Journal of World-Systems Research, IX:1, Winter 2003


37

Spatial Synchrony Among and Within World-
Systems: Insights From Theoretical Ecology*

Peter Turchin
Th omas D. Hall

Peter Turchin
Department of Ecology and Evolutionary Biology
75 N. Eagleville Rd
University of Connecticut
Storrs, CT 06269-3043
turchin@uconnvm.uconn.edu
http://www.eeb.uconn.edu/faculty/turchin/turchin.htm

Th omas D. Hall
Department of Sociology & Anthropology
DePauw University
Greencastle, IN 46135
thall@depauw.edu
http://acad.depauw.edu/~thall/hp1.htm

journal of world-systems research, ix, 1, winter 2003, 37–64
http://jwsr.ucr.edu
issn 1076–156x 
© 2003 Peter Turchin & Th omas D. Hall

I N T RODUC TION

Political processes within world-systems are often characterized by cycles 
or waves. Chiefdoms cycle (Anderson 1994, 1996), empires rise and fall, and 
the modern state system undergoes “power cycle” or “hegemonic sequence.” 
Furthermore, all world-systems “pulsate”—expand rapidly, then more slowly, 
or even contract (Chase-Dunn and Hall 1997, 2000). Because spatial waves of 
expansion/contraction occur across all types of world-systems, such pulsations 
cannot be rooted in a specifi c mode of production or mode of accumulation. 
Rather, these cycles are themselves evidence that polities and world systems are 
dynamical systems with various feedback loops. 

Afroeurasia (in conventional terms Asia, Europe, northern Africa) has been 
linked, at least at the information and luxury goods exchange levels (Chase-
Dunn and Hall 1997), for two and a half millennia or more. Th us, events and 
processes in Europe cannot be explained solely by examining European pro-
cesses, a conclusion strongly supported by Pomeranz (2000). On the other hand, 
the degree of Afroeurasia-wide linkage fl uctuated, so that world-systems at 
opposite ends of Afroeurasia were nearly isolated for long periods of time. One 
interesting puzzle is why there is a substantial linking of rise/fall processes at the 
western and eastern ends of Afroeurasia during the last two millennia (Teggart 

* We would like to thank the two anonymous reviewers for cogent suggestions. Th eir com-
ments improved the clarity of our argument. We also thank Eric Titolo for his help in formatting 
Figure 1. We retain responsibility for remaining errors.Th is paper reports on research in 

population ecology and suggests ways it might 
be useful in explaining spatial dynamics of 
states, groups, and world-systems.  In particular 
it focuses on how and why populations at 
opposite of ends of Afroeurasia come to rise 

and fall simultaneously over long periods of 
time.  We call for exploration of research in 
population ecology for understanding world-
system evolution and suggest directions for 
possible future research.

abstract

mailto:turchin@uconnvm.uconn.edu
http://www.eeb.uconn.edu/faculty/turchin/turchin.htm
mailto:thall@depauw.edu
http://acad.depauw.edu/~thall/hp1.htm
http://jwsr.ucr.edu/


Peter Turchin & Th omas D. Hall38 Spatial Synchrony Among and Within World-Systems 39

1939; Frank and Gills 1993; Frank 1992, 1993; Chase-Dunn and Hall 1997, 2000; 
Denemark et al. 2000). For example, increases and decreases in the territorial 
sizes of empires and the population size of cities correlate between East Asia 
and West Asia/Mediterranean (e.g., Chase-Dunn, Manning, and Hall 2000). 
Yet, there appears to be little linkage to cyclical processes in South Asia (Chase-
Dunn, Manning, and Hall 2000). Interestingly, archaeologists have noted seem-
ing parallels in rise and fall of ancient cultures in what is now southeastern and 
southwestern United States (Neitzel 1999).

Th ere has been much speculation about what processes drive various 
cycles within world-systems, what mechanisms may lead to (partial) synchrony 
between some world-systems separated by great distances, and why there is little 
or no synchrony between others (Denemark et al. 2000; Frank 1993; Grimes 
2000). Th e current state of the fi eld bears a striking similarity to the debates 
that occurred among population ecologists a few decades ago. Ecologists also 
found that many population systems go through regular oscillations, and that 
these population cycles are synchronized across distances of hundreds, and 
sometimes thousands of kilometers. We argue in this paper that there is much 
to be learned from what ecologists have found from their studies, analyses, and 
models of oscillatory population systems. While ecological models and analytical 
approaches cannot be imported wholesale, or without adjustment, into world-
system problems, they do off er a number of useful insights, and suggestions for 
future research.

Many ecological studies are highly analytical, and current standards of scien-
tifi c rigor in the discipline (especially in the study of population oscillations and 
spatial synchrony) require translation of verbal hypotheses into mathematical 
equations. Th e benefi ts of this approach are the ability to subject predictions 
from rival hypotheses to rigorous quantitative tests. However, model construc-
tion requires making simplifying assumptions. Surprisingly, however, the resul-
tant models are often quite robust with respect to these initial assumptions. Th at 
is, “fi rst-cut” models can be investigated mathematically as to the consequences 
of relaxing the initial assumptions for theoretical predictions. Repeated applica-
tions of this process can extend theory and simultaneously increase confi dence 
in the answers that it provides. Th e conditions under which population cycles 
become synchronized have been a focus of an intense theoretical (and empiri-
cal) investigation over the last several decades, leading to a fairly mature state of 
understanding of synchrony.

A key insight from ecological theory is that the processes driving oscillations 
(the rise/fall dynamics) and the processes causing large-scale synchrony need not 
be the same. In fact, current empirical research shows that in ecological systems 
they are typically distinct. Ecological models show that if two (or more) sys-

tems separated in space are driven by largely endogenous dynamics, and if their 
endogenous dynamics are broadly similar (e.g., have approximately the same 
period), then their cycles may be synchronized by a variety of shared exogenous 
perturbations, and these perturbations need not be very strong. Th e process of 
bringing spatially distant oscillations into phase by weak exogenous infl uences 
is sometimes called “entraining” or “phase-locking.” Th is insight, in particular, is 
suggestive for possible explanations for the synchrony of population and city-
size changes in east and west Asia.

