population is due to famines, emigration, economic disruptions and failures of infrastructure.         

The left side depicts state recovery and expansion. This is the part that is needed for explaining both upswings and the upsweeps that our research has found.  Population pressure has a negative effect on equality. This is the same as the positive effect on inequality shown on the right side of the diagram. Population pressure causes both state collapse and state recovery.  But it is under conditions of state collapse that it leads to state recovery. State collapse causes greater inquality both directly and through its negative effects on population. People get tired of conflict and killing, and new elites emerge who reorganized the state and the economy.

Ibn Khaldun Cycles

The structural demographic cycle of political instability has been theorized to occur entirely within polities (states), but this kind of model recalls Ibn Khaldun’s (1958) model of both state formation and state breakdown – dynastic cycles. Ibn Khaldun was a Tunisian Arab from an Andalusian family.  In the 14th century CE he argued that dynasties typically lasted three or four generations.  A dynasty would get old and corrupt, and “barbarians” (what we call non-core marcher states) would take over.  The leader of a “barbarian” marcher polity had to be generous, charismatic, and a brilliant and sophisticated war leader as well as a good manager of men in order to inspire his warriors and get their support.  His followers thus developed ‘asabiyah, basically loyalty, but more than loyalty -- an obligation formed by the leader’s generosity (they owed him for feasting, presents, etc.) and by respect for his ability and success.  Thanks to genius and asabiyah, a particular marcher polity could take over and start a new dynasty.  The first generation went well.  The leader was the charismatic founder.  There was lots of land and loot, to say nothing of women and slaves, captured from the former dynasty.  The warriors were duly rewarded for their asabiyah by getting tons of goodies.  They settled down, but they were still warlike enough to hold the state against all comers.

            The second generation was often a Golden Age, with the dynasty ruling over a realm of peace and prosperity.  Wealth derived from using the land and other resources, producing taxes which were used to support brilliant culture, science, and literature.  The empire tended to expand at the expense of neighbors and the population grew.

            The third generation was a time of decline.  The land filled up with people.  Production declined because of environmental degradation and taxes also declined.  The rulers therefore had to extort more to keep going.  Military expansion hit a limit – the costs of war now exceeded the returns. The ratio of war expenses to captured loot declined because the low hanging fruit had already been picked and remaining targets were further away, requiring greater expenditures for conquests.  Meanwhile the court was now far from its charismatic founder.  The royal family had expanded, and there were large numbers of supernumerary princes running around desperate for wealth.  The bureaucracy had expanded to try to control the mess.  Princes and bureaucrats fell prey to corruption. How else could they keep up their lifestyle?  This meant still more taxes on a population that had expanded while the land based had ceased to grow.

            The fourth generation saw overpopulation, corruption, and a broken system.  The population became disloyal and rebellions broke out.  The stage was now set for the next another barbarian to take-over.  The whole cycle took from 75 to 100 years (generations are typically 25 years).

            This cycle played out with incredible faithfulness throughout Near and Middle Eastern history.  Turchin and Nefedov (2009) pointed out that in areas like China and Europe, that were less exposed to pastoralist nomadic marchers, the cycle usually took more generations, typically 200 to 300 years. And the dynastic changes were more often due to internal coups, rather than barbarian takeovers. China tended to alternate between periods of disunion ruled by small dynasties that did indeed last about 75 years and periods of union under dynasties that ruled from 200 to 400 years, but which followed the dynamics of Ibn Khaldun’s cycles (charismatic leader, golden age, overpopulation, corruption, collapse) to the letter except that some of the new dynasties were founded by Chinese generals who co-opted popular revolutions, not by marcher lords.

Lieberman’s Model of State Formation

          A somewhat different model of state formation is presented by Victor Lieberman (2003, 2009) that combines both internal and external factors to explain cultural integration (ethno-nation-building) and state formation and how these played out somewhat differently in regions of Eurasia depending on how exposed they were to nomadic or seaborne invaders. While the demographic structural approach focusses on state breakdown, Lieberman focusses on state-building projects and their consequences for cultural integration and the emergence of ethnic and national identities. Lieberman is careful not to use the word “nationalism” because of the huge literature that sees nationalism as a modern form of collective identity that did not exist until the “springtime of nations” in 19th century Europe. But his analysis of the emergence of cultural homogeneity among elites and the development of religious and linguistic integration of peasants and workers as an important component of state formation is an important contribution. We suggest the use of Immanuel Wallerstein’s term “ethno-nationalism” and the process as “ethno-nation-building.” Lieberman employs his vantage point as an historian of Burma to study the history of mainland Southeast Asia, and then, in a refreshing version of positionality, uses his Southeast Asian model to examine similar developments in other regions of Eurasia.