Our goal in this paper is to review recent developments in ecological theory 
of spatial synchrony, and discuss its possible applications in world-system 
research. Because the nature of endogenous processes underlying systemic oscil-
lations is a key ingredient in the explanation of large-scale synchrony, we begin 
by reviewing cyclical processes aff ecting the dynamics of polities and world-sys-
tems. Second, we review the theoretical results from ecological models. Th ird, 
we discuss some broad patterns in the Afroeurasian history from the point of 
view of the theory we present here. Fourth, we conclude that this preliminary 
examination is suffi  ciently promising to warrant further theoretical and empiri-
cal investigation of this extension of ecological theory to world-systems prob-
lems. Finally, we discuss directions for future research suggested by the theory, 
and, in particular, how some of these hypotheses might be tested with data.

C YC LIC PRO C E S SE S I N WOR LD SYST E MS

For the most part world-system analysts have focused on two cyclical 
processes: the Kondratieff  wave (K-wave) and the hegemonic cycle. K-waves 
are shown by approximately 50–year cycles in prices. Th e upswing is called 
the A-phase, the downswing the B-phase. K-waves are notoriously diffi  cult to 
date precisely because they must be measured indirectly via trade volume and 
prices (Barr 1979; Boswell and Misra 1995; Goldstein 1988; Grimes 2000). Th e 
basic dynamic is that a new technology allows economic expansion. Eventually 
the market saturates, and competition increases, and the expansion slows until 
another cycle, based on yet another new or renewed technology develops. 
Kondratieff  waves have been discussed primarily in the context of the modern 
capitalist world economy. However, several authors (Modelski and Th ompson 
1996, 2000) have traced K-waves back into the 12th century.

Hegemony, in a non-Gramscian sense, is a condition in which one state in 
a core region dominates a world-system through economic and political power, 
typically without overt coercion. Once its power peaks, hegemony is lost, or at 
least declines, and the core is marked by much more intense inter-state rivalry 
and competition. Hegemonic cycles are about a century long, and may be related 
to K-waves in complex ways that are currently debated (Th ompson 2000).



Peter Turchin & Th omas D. Hall40 Spatial Synchrony Among and Within World-Systems 41

sociopolitical instability suggests that agrarian societies should go through cycles 
of alternating phases of political centralization/population growth and political 
decentralization/population decline. A typical period of such “secular cycles” is 
two to three centuries (although the theory predicts that in societies character-
ized by widespread elite polygyny, the cycle period should be shorter, around one 
century—these are “Ibn Khaldun” cycles, which we will discuss in later section). 
A recent survey by Turchin and Nefedov (2004) suggests that secular cycles are a 
ubiquitous feature of Afroeurasian history during the last 3–4 millennia. 

Eff ects of hegemonic cycles and secular waves ripple through world-systems 
and, perhaps, beyond. Sociopolitical cycles give rise to cycles of colonization and 
decolonization, war and peace, state-formation and state collapse, and a variety 
of social and cultural movements. Th ese cycles do not necessarily determine or 
cause these processes. Rather, they may create structural conditions that facili-
tate, or retard, their course (see Grimes 2000; Boswell 1989; Boswell and Sweat 
1991; Boswell and Chase-Dunn 2000:Ch. 2). 

Arrighi and Silver (1999; Arrighi 1999) argue that globalization also has 
spread in waves, corresponding to cycles of hegemony. A key part of their argu-
ment is that state capacity to govern is never entirely stable but waxes and wanes 
with world-systemic cycles. Waves of globalization are yet another example of 
how these cycles shape social processes. Chase-Dunn et al. (2000) document 
waves of globalization in the late 19th and late 20th centuries.

We also note that a world-system typically has multiple kinds of boundar-
ies, and except for small systems, islands, and the 20th century world-system, 
these boundaries do not coincide—they are nested within each other. Th ere 
are at least four diff erent types of boundaries (Chase-Dunn and Hall 1997). At 
the smallest scale are the bounds of bulk goods trade, the bulk goods network 
(BGN). Next in size are the bounds of regular political-military interaction, the 
political-military network (PMN). Th en there are two much larger, but typi-
cally diff erent boundaries. Often the slightly smaller of the two is the luxury or 
prestige good net (PGN), and the typically somewhat larger, information or cul-
tural net (IN). All four boundaries can be fuzzy. If one thinks of a topographic 
map of each of these features, the “boundary” would be zone of a sharp drop off , 
what would look like a cliff  or very steep slope. Synchronization can occur at any 
of these four levels. However, each level would have its own mechanisms and 
dynamics. Th ese diff erences between networks and corresponding boundaries, 
of course, are more salient in ancient world-systems than they are in the contem-
porary world-system.

Clearly, there are many potential levels of synchrony among the various 
world-system cycles. As noted in the introduction, several have been docu-
mented empirically (e.g., Chase-Dunn, Manning, Hall 2000). Other than the 

“Secular cycles,” periodic waves of state breakdown accompanied by oscilla-
tions in population numbers, are a third type of cycle (Goldstone 1991; Fischer 
1996; Nefedov 2001; Turchin 2003). Secular waves arise as a prediction from 
demographic-structural theory, which focuses on the dynamic interaction 
between population numbers and sociopolitical stability. Jack Goldstone (1991) 
analyzed the eff ect of population growth on state breakdown. Briefl y, population 
growth in excess of the productivity gains from the land leads to persistent infl a-
tion and rising real costs, which outstrips the ability of the state to increase tax 
revenues. Rapid expansion of population also results in an increased number of 
aspirants for elite positions, putting further fi scal strains on the state, and inten-
sifying intra-elite competition and factionalism. Increased rural misery, urban 
migration, and falling real wages lead to frequent food riots and wage protests; 
expansion of youth cohorts contributes to the population mobilization potential; 
and elite competition and popular discontent fuel ideological confl icts. As all 
these trends intensify, the end result is state bankruptcy and consequent loss of 
military control, elite movements of regional and national rebellion, and a com-
bination of elite-mobilized and popular uprisings that manifest the breakdown 
of central authority (Goldstone 1991:25).

State breakdown and resulting sociopolitical instability cause a population 
decline, both through their eff ects on demographic rates, and by damaging a 
society’s productive capacity (Turchin 2003). First, political instability causes 
lower reproduction rates, because during uncertain times people choose to 
marry later and to have fewer children. Also, family limitation practices may be 
disguised as increased child mortality. Second, mortality rates rise as a result 
of increased crime, banditry, and internal and external warfare. Migration from 
war– or famine–aff ected areas leads to increased emigration, declining birth 
rates (because people on the move cannot aff ord to have children), and epidem-
ics. Increased vagrancy, movements of armies, and movements of rebels spread 
disease by connecting areas that would stay isolated during better times. Political 
stability or instability can also aff ect the “carrying capacity.” Strong states sup-
port the agricultural productivity by constructing irrigation canals and roads, 
by implementing fl ood control measures, by clearing land from forests, etc., thus 
increasing the numbers of people that can be gainfully employed growing food. 
Additionally, a strong state off ers protection. In an anarchic society people can 
live only in natural strongholds, or places that can be made defensible. Fear of 
attack can lead farmers to cultivate only that proportion of productive area that 
is near fortifi ed settlements. A strong state protects the productive population 
from external and internal (banditry, civil war) threats, and thus allows nearly all 
cultivable area to be put into production. 

Mathematical modeling of the interaction between population dynamics and 



Peter Turchin & Th omas D. Hall42 Spatial Synchrony Among and Within World-Systems 43

speculations by Chase-Dunn, Manning and Hall (2000), very little has been 
off ered by way of explanation. Furthermore, synchrony, or entraining, between 
east and west Asia does not extend to south Asia, which itself is another puzzle. 
We argue that an examination of what ecologists have found about synchrony 
may provide leads for exploring the mechanisms and hence explaining the causes 
of synchrony across world-systems. We begin that task with a brief overview of 
synchrony from an ecological perspective.

W H AT T H E E COLO GICA L T H EORY SAYS A BOU T SY NC H RON Y

Ecologists have long puzzled over why many oscillatory population systems 
exhibit large-scale spatial synchrony. In fact, in the very paper that inaugurated 
the scientifi c study of population cycles Charles Elton also speculated why lem-
ming peak years should be synchronized across much of Norway (Elton 1924). 
An even more striking pattern of spatial synchrony was later observed in the 
Hudson Bay Company data on lynx pelts (Elton 1924). It turned out that the 
ten-year lynx cycle is synchronized over the whole taiga region of Canada. In 
1953 P.A.P. Moran developed statistical approaches for analyzing spatial aspects 
of lynx population cycles, and proposed a formal mechanism that could explain 
large-scale synchrony (Moran 1953). Th is mechanism is currently known in the 
ecological literature as “the Moran eff ect” (Bjornstad, 1999; more on the Moran 
eff ect below). Moran’s pioneering work inspired an enormous number of model-
ing, statistical, and empirical studies, leading to a rapid maturation of the theory 
of spatial population dynamics during the 1990s (for a review see Bjornstad, 
1999). A key issue was determining which mechanisms may cause synchrony. 

Synchronizing Mechanisms 

Ecologists have classifi ed mechanisms that induce spatial synchrony along 
two continua: exogenous versus endogenous and local versus “global.” A factor 
X is called an exogenous mechanism if it is not part of the feedback loop: X 
aff ects the variable of interest, while the variable of interest does not aff ect X. By 
contrast, an endogenous factor is one that is part of a feedback loop: the variable 
of interest aff ects X and then the change in X aff ects the variable of interest. 
Of course, we do not always (or even often) know all the feedback loops that 
aff ect the dynamics of the variable of interest. Th us, in practice, we call endog-
enous only those mechanisms, whose feedback infl uences are explicitly taken 
into account (e.g., modeled). For example, in human-dominated ecosystems 
the usual assumption that climate aff ects population, but population does not 
aff ect climate, does not necessarily hold. Chew (2001) shows that early human 
civilizations so denuded forests and salinized agricultural land that they may, 
indeed have changed local, if not regional, climates. Some of these changes may 

be system-wide. Planetary changes are probably only a 20th or 21st century phe-
nomenon (see also Crowley 2000; Hornborg 2001; Mann 2000; Th omas 1956; 
Turner 1990). Still, in world-system applications some climatic changes may 
need to be modeled as endogenous, rather than exogenous processes.

Ecological theorizing uses the terms “local” and “global” in ways that diff er 
signifi cantly from usage in world-systems analysis, a diff erence that can gener-
ate confusion. We review these diff erences since virtually all ecological research 
uses these terms in a consistent way. A “local” mechanism is one whose eff ects 
fall off  with distance. By contrast, a “global” mechanism aff ects all points in the 
relevant space similarly, without any regard to how far these points are from each 
other. Th us, the term “global,” as used in ecological literature, might be glossed 
as “system-wide” in world-system terms. For clarity, we use “planetary” when we 
mean the entire world, and “global” only as in ecological theory. Th e spatial scale 
of a local mechanism can be measured in a variety of ways. One of the most 
useful approaches is to calculate the spatial autocorrelation function (ACF). A 
typical ACF is close to 1 for small spatial lags (because points located near each 
other tend to be highly correlated). As spatial lag is increased, ACF declines to 
zero (refl ecting lack of correlation between points separated by large distances). 
Th us, a rough measure of the spatial scale of spatial autocorrelation is the spatial 
lag at which ACF becomes statistically indistinguishable from zero. As the spa-
tial scale on which a process operates increases local mechanisms grade smoothly 
into global. In practice, whenever the spatial scale of a mechanism is greater than 
the extent of the spatial domain, within which the dynamics of interest occur, 
it should be treated as global. ACFs of global processes remain positive (do not 
decline to zero) for the whole range of spatial lags possible within the spatial 
domain. In other words, even points situated at the opposite sides of the domain 
exhibit some degree of synchrony. 