            Lieberman’s approach is relevant to our study of upsweeps of polity size and non-core marcher states because he contends that the processes of integration differed because some regions were less exposed to invasion than others.  What he calls the six “protected rimlands” of Eurasia were regions that were on the edges of earlier civilizational complexity, and that were less exposed to conquest because of geographical barriers to nomadic or seaborne invaders. His six protected rimlands are Burma, Siam, Vietnam, Russia, France and Japan. Because these areas were less exposed to marcher states and incursions they were able to forge strong states and strong national cultures. On the other hand, China, much of Southwest Asia, the Indian subcontinent and island Southeast Asia were vulnerable to maritime or nomadic invaders and so integration was slowed down because of conquest by culturally different people (Lieberman 2003: 79).

            Lieberman (2003: 44-5) models the causes of political, cultural and economic integration, but he is also careful to note that:

External and domestic factors remained influential throughout the period under study, but their relative weights and interconnections varied widely by time and place. I therefore argue less of a single lockstep pattern than for a loose constellation of influences whose local contours must be determined empirically and without prejudice.

            His model is described thus (Lieberman 2003: 44-5) :

…: External, including maritime, factors enhanced the economic and military advantages of privileged lowland districts. In reciprocal fashion, multicausal increases in population, domestic output, and local commodification aided foreign trade, while widening further the material gap between incipient heartlands and dependent districts. So too, by stimulating movements of religious and social reform and by strengthening transportation and communication circuits between emergent cores and outlying dependencies, economic exchange enhanced each core’s cultural authority. As warfare between cohering polities grew in scale and expense, and as the subjugation of more alien populations aggravated problems of imperial control, those principalities that would survive were obliged systematically to strengthen their patronage and military systems, to expand their tax bases, and to promote official cultures over provincial and popular traditions.  Insofar as sustained warfare increased popular dependence on the throne, it heightened the appeal of ethnic and religious patterns championed by the capital. Pacification and military reforms also had a variety of unplanned economic and social effects generally sympathetic to integration. ….

 And he presents a diagram that also shows the effects of climate change and epidemic diseases:

Figure 3: Some elements in the political and cultural  integration of mainland realms to 1830 and their potential interactions. Dotted lines indicate the ambiguous, potentially centrifugal implications of frontier settlement in the eastern lowlands during the 17th and 18th centuries. Source: Lieberman 2003:65

 Lieberman’s model is also relevant for earlier waves of political integration and state expansion of the sort we are considering in Mesopotamia, Egypt and the early Central PMN and probably for polity formation in the Americas as well. His contention that external invasions slowed down integration is supported by the case of Egypt, where there were fewer early incursions and regional state formation emerged quickly. China, despite being exposed to Central Asian steppe nomads and forest conquerors from the north, managed to have some upsweeps that were caused by internal processes of the kind theorized by the structural demographic model.  The Khmer Empire never recovered after its first charter floration because its stronger neighbors (Siam and Vietnam) were able to prevent the reformation of an integrated Cambodian state. Lieberman’s state formation model, when combined with the factors of the demographic structural approach that explain state breakdown, provides us with a good overall model for explaining waves of political consolidation and regime collapse in agrarian systems. Though Lieberman is careful to consider the effects of economic integration and commodification on local integration, he does not explain how centrality in global circuits of trade and investment could eventually lead to the modern hegemonies. Does this mean that a completely different model is needed for the capitalist world-system or can we have a model that is general enough to explain the emergence of complexity and hierarchy from the Stone Age to the present?

Network Hub Theories

Trade leads not only to exchange of resources, goods and services but also to the exchange of ideas and innovations (e.g. McNeill and McNeill 2003; Neal 2019). Interpolity trade spatially binds regional world-systems and is important for generating innovations at central network nodes that can be important spurs of systemic evolution. Innovations that occur at centrally located network nodes may be important causes of polity and urban upsweeps.  Network hub explanations of innovation have been popular among some world historians (McNeill and McNeill 2003; Christian 2004) and human ecologists (Hawley 1986: 92). The hub theory holds that new ideas and institutions tend to emerge in large, complex and central settlements where information cross-roads bring different ideas into interaction with one another. These large settlements often have the most complex and hierarchal polities and the highest concentrations of appropriated energy and accumulated wealth. These are core polities.