Given the two classifi catory dimensions (endogeneity and locality), we can 
defi ne four regions of a universe of potentially synchronizing processes (Figure 
1). Ecologists have tended to concentrate on two: the global exogenous and local 
endogenous mechanisms. Th e most discussed global exogenous factor in ecology 
is climatic variation. It is a quintessentially exogenous process because variation 
in temperature and rainfall can have a very strong eff ect on survival and repro-
duction of organisms, while fl uctuations in organism population numbers almost 
never have an eff ect on weather (although in humans this is not necessarily true, 
as noted above), especially on the short time scales of interest to population 
dynamicists. On the spatial scale at which ecologists study most populations, 
weather patterns are best thought of as global. For example, variations in temper-
ature are highly cross-correlated across hundreds of kilometers. On short tem-
poral scales, precipitation may have a distinct local character (when a summer 



Peter Turchin & Th omas D. Hall44 Spatial Synchrony Among and Within World-Systems 45

thunderstorm dumps a couple of cm of water in one locality, while leaving 
another, only a km away, dry). On a longer time scale, however, such local eff ects 
tend to even out (wet versus dry summer conditions aff ect large areas, hundreds 
of km in extent). In any case, close examination of specifi c mechanisms shows 
that the global-local distinction defi nes a continuum, and not a dichotomy. For 
world-systems analysis, given the potential eff ects of human activity on climate 
(see Chew 2001), clearly “global” or system-wide mechanisms would be a massive 
volcanic eruption or collision with a sizable comet. Alternatively, if there is a truly 
exogenous climatic shift (due, say, to sun spot cycles or some such mechanism 
that humans could not aff ect) and if it were planetary, then we should see global 
synchrony, across Afroeurasia, Meso– and South America, Southeast Asia, and 
sub–Saharan Africa. Th is would still require some subsidiary explanation for the 
already documented lack of synchrony in South Asia.

Th e quintessential local endogenous mechanism is movement. It is endog-
enous because the number of organisms spreading from a source depends very 
much on the population density at the source. It is local, because organisms 
do not “teleport”—in order to get to there from here, an organism must travel 
through the intervening space. Th e result is a characteristic pattern of movement, 
in which the density of dispersers declines with the distance from source. We 
note that movement is not limited to the population under study; it may also 
refer to movement of other components in the dynamical system, such as preda-
tors or pathogens. Socially, disputes in family succession among elites, as among 
Mongols who had competing lines of succession (Barfi eld 1989; Chase-Dunn 
and Hall 1997: Ch. 8) would be examples (laterally and lineally). Rules of suc-

cession or descent vary by cultural group, and thus are typically highly localized. 
Such rules do change, but typically only very slowly, often pushed by changes in 
the ecology of production and adaptation. 

Once again, although movement tends to the local endogenous corner of 
the classifi catory universe, under certain circumstances it may become either 
exogenous or global (or both). An example of movement acting in an exog-
enous manner is when the area under study is subjected to recurrent invasions 
of predators or pathogens from outside. Movement may act globally (or in a 
system-wide manner), rather than locally, when the scale of dispersal is much 
larger than the extent of the spatial domain. In ecological applications, move-
ments by predators often occur on a much larger scale than movements of their 
prey. For example, lynx—the main predator of snowshoe hares—have been 
known to travel over a thousand kilometers. To give another ecological example, 
many fungal pathogens disperse by spores that may be carried by wind over very 
large distances. An analogous feature among humans would be the propensity 
to bring small, exotic souvenirs from distant places, and/or to trade them over 
great distances (Helms 1988). Another example might be the appearance of new, 
airborne pathogen that (nearly) simultaneously aff ected all human populations. 
Th e diff usion of the Black Death in the 14th century, might be such an instance, 
since it appears to have spread from Central Asia to both East Asia and West 
Asia (and Europe) (McNeill 1976). Finally an ecumene-spanning empire, or a 
world-economy might be considered an endogenous global factor. Consider the 
widespread eff ects of the Roman Empire or the current eff ects of U.S. foreign 
policy, which may be the analog of “highly mobile predator.” Th us, both Iraq and 
North Korea, separated by thousands of kilometers, are under similar kinds of 
pressure to change.

Finally, there is the local, exogenous corner of the classifi catory universe. Th is 
is essentially the “random” corner, where noise, or contingency seems most likely. 
In social terms, this would be “historical accident.” We note, however, that while 
the event(s) may be accidental or random, their consequences are not (in the 
sense that their eff ect may depend on the state of the system). 

We reiterate that local-global and exogenous-endogenous are not discrete 
dichotomies, but rather continua between extremes. As one moves toward the 
center of the classifi catory universe, these distinctions begin to blur and fi nally 
merge together.

Types of Oscillatory Dynamics 

Th e effi  cacy of diff erent mechanisms described above to synchronize oscil-
lations depends on the nature of the dynamics characterizing the synchronized 
systems. Th e key distinction is between stable and chaotic oscillations. Chaos 

Figure 1– Dimensional Continua of Mechanisms of Spatial Synchronicity

Local
Exogenous

Global 
Exogenous

Endogenous 
Local

Endogenous 
Global

“noise,”  contingency

historical accident

climate, invasions by 
predators or pathogens

comet or volcano 

pandemic,
or world-empire,
or world-economy

movement

family succession dispute

movement by highly mobile 
predators or pathogens



Peter Turchin & Th omas D. Hall46 Spatial Synchrony Among and Within World-Systems 47

is defi ned as bounded oscillations with sensitive dependence on initial conditions 
(Eckman and Ruelle 1985). Sensitive dependence can be illustrated with the fol-
lowing mental experiment (or even better, a computer experiment). Suppose we 
have a dynamic system, which started from a certain initial condition and then 
generated a certain trajectory. Now imagine that we restart the system from an 
initial condition that is slightly diff erent (on the computer, we simply rerun the 
program, but give it a diff erent initial data). If the system is chaotic, then we will 
observe that the two trajectories starting from very similar but diff erent initial 
points will diverge with time, and eventually oscillate in a completely uncorre-
lated fashion. If the system is stable, then the two trajectories will converge and 
soon become completely indistinguishable from each other; they will oscillate 
in perfect synchrony. Returning to the chaotic system, the faster trajectories 
diverge the more sensitive to initial conditions (and therefore the more chaotic) 
the system is. 

Th e same argument applies to the behavior of two identical or very similar 
systems. If their dynamics are stable, then the two systems starting from similar 
initial conidtions will tend to oscillate in synchrony. Small random perturbations 
will keep them out of perfect synchrony but the stable nature of the two systems 
will act to bring the two trajectories back in synchrony. By contrast, two identi-
cal chaotic systems starting even from very similar initial conditions will rapidly 
diverge and oscillate asynchronously (this is sometimes known as the “butterfl y 
eff ect”). Small random perturbations will make this process of divergence even 
faster. Th is is why the dynamical stability is such an important factor in allowing 
synchronous oscillations. It is very hard to synchronize two chaotic systems.

The Effect of Different Synchronizing Mechanisms on Spatial Dynamics 

Th e ability of any particular mechanism to synchronize dynamics depends 
on its nature, as well as on the nature of local population dynamics. In general, 
exogenous drivers are not particularly powerful synchronizing mechanisms. A 
substantial degree of spatial synchrony requires, fi rst, that local dynamics are 
stable (nonchaotic) oscillations and that, second, the exogenous factor acts in a 
global (or system-wide) manner. Th e mechanism of entrainment is the Moran 
eff ect, which acts as follows. Consider two stable dynamical systems driven by 
identical (or, at least, similar) mechanisms. For example, two spatially separate 
locations are inhabited by the same prey and predator species that undergo 
cyclic population interactions. Subjecting the two stable systems to similar per-
turbations from an exogenous driver is akin to starting them with similar initial 
conditions: eventually both systems will oscillate in synchrony. By contrast, sub-
jecting two chaotic systems to identical perturbations will not synchronize them, 
because they will diverge from each other due to their sensitive dependence 
properties. 

If an exogenous factor acts in a local manner, then its synchronizing strength 
will depend on how eff ectively the exogenous perturbations acting on each local 
system are cross-correlated. Furthermore, the eff ects of synchronizing external 
drivers may be degraded by other exogenous drivers, which may act indepen-
dently on each system. 

Note that the usual way of modeling exogenous infl uences in dynamical sys-
tems is by assuming that exogenous drivers aff ect the rate of change of a dynamic 
variable such as the population density of the studied organism. For example, an 
unseasonable freeze may impose 50 mortality on a population, which means 
that the population size will be halved. Such relative changes cannot synchronize 
chaotic systems for reasons given above. Another kind of an exogenous infl u-
ence is one that “resets” each system to approximately the same value, instead of 
aff ecting its rate of change. Th at is, it makes the initial conditions in both systems 
virtually identical, hence they will be synchronized for some time, until the cha-
otic process begins to produce divergence. Multiple “resetting” perturbations can 
impose a fairly high degree of synchrony even on chaotic systems. Th e average 
degree of synchrony will depend on how frequently “resetting” events occur, and 
how fast trajectories of local systems diverge after each resetting event. 

Endogenous factors such as movement have a greater potential for induc-
ing spatial synchronization, especially if the local dynamics are characterized 
by stable limit cycles. Ranta et al. (1998) showed that even relatively low rates 
of movement can induce a near-perfect synchrony of local cycling populations. 
Th is property of nonlinear systems is called phase-locking (Bjornstad 1999). 
However, populations coupled by movement will remain uncorrelated if they are 
characterized by locally chaotic dynamics.

Oscillatory dynamics in ecology arise most often as a result of population 
interactions between predators and prey (or, more generally, between ecological 
consumers and their resources, see Turchin 2003). It is important to remember 
that both predators and prey can move around. Depending on the dynamical 
nature of interaction (e.g., stable equilibrium, stable limit cycles, or chaos), and 
on the details of movement behavior (e.g., the movement rate of predators rela-
tive to that of prey, ability of predators to track prey aggregations) predator-prey 
systems in space can give rise to second-order spatial covariance, which can take 
the form of traveling waves and static patchy patterns (Bjornstad 1999). We do 
not have space here to give justice to this rich and subtle theory, but wish to men-
tion one kind of behavior, which may be of relevance to world-system dynamics 
—out-of-phase oscillations. 

To illustrate this kind of behavior, consider a two-patch system incorporat-
ing both dispersal and local dynamics, coupling two discrete-time logistic equa-
tions (Hastings 1993). Th is deceptively simple system is capable of a surprising 



Peter Turchin & Th omas D. Hall48 Spatial Synchrony Among and Within World-Systems 49

diversity of dynamical behaviors, depending on parameter values and initial 
conditions, but we are interested only in the out-of-phase cycles. What happens 
is that when patch 1 is low, patch 2 is high. On the next step, population in patch 
1 grows, plus the patch gets a lot of migrants from patch 2. Th is causes patch 1 
to overshoot its equilibrium, so on the subsequent step the population in it col-
lapses. Meanwhile, patch 2 is aff ected by the same events, except they are shifted 
in phase with respect to patch 1. In other words, the interplay of movement and 
local dynamics leads to the behavior in which population size in each patch goes 
through recurrent cycles, while the total population (the sum of both patches) 
is constant. 