The hub effect is probably a significant cause of upsweeps, but it cannot be the whole explanation of human sociocultural evolution. If an information cross-road was able to out-compete all contenders, then the original information hub would still be the center of the world. But that is not the case. We know that cities and states first emerged in Bronze Age Mesopotamia. Mesopotamia is now Iraq. It had 100% of the world’s largest cities and the most powerful polities on Earth in the Early Bronze Age (Morris 2010, 2012). Now it has neither the largest cities nor the most powerful polities. Most of the regional world-systems have undergone a process of uneven development in which the old centers were eventually replaced by new centers out on the edge. The node theory does not well account for the spatially uneven nature of evolutionary change. The cutting edge of evolution moves. Old centers have often been transcended by polities out on the edge that were able to rewire network nodes in a way that expanded the spatial scale of networks. This is the non-core development thesis discussed above.

The Unrevised Iteration Model

The Iteration model shows the main sources of causation in the development of more hierarchical and complex social structures as well as technological changes in the processes of production.  The significant factor of the model is that the variables both cause and are caused by the main processes iterate, causing cyclical dynamics overtime.  The positive feedback explains systemic expansion, hierarchy formation, and technological development as consequences of population pressure. 

Much like the structural demographic theory, the iteration model has population growth as an initial driving force of the positive feedback loop that causes upsweeps of complexity and hierarchy since the Paleolithic Era (Chase-Dunn and Hall 1997: Chapter 6; Chase-Dunn and Lerro 2014: 29).[13] The iteration model assumes a system of polities that are interacting with one another in ways that are important for the reproduction and transformation of social structures and institutions (a world-system).

The model shows the causes of cycles of increasing and decreasing levels of conflict between polities (warfare) but does not include conflict within polities (political instability).  Population growth leads to the intensified use of natural resources, which leads to population pressure. The costs of providing food and other needed resources go up as the low hanging fruit is depleted and human production activities cause pollution of the environment. Population pressure causes migration if there are better locations available. But when better locations are not accessible due to geographical or social barriers (circumscription), population pressure causes a rise in the level of between-group conflict.  Conflict may make things worse, but it may also kill off some of the conflicting people, thus reducing population pressure.  Some regional world-systems get stuck in a vicious cycle of population growth, population pressure and rising conflict which operates as a demographic regulator that is similar in form to the population cycles that operate among insects and animals (Kirch 1991; Fletcher et al 2011).  In other systems increased levels of conflict produce opportunities for the emergence of a new dynasty or a larger and more hierarchical polity by means of conquest. War weariness lowers the resistance to hierarchy formation. It becomes less objectionable to accept the authority claims of a new chief or king or the rule of an invader than to continue fighting. Hierarchy formation creates an institutional mechanism for mobilizing and accumulating resources in the form of taxes or tribute, and some of these may be invested in new production technologies such as fish ponds or irrigation systems, thus reducing population pressure by producing additional resources (see Figure 4).


Figure 4: Unrevised Iteration Model of World-System Evolution (Chase-Dunn and Lerro 2014: 29)

Figure 4 illustrates several hypotheses about the causal relations among the main variables that cause greater complexity and greater hierarchy. In this unrevised version of the iteration model the main indicators of complexity and hierarchy are on the left side of the figure – hierarchy formation and technological development.  At the top of Figure 4 is Population Growth. Procreation is socially regulated in all human polities, but despite this there has been a long-run tendency for population to grow.  Population Growth leads to Intensification, defined by Marvin Harris (1977:5) as “the investment of more soil, water, minerals, or energy per unit of time or area.”  Intensification leads to Environmental Degradation as raw material inputs become scarcer and the unwanted byproducts of human activity increase (soil erosion, deforestation, pollution, etc.) modify the surrounding environment (see Chase-Dunn and Hall 1998).  Together Intensification and Environmental Degradation lead to rising costs in terms of labor time needed to produce the food and raw materials that people need, and this condition is called Population Pressure.  In order to feed more people, farmers must use more marginal land because the best soils have become degraded. Or deer hunters must travel farther to find their quarry once deer have become depleted in nearby districts. Thus, the cost in time and effort of producing a given amount of food increases (Boserup 1965; 1981). Some resources are less subject to depletion than others (e.g. fish compared to big game), but increased use usually causes rising costs. Other types of environmental degradation are due to the side effects of production, such as the build-up of wastes and pollution of water sources. These also increase the costs of continued production or cause other problems.