Statistical Issues

Above we have devoted a lot of attention to the issue of what mechanisms 
may bring about large-scale synchrony. Th e implicit assumption here is that we 
are dealing with an empirical case of synchronous dynamics and the question 
is how to explain it. Given limited and noisy data, however, how do we know 
that there is a pattern to be explained, in the fi rst place? Th us, we need to say 
something about the null hypothesis of no synchrony, and how to distinguish 
it statistically from cases where synchrony is present. Th e problem is that two 
unconnected systems, but with similar dynamics (for example, the same period 
of oscillations) may look like they are synchronized, especially in limited runs 
of data. If, purely by chance, the two systems are in phase at the beginning of 
the observed period, they will continue cycling in phase for several oscillations, 
simply because the endogenous dynamics of each system generate cycles of the 
same period. Such a spurious synchrony may continue for some time before the 
systems diverge, either because their periods are not exactly the same, or because 
each system is aff ected by a diff erent set of exogenous infl uences (or because 
of sensitive dependence). If data are limited, however, it may appear as though 
the two processes have been synchronized by some external force. An example 
of spurious synchrony is Charles Elton’s proposal that the lynx cycle in boreal 
Canada is driven by the sunspot cycle. Indeed, during the 19th century, the two 
series were largely in phase. However, eventually the two series diverged, so that 
by mid–20th century they were in a perfect antiphase! Th ese two dynamical 
systems appear to be entirely unconnected, and the spurious synchrony observed 
during the 19th century arose as a result of very similar periods of oscillations 
(both slightly above 10 years). 

Th us, it is important to keep in mind that simple-minded approaches, such 
as measuring cross-correlations and testing their statistical signifi cance with 
some standard formula such as Bartlett’s rule (Chatfi eld 1989) can be very mis-
leading. Standard measures of signifi cance assume that data are independent of 

each other, while in an oscillatory system subsequent data points are positively 
autocorrelated, infl ating the statistical signifi cance of the test. Methods for cor-
recting signifi cance level in such situations exist (e.g., Sciremammano 1979), 
but perhaps the best approach is to use some version of bootstrap (Efron and 
Tibshirani 1993).1

Th e problem is that rigorous approaches require rather long data sets. In 
other words, tests for signifi cant cross-correlation between two oscillatory time 
series are characterized by low power. Th e problem is not lack of cleverness in 
designing powerful tests, but in the nature of the problem. In order to be sure 
that two series are not spuriously correlated may require a very long wait to see 
if they diverge. Fortunately, mechanism-free statistical tests are not the only 
way to investigate spatial synchrony. An alternative (or, rather, complementary) 
approach is to characterize the potential mechanisms that may (or may not) 
bring about spatial autocorrelation. Th us, in practice the question of whether 
there is synchrony and what factors explain it are not completely separable, and 
need to be addressed jointly.

Summary 

Spatial dynamical systems are capable of a very diverse spectrum of behav-
iors. Nevertheless, certain common themes emerge from this review. First, spatial 
synchrony is promoted when two local systems are driven by similar dynamical 
mechanisms. In fact, such systems can exhibit spurious synchrony: even though 
there is no synchronizing mechanism, the two systems oscillate in step because 
they happened to start from similar initial conditions. Second, processes that act 
globally (that is, on a system-wide basis) promote large-scale spatial synchrony. 
Th ird, the type of local dynamics aff ects very much whether any particular 
mechanism will induce synchrony. Systems with stable oscillations can be syn-
chronized over vast geographic distances by global exogenous infl uences. Th e 
degree of synchrony will usually not be very high, because each local system will 
also be aff ected by other exogenous factors that are not highly autocorrelated 

1. A bootstrap is a computer-intensive method for testing hypotheses. Th e basic 
idea is to construct a model for the null hypothesis—in this case, two oscillating system 
without any synchronizing connections. One then generates many data sets similar to this 
situation (e.g., same length of time-series and same degree of noise), and calculates the 
test statistic—here the cross-correlation coeffi  cient. Th en the data-base correlation coef-
fi cient is compared to the bootstrapped correlations. For example, for a p-level of 0.05, 
the data-based statistic should be greater than 95 of bootstrap statistics (see Efron and 
Tibshirani [1993] for more elaborate discussion).



Peter Turchin & Th omas D. Hall50 Spatial Synchrony Among and Within World-Systems 51

the late 2nd and most of the 1st century bce, then the Principate, followed by 
the troubled 3rd century, and fi nally, the Dominate, followed by a fi nal collapse 
in the West during the late 5th century. By contrast, the fi rst peak of the Chinese 
empire (Western Han Dynasty) occurred during the 1st century bce, just when 
the Roman polity was convulsed by a series of civil wars. Th e interregnum 
between the Western and Eastern Han dynasties was during the 1st half of the 
1st century ce, the Eastern Han peak was during the 2nd century, and the collapse 
of the Han dynasty occurred during the 3rd century, which coincided with the 
similar period of the Roman Empire. Th ere was no third secular wave in China, 
however, but a long period of disunity until the Sui-Tang unifi cation. Population 
fl uctuations, as far as they are known, followed closely the sociopolitical dynam-
ics. Th us, while the broad period of 200 bce–200 ce was characterized by large 
empires and high population densities at both ends of Eurasia, fi ner dynamics 
within the period came into and out of phase. 

A similar pattern appears to hold during the next warming period (roughly 
from 700 to 1200 ce). Th e peak of the Early Tang dynasty occurred around 700 
ce. It experienced a collapse during the middle of the 8th century, a restoration 
(the Late Tang dynasty) during the 9th century, and a fi nal collapse in 907. By 
contrast, Carolingian empire reached its peak around 800 ce, and disintegrated 
during the 9th century. During the same period another large Eurasian empire, 
the Caliphate, went through two shorter cycles: Omayyads (661–750) and the 
Abbasids (750 to around 860 when the dynasty became a pawn of the Turkic 
ghulams [slave-warriors]). 