As long as there were available lands to occupy, the consequences of population pressure led to Migration. Humans populated the whole Earth. The costs of Migration are a function of the availability of desirable alternative locations, moving costs, and the effective resistance to immigration that is mounted by those who already live in these alternative locations.

Circumscription (Carneiro 1970) occurs when the costs of leaving are higher than the costs of staying. This is a function of available lands, but lands are differentially desirable depending on the technologies that the migrants employ. Generally people have preferred to live in the way that they have lived in the past, but Population Pressure or other push factors can cause them to adopt new technologies in order to occupy new lands.

      The factor of resistance from extant occupants is also a complex matter of similarities and differences in technology, social organization and military techniques between the occupants and the groups seeking to immigrate. Circumscription increases the likelihood of higher levels of Conflict in a situation of Population Pressure because, though the costs of staying are great, the exit option is closed off.  This can lead to several different kinds of warfare, but also to increasing intrapolity struggles and conflicts (civil war, class antagonisms, etc.)  A period of intense conflict tends to reduce Population Pressure if significant numbers of people are killed off. And some systems get stuck in a vicious cycle in which warfare, cannibalism and other forms of conflict operate as a demographic regulator, e.g. the Marquesas Islands (Kirch 1991). This cycle corresponds to the path that goes from Population Pressure to Migration to Circumscription to Conflict, and then a negative arrow back to Population Pressure. When population again builds up, another round of heightened conflict knocks it back down again. This negative feedback loop` is the “nasty bottom” of the iteration model (see Figure 5 and Fletcher et al 2011).


Figure 5: The Malthusian “Nasty Bottom” of the iteration model

      Under the right conditions a circumscribed situation in which the level of conflict has been high will be the locus of the emergence of more hierarchical institutions, larger states and larger cities. Scott (2017), Carneiro (1970) and Mann (1986) point out that most people are inclined to run away from state-formation if they can in order to maintain autonomy and equality. But circumscription prevents exit, and exhaustion from prolonged or extreme conflict makes subservience to a new state the lesser evil for both elite factions and for peasants and workers. It is better to accept a king than to continue fighting. Kings (and big men, chiefs and emperors) emerged within polities in situations in which conflict had reduced the resistance to centralized power. This is quite different from the usual portrayal of those who hold to the functional theory of stratification.  The world-system insight here is that the newly emergent elites most often come from regions that have been semiperipheral. And they often conquer other polities to produce an upsweep in the territorial size of the largest polity. These larger polities often build new (or expand existing) settlements (cities). 

Interpolity systems are often structured as hierarchies in which powerful core states dominate and/or exploit less powerful semiperipheral and peripheral peoples. Yet, some semiperipheral agents of change are unusually able to put together effective campaigns for erecting new levels of hierarchy.  This may involve both innovations in the “techniques of power” and innovations in productive technology (Technological Change). Newly emergent elites often implement new production technologies as well as new waves of intensification. This, along with the more peaceful regulation of access to resources structured as legal regulation of property, creates the conditions for a new round of Population Growth, which brings us around to the top of Figure 4 again. Female education and involvement in the world of work outside the household lowers the birth rate, and many countries in the contemporary world have stable population sizes, but the world as a whole has not yet reached that point and so the iteration model is still working. In about 50 or 75 years humans are likely to reach a stable population maximum, that will then oscillate around a total human population of 10 or 12 billion, depending on how long it takes to stabilize. The iteration model may need to be modified to explain subsequent development though population pressure will likely continue to influence development because it is composed of the relationship between population size (which will cycle around a high number) and the economical availability of necessary resources for sustaining the high population. If a cheap and sustainable source of energy is developed it will greatly reduce the importance of population pressure in a context in which the total population size has stabilized around a high normal.  At that point human sociocultural evolution will cease to be mainly driven by population pressure.