In the next wave, North Sung declined during the 12th century, followed by 
the Mongol conquest of the 13th century (South Sung fell to the Mongols only 
in 1279). Chinese population declined catastrophically during the 13th century 
dynastic collapse and nomadic conquest. By contrast, in Western Europe the 
population peaked around 1300 ce, and the actual collapse occurred only in 
post-Black Death period. Political disintegration in Western Europe, however, 
occurred in patchy manner. Th e German–Roman (later known as Holy Roman) 
Empire disintegrated fairly synchronously with the Sung (although the process 
was by far less violent). On the other hand, France experienced the worst periods 
of civil war around 1370s and 1420s (two peaks of the Hundred Years War), while 
England’s turn came only in 1450–1485 (the Wars of the Roses). By that time the 
Chinese had already expelled the Mongols (in 1368) and unifi ed all China under 
the Ming dynasty. Again, when viewed broadly, the Medieval Warm Period is the 
time of strong empires and dense populations, but when we consider dynamics 
within the period, synchronicity largely falls apart. Th is observation supports the 
idea that climate did not directly drive the secular wave, but rather modifi ed it 

across space (noise, contingency). Endogenous factors such as movement may 
result in a very high degree of synchrony—phase-locking, but the spatial extent 
of such synchronous oscillations may not be great, because the eff ect of move-
ment tends to attenuate rapidly with space. Additionally, endogenous processes 
may cause out-of-phase cycles (anti-synchrony, so to speak).

Finally, chaotic systems are very diffi  cult to synchronize either by exogenous 
or endogenous mechanisms. Only global catastrophes that reset all locations to 
approximately the same initial conditions can impose some (fl eeting) degree of 
synchrony on chaotic systems. Examples include events such as collision with 
a large comet, like the one that is hypothesized to have led to the extinction of 
dinosaurs, or a massive volcanic eruption, such as Th era (see also Weiss, et al. 
1993).

I M PLICATIONS FOR WOR LD SYST E M R E SE A RC H

East-West Synchronicity and Global Climate 

As we mentioned in the Introduction, one empirical pattern that requires 
explanation is synchronous changes of empire sizes in West and East 
Afroeurasia. Ecological theory suggests several hypotheses, the simplest one 
being the eff ect of an exogenous global factor—climate. World-system theorists 
(Chase-Dunn et al 2000) have already suggested this explanation, but historical 
demography (Galloway 1986) presents it in its most developed form. Galloway 
(1986: Figure 6) plotted the solar activity index (considered to be one of the most 
important drivers of global climate change) and populations of Western Europe 
and China from 400 bce to 1800 ce. Dynamics of the solar activity index (see 
Eddy 1977: Table 1) suggests that there was a long-term period of warm climate 
with the peak around 20 bce–80 ad (the Roman Maximum). Th e second such 
warm period was from 1120 to 1280 ce (the Medieval Maximum). Between these 
two maxima, there was a period of cooler temperatures (the Medieval Minimum, 
640 –710 ce). After the Medieval Maximum, solar activity declined (the Spoerer 
Minimum, 1400–1510 ce), then increased somewhat, declined again (the 
Maunder Minimum, 1640–1710), and increased again in the late 19th and 20th 
centuries. As noted by Galloway, populations of Western Europe and China 
increased and decreased roughly in parallel with solar activity.

Th e Roman Maximum in solar activity coincides with two great empires 
dominating the eastern and western ends of Eurasia: Han China and the Roman 
Empire. However, while this is a remarkable correlation when examined at a 
coarse time scale, fi ner scale resolution does not reveal a close parallelism in the 
sociopolitical dynamics of the two empires. Th e Roman polity went through 
three secular cycles: the Republic, followed by the decentralization phase during 



Peter Turchin & Th omas D. Hall52 Spatial Synchrony Among and Within World-Systems 53

in a way that imposed a certain degree of synchrony between the East and the 
West.2

The 17th Century Crisis 

What is highly interesting is that the next wave of state collapse—the so-
called crisis of the 17th century—aff ected practically all Eurasian empires (apart 
from the South Asian region) essentially simultaneously (Goldstone 1991). Th e 
“long 17th century” began ca. 1570 with religious warfare in France, the Dutch 
Revolt, the troubled second half of Ivan the Terrible’s reign in Russia, and the 
daimyo-led civil war in Japan. During the fi rst half of the 17th century, Russia 
went through the Time of Troubles, Central Europe was devastated by the 
Th irty Year War (during which Germany lost a third to half of its population), 
the Ming dynasty fell in China and was replaced by the Manchus, Spain experi-
enced the Portugese and Catalonian revolts, the Ottoman Empire almost disin-
tegrated, and the English decapitated their king. Th e 17th century was also the 
period of widespread famine and epidemics. All regions of Eurasia (apart from 
India and Iran) experienced population declines, in some cases quite extreme (as 
in Central Europe). 

Th e crisis in the 17th century was unique in the history of Eurasia. Th e next 
wave of state collapse was not as tightly bunched. Th us, the Age of Revolutions 
in continental Europe started with the French revolution of late 18th century, and 
ended with the revolutions of 1848–1849. By contrast, Russia, China, Turkey, 
and Iran went through their revolutions during the early 20th century. England 
entirely avoided state collapse during the 19th century, but had to let its empire 
go in the 20th century (Ireland in 1920, India in 1947, Africa in early 1960s). In 
fact, it appears that the revolutions in the 19th – early 20th centuries are “echos” 
of the 17th century; oscillations that began to diverge as a result of, perhaps, 
slightly diff erent periods, and an accumulation of historical accidents peculiar to 
each specifi c polity.

Why was the 17th century crisis Eurasia-wide? One possible explanation 
is again the global climate. Th e 17th century saw a trend to lower tempera-
tures, which in most Eurasia (apart from the Indian subcontinent) should have 
resulted in decreased harvests. According to the demographic-structural theory, 

the root cause of crisis is in the imbalance between population numbers and the 
productive capacity of the land. Th is imbalance can be achieved either by exces-
sive population growth, or by a rapid decline in the productive capacity of the 
environment, for example, as a result of a string of colder, wetter years. Note that 
in this scenario climate change does not directly cause state collapse: its eff ect 
is, rather, mediated by social structure (population numbers in relation to the 
productive capacity of land). 