The emergence and expanding importance of interpolity market exchange and states that specialize in trade instead of conquest reduced the role of warfare and increased the role of economic competition but did not eliminate warfare as an important selection mechanism. The modern capitalist world-economy has continued to experience waves of warfare, though the use of military power has increasingly become directed toward goals that enhance the profitable production of commodities and profitable financial services.

Non-core development, long cycles, the secular cycle and world revolutions

Insights from the structural demographic (secular cycle) and panarchy approaches can be combined with the world-system iteration model and the non-core development hypothesis to produce a new synthetic multilevel model of sociocultural evolution.  The within-polity dynamics of the structural-demographic model should help account for those upsweep instances that do not involve conquests by non-core marcher states by taking account of within-polity population pressures, fiscal crises, intra-elite competition, social movements and political instability that have led to state collapse and recoveries  (upswing trend reversals) that have in some cases led to upsweeps of territorial size and the population size of large cities. Some variables operate both within and between polities and at the level of whole systems, but they may work somewhat differently at different levels. Social movements, rebellions, and incursions from the non-core may cluster in time. World revolutions (periods in which rebellions across a system cluster in time) have been conceptualized and studied only with respect to the modern Europe-centered system (Chase-Dunn and Khutkyy 2016).  But other studies indicate that earlier regional world-systems may have also experienced periods in which collective behavior events clustered during the same time periods with consequences for the whole system (Thompson and Modelski 1998; Chase-Dunn, Gao and Nagy 2018).). We are convinced that a new synthetic theory of sociocultural evolution that combines the insights and research results from these approaches is nigh.

            The variables in both the unrevised and the revised iteration models are intentionally general and abstract because this model is intended to capture those features of whole human world-systems that are transhistorical – that work for both hunter-gatherer world-systems and the modern global system.  As Peter Turchin (2017) does for the secular cycle, which was developed to explain state collapses in agrarian societies but is respecified to apply to the United States in the industrial era, we may need to translate our general and abstract variables into less abstract measurable proxies that work in specific cases in order empirically test our models. The most concrete quantitative indicators of complexity that we can use transhistorically are the population size of largest settlements and the territorial sizes of largest polities, but even these have somewhat different implications in different systems.  

The Multilevel Spiral Model

As we have said above, the panarchy model implies that multi-scale interactions are consequential for social transformation. The 3-level panarchy model has bidirectional causation among micro-meso and meso-macro levels.[14] Our multilevel model will, for the present, have only two levels, as we have explained above on page 9.

As we have said, our empirical studies imply that processes that are internal to states are often the causes of upsweeps.  The dynamics of rebellions need to be included in the iteration model as a cause of evolutionary transformation.  The spiral model will include clusters of rebellion and revolutions that occur at the level of whole world-systems – so-called world revolutions. The expansion of economic exchange reduces the role of raiding and warfare but does not eliminate these, at least so far.

As with the panarchy model, cycles occur in both the within-polity and the system-levels raising the issue of synchrony across polities and in whole systems. In the panarchy model, the interactions of different levels are important — the process of “revolts” from the bottom and the process of “remember” from the top. We want to specify these connections but will begin by building a model for each level and then connecting them. In the panarchy model system transformations are mainly caused by processes within the smaller systems that exceed the ability of the larger system to regulate, resulting in transformations.  Our multilevel model will leave the issue of the origins of transformations open and will consider the possibility that conditions emanating from the whole system could also cause transformations.

The panarchy model shows a transformation of the system, but the model does not necessarily indicate the resulting cycles of the system size (or rise and fall of a system).  The iteration model connects it with another cycle of rise and fall of polities/cities that are resulting from the iteration cycles.  Our empirical studies (Chase-Dunn et al. 2006; Inoue et al. 2012; Inoue et al. 2015; Inoue et al. 2016) suggest the systemic transition of size of polities, including collapse of the polities and the rise of them to form larger connected world regional systems.    

The multilevel spiral model will include variable characteristics that operate within polities and variable characteristics that operate in sets of polities or in the whole system of interacting polities. The main variables we are trying to explain are proxies for sociocultural complexity and hierarchy and these can be operationalized both within polities and in whole interpolity systems. 

The Revised Whole System Iteration Model

We want to add several variables to the whole system level model that were not included in the original iteration model in Figure 4 above.. Recall that the variable characteristics in this model are attributes of the whole world-system under study. For example, total population is the number of humans who are residents of the whole system and the other variables are also attributes of the whole system.

The whole-system variables are:


1.       Total Population of the whole system

2.       Resource availability (food, energy, size of the economy, etc.)

3.       Population Pressure (relationship between population size and available resources)

4.       Epidemic Diseases

5.       Non-anthrogenic Climate Worsening

6.       Environmental Degradation (includes anthropogenic climate worsening)

7.       Emigration

8.       Circumscription

9.       Warfare (level of interpolity conflict)

10.   World Revolutions (periods in which local rebellions and unrest cluster in time)

11.   Technological Development (includes production, distribution (transportation) and organizational techniques)

12.   Interpolity trade

13.   Non-Core Development (includes non-core marcher and specialized trading polities)

14.   Interpolity Hierarchy (degree of power concentration in the interpolity system)

15.   Interpolity Complexity (interpolity division of labor and specialization)

Figure 6: The Revised Whole System Iteration Model

The new variables are climate worsening, epidemic diseases, interpolity trade and world revolutions.  Interpolity trade is inspired by our discussion of the hub theory of innovation and implementation.  This is a system variable because network centrality in trade and information network is a contextual and relational variable that should include the whole network of interactions among polities and settlements. Climate worsening is suggested by all the studies that show the effects of climate change (both improvement and worsening) on the growth of cities and polities.  We call it worsening so that we can include a direction of the hypothesized effect. Epidemic diseases are known to have had large effects on historically known world-systems, and several social scientists plausibly suppose that epidemics were important causes of demographic collapses before the emergence of writing and documents (Scott 2017; Roberts 2010). We also include world revolutions in which rebellions within polities cluster together in time.

The Revised Secular Cycle Model:

The revised secular cycle model, like the original, includes variables that are characteristics of single polities. We add trade, warfare, climate change, and epidemics that are suggested by the hub theory, 

panarchy, Diamond and Lieberman, ibn Khaldun and Wilkinson. 

The within-polity independent variables are:

16.   Total population of the polity

17.   Resource availability (arable land, size of the economy, etc.)

18.   Population pressure within the polity

19.   Epidemics

20.   Interpolity exports and imports

21.   Non-anthropogenic climate worsening

22.   Environmental degradation (including anthropogenic climate worsening

23.   Emigration

24.   Immigration

25.   Circumscription

26.   Warfare

27.   Technological Development

28.   Inequality overshoot (greater overall inequalities of income and wealth and size of elite)

29.   Political instability, social movements, intraelite conflict and economic contraction

30.   Political stability, economic growth and ethno-nation-building

31.   State collapse

32.   State recovery and expansion

Figure7: Revised Structural Demographic Secular Cycle Model 

As with the original model in Figure 2 above, the right side depicts the processes that cause state collapse and the left side depicts those that cause state recovery and expansion. Population pressure is a key cause of both, but it causes expansion only after a state collapse. Political instability and economic contraction include elite competition and conflict, mass rebellions and social movements from below, banditry, peasant revolts, civil wars, coups and revolutions.  Warfare causes greater equality because elites need to mobilize masses to support them (Schiedel 2017).  Political conflict and state collapse decimate both winners and losers, also resulting in great equality.  We also add interpolity trade, epidemics and climate worsening, migration and environmental degradation to the model. Technological development is also included in the revised secular cycle model and political stability, economic growth and ethno-nation-building are combined inspired by Victor Lieberman.

The Multilevel Model: The Whole System and Within-Polity Subsystems

            The purpose of building an explicit multilevel causal model is to make clear how processes operating at the whole system level relate to processes operating within polities. Because our top level is whole world-systems we will not be able to empirically test our multilevel model using the statistical method of hierarchical linear modeling (HLM) because we will not have enough whole systems with quantitative empirical estimates. A minimum of thirty whole systems with quantitative data at temporal intervals of 25 to 50 years would be required for testing a hierarchical linear model that does not have identification problems do reciprocal causality among variables. Our studies so far show that we have at most about six or seven whole world-systems for purposes of comparison. But the construction of a multilevel model can help to clarify the results we are able to obtain comparing the systems that we have.  And we hope to be able to use a combination of agent-based modeling with our polity models as interacting agents inside our system-level model for purposes of simulation.

Figure 8: A picture of the Multilevel Model

Figure 8 depicts a simplified version of the multilevel model with the whole system model in the middle and four polity models around the edges. For purposes of simplicity we do not allow the polities to have direct causal relations with one another that do not go through the system model. So the system model contains both whole system contextual variables and international relations.   

Figure 9: Variables in the polity level and whole system level models

The variables in the two models are related to one another in two different ways. Looking at Figure 9, the variables within the box include all those for which the value of the polity variable is an additive component of the corresponding system-level variable at the level of measurement. These variables may also have causal effects on one another that are somewhat different from their compositional aspects. The remaining variables (those not inside the box) are not compositionally related.  They are characteristics of polities or of the whole system, that may be related causally but not compositionally.

Techniques for constructing multilevel simulation models

Ideally, we would be able to use a combination of structural and agent-based models for our multilevel model. Agent-based models construct the interactions of causes on outcome variable within an agent and then populated an interaction field with multiple agents and allow them to interact to produce changes in size and location over time. This is a good way to study the interactions among polities, but it does not allow for the simultaneous operation of processes at the whole system level.

The first and simplest multilevel simulation model that we will develop is inspired by the revised the iteration model and the revised secular cycle model have been conceptually developed in the early sections of this paper. But the simplified first model requires that we decrease the number of variables from the conceptual model.  The goal of the modeling is to understand the dynamics of the evolution of sociocultural complexity and hierarchy utilizing two levels analyses—within-polity dynamics and whole world-system dynamics. Our first effort will employ the Price equation

Peter Turchin (Turchin et al. 2018) has developed a multi-level selection approach to explain the evolution of social complexity.  In this approach, the Price equation is used to develop a model of cultural evolution.  The Price equation was originally developed to predict how a trait or gene changes in frequency over time as a function of the relationships between within-group and between-group variation and selection (Wikipedia 2019). [15]

Peter Turchin (2016: 81-91) explains how the Price equation can be used to examine the relationships between evolutionary selection based on within-group and between-group traits. This approach recognizes that competition and conflict between polities is an important selection mechanism that produces both biological and sociocultural evolution (see also Gintis 2009 and Gilbert and Troitzsch. 1999).

            Turchin et al (2017:1) construct a selection model framed like the Price equation to examine the conditions under which cultural variation and selective pressures promote the emergence of larger polities.  The model predicts that the conditions of cultural diversity and interpolity competition (warfare) produce selection pressures that cause the formation of larger states. 

In our model the conceptual framework of multilevel selection that Turchin used for the explanation of group and state level dynamics is modified and applied to the study of the evolution of world-system complexity.   The framework provides a linkage between the state-level dynamics and world-systems level dynamics. 

In earlier work (Fletcher et al 2011), we developed a simulation model based on the Iteration model.  That work examined the dynamics of human populations in regional systems and its relationship with the development of technology, the division of labor and hierarchy within polities.  Starting with this simulation model we will examine the multilevel dynamics between state-level and world-systems dynamics in the present study.  We are interested in investigating how world-system dynamics impact upon state-level dynamics and vice versa.  

In the model we are developing here within- and between-polity hierarchy (power concentration) and complexity (division of labor and specialization) develop due to population pressure and technological development (see previous discussion of the revised iteration model). 

From the conceptual iteration model discussed earlier, we draw the major variables: 

Dependent variables:

1.Interpolity Hierarchy (degree of power concentration in the interpolity system) and Complexity (interpolity division of labor and specialization)

Independent variables:

2.Population Pressure (relationship between population size and available resources)

3. Technological Development (includes production, distribution (transportation) and organizational techniques)

4.       Warfare (level of interpolity conflict)

The basic structure of the model is explained as follows:  These are very simplified conceptual frameworks, and model specification will be developed in later work. 

(1) Interpolity hierarchy & complexity = population x n + tech. level + interpolity war

(2) Intrapolity hierarchy & complexity = population + tech. level + intrapolity conflict

We use multilevel selection framework that connects the dynamics of the two levels.


The price equation contends that the ratio of between-group diversity over within-group diversity is always larger than the ratio of selection pressure on individuals over selection pressure on groups (Turchin 2016: 82).  That is, as between-group diversity increases, selection pressure for group increases.  Applying the implication of the equation, Turchin develops a model that explains how larger and more complex polities arise due to the selection pressure for group cooperation over smaller units of group’s advantages.  For instance, as a polity encounters culturally dissimilar other polities, the between-polity variation increases in the region, and war intensity is elevated (Turchin et al. 2017: 14).  Further, military technologies intensify warfare, which increases the selection pressure in favor of larger polities (ibid).

We apply the conceptual framework of the Price equation developed by Turchin (Turchin et al 2017; Turchin 2018) to world-system evolution as a linkage between polity-level and world-system level interactions.  The equation (3) explains that, as a polity starts to interact and develop hierarchy between polities, polities engage in and intensify inter-polity warfare. 

Hierarchy is one of socio-cultural traits where developing hierarchy is not advantageous for a polity since it produces inequality within a polity, yet hierarchy allows the integration of a system of polities which promotes (is advantageous) for co-existence of polities.   Between-polity warfare promote the formation of hierarchy between polities, resulting in the evolution of world-systems complexity.

Further, we expect that once world-system hierarchy is established, the structure of hierarchy creates systemic force to sustain the hierarchy, making the change of the system difficult. However, as the world-systems evolution explain the systemic changes in the earlier section of this paper, the world-systems perspective comprises the mechanisms of regional and global level system change (e.g. semiperipheral marcher state, world revolutions). The explanations of how these system change occur will be modeled in a different work.  In the current study, we focus on the ways world-system complexity evolves having two-level dynamics—interpolity and world-systems dynamics.  We also consider world-systemic dynamics or network of polities have impact on the state-level dynamics. (inter-polity dynamics), which is not explained by Turchin’s or any other state-model dynamics. 

The formal model will be written in a computer programming language for purposes of running simulations.  The data created from the simulation will be examined for logical consistency with known parameters of systemic growth and decline and empirical proxies for variables will be used to examine the fit between the theoretical models and what we know about historical changes in several independent world-systems.


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[1] The Kondratieff wave is a 40 to 60-year business cycle in which upturns are usually brought about by successful class struggles that incentivize a wave of new investments in labor saving technology (Mandel 1978).


[2] We distinguish between an “upswing,” which is any upturn in a growth/decline sequence, and an “upsweep”, which goes to a level that is more than 1/3 higher than the average of three prior peaks (Inoue et al 2012).  We are now studying both sweeps and swings (Chase-Dunn, Inoue, Welch and Gao 2019).

[3] Most of our estimates of the territorial sizes of large polities come from the work of Rein Taagepera 1978a, 1978b,1979,1997).

[4] Most of our estimates of the population sizes of largest cities come from Modelski (2003).

[5]  This research has been carried by the Settlements and Polities Research Working Group (SetPol) at the Institute for Research on World-Systems at the University of California-Riverside. The project web site is at http://irows.ucr.edu/research/citemp/citemp.html 

[6] The five PMNs we have studied quantitatively are Mesopotamia from 2800 BCE to 1500 BCE, Egypt from 2850 BCE to 1500 BCE, the Central PMN from 1500 BCE to 1991 CE, South Asia from 420 BCE to 1008 CE and East Asia from 1300 BCE to 1830 AD.

[7] When a conquering polity is peripheral within a regional system, we designate this as a peripheral marcher state. The term we use to combine peripheral and semiperipheral states is “noncore.”



[8] The names of the polities included in Table 1 can be found in Inoue et al (2016: Table 1).

[9] Recall that world-systems are defined as nested systemic interaction networks.


[10] Because of its complex holistic features and relatively abstract concepts the panarchy model has been difficult to test (Odom et al. 2015). 

[11] Gotts (2007) presents a useful summary and critique of the panarchy approach and its overlaps with, and possible usefulness for, the study of the evolution of world-systems.


[12] The structural demographic theory explicitly treats processes involving interactions that are external to individual states as exogenous, but a recent article by Turchin, Gavrilets and Goldstone (2017) proposes the development of a multilevel model that would include interpolity variables such as warfare and economic globalization as well as processes operating at the level of individual decision-making.


[13] Chase-Dunn and Hall (1997) were inspired by the theorizing of Johnson and Earle (1987).

[14] In panarchy, the interactions among different levels are either micro-meso or meso-macro. Micro-macro interactions are not considered (Gotts 2007). 

[15] The Price equation has been applied to genetic group selection to explore cultural evolution (Turchin 2016: 81-91 and Turchin et al 2018).