The Mongol conquest as a “resetting catastrophe” 

Another explanation of the 17th century crisis would look back to the events 
during the previous secular wave. Most world-system theorists agree that the 
Mongol conquest in the 13th century was a key event in the Afroeurasian his-
tory. Not only did the Mongol Empire briefl y connect East with the West, it also 
started a series of remarkably coherent oscillations in Central Asia and adjoining 
regions. 

Th e huge territory conquered by the Mongols during the fi rst half of the 
13th century contained four large “cultural areas” inhabited by settled people: 
China, Transoxania, Persia (including Mesopotamia), and eastern Europe. 
From the middle in the 13th century, these four areas were ruled by four separate 
Chingissid dynasties: (1) Kublai and his successors (the Yuan dynasty) in China; 
(2) Jagataids in Turkestan (which included Transoxania); (3) Hulagu and his 
successors (Il-Khans) in Persia; and (4) Juchids (Batu and his successors) in 
the Kipchak Steppe (the Golden Horde). According to the theory advanced 
in Turchin (2003: Chapter 7), these four polities should be subject to the Ibn 
Khaldun cycles of around a century in period. 

Th e Ibn Khaldun cycle, named after the 14th century Arab sociologist who 
fi rst described it, is a variety of a secular wave that tends to aff ect societies with 
elites drawn from adjacent nomadic groups. Th e dynamics of the Ibn Khaldunian 
world-system are determined by the interaction between a sedentary, agrarian 
state and surrounding steppe or desert pastoral “tribes.” Th e sedentary state 
region is the site of recurrent state building/collapse episodes. It is inhabited by 
indigenous commoner population, that provides the productive basis of the soci-
ety. Th e steppe or desert is inhabited by stateless tribes that periodically conquer 
the civilized region and establish a ruling dynasty there. Steppe or desert tribes, 
thus, supply the elites (nobility) for the sedentary state. Ibn Khaldun cycles tend 
to operate on a faster time scale, so that their period is about 4 generations, or a 
century.

Th e events in Eurasia after the Mongol conquest appear to provide a reason-
able fi t to this theory:

2.  One anonymous reviewer noted that Galloway’s data focuses on long-term fl uctu-
ations, of much longer period than city-size or empires. We actually concur with obser-
vation. Th us, this type of climate change may not be the mechanism for East—West Asia 
synchrony. Still, it illustrates how other climatic changes, occurring on a shorter scale, 
might produce such synchrony.



Peter Turchin & Th omas D. Hall54 Spatial Synchrony Among and Within World-Systems 55

1. In China, the civil war between the successors of Kublai broke out in 
1328. The 1350s saw numerous revolts led by native leaders, and in 1368 
one of these leaders expelled the Mongols and established the Ming 
dynasty. 

2. Turkestan was unified until 1333–1334, when a nomad-led insurrection 
broke out against the Jagataid regime in Eastern Turkestan. By 1350 
the power in Transoxania passed into the hands of local Turkic nobles. 
After a period of turmoil, Timur established a new dynasty. Timur 
unified Transoxania in 1379, and conquered Iran during the 1390s. The 
Timurids dynasty also lasted about a century. In 1469 Persia was lost 
to the White Sheep Horde, while Transoxania splintered between 
warring branches of Timur’s descendants. 

3. The Persia of Il-Khans underwent dissolution in 1335. After a period 
of civil war it was conquered by Timur (see above). When the 
Timurids lost Persia in 1469, another turbulent period followed, and 
eventually, by 1500, Persia was unified by a native dynasty (Safavids).

4. A similar course of events occurred in the Kipchak Steppe. The 
Juchids’ rule ended in 1359, when the Kipchak steppe fell into anarchy. 
After a period of civil war, the Golden Horde underwent a revival 
under Timur Qutlugh, who re-consolidated his dominion over Russia, 
although a series of punitive expeditions were required during the 
early 15th century to keep the tribute flowing. In the middle of the 
15th century, however, the revived Golden Horde began disintegrating 
again. The first part to secede was the Crimean Khanate in 1430. 
The Khanates of Kazan and Astrakhan followed (in 1445 and 1466, 
respectively). The Moscovite polity went through its own period 
of civil war during the second quarter of the 15th century, which, 
curiously, coincided with the civil war on the steppe that lead to the 
final splintering of the Golden Horde. As soon as the civil war ended, 
Muscovy became de facto an independent state (de jure independence 
had to wait until 1480). 

Th is is an alternative way of viewing the analyses of Barfi eld (1989) and 
Chase-Dunn and Hall (1997: Ch. 8). As Barfi eld notes, however, the Mongol 
conquest was somewhat exceptional with respect to the usual strategy employed 
by the central–Asian nomads. First, the Mongols succeeded in capturing much 
vaster regions, due in the main part to innovations in organization by Chinggis. 
Second, instead of merely exploiting sedentary states via the outer frontier strat-
egy, the Mongols actually conquered large empires and had to run them. Finally, 

the break-up grew out of Mongol rules of dynastic succession that emphasized 
both lateral and linear descent. Th ese extensive Mongol conquests also disrupted 
the Ibn Khaldun cylces, in eff ect resetting them in several diff erent areas simul-
taneously. 

Among nomads this contradiction produced confl icts that both allowed 
one strong leader to emerge and tended to eliminate rivals. While useful for 
pastoralists, this multifaceted civil war strategy for succession is disastrous for 
states. Chase-Dunn and Hall (1997: Ch. 8) argue that the issue was not that the 
Mongols could not change their system of succession—they clearly knew how 
states worked. Rather, it was that they could not change their system and remain 
Mongols. To have a more orderly system of succession like those found in states, 
would have destroyed the very mechanisms that allowed leaders like Chinggis to 
emerge. Th e Ottomans, however, seem to have solved this problem. Th ey insti-
tutionalized succession so that change happened very quickly—one heir wins, 
all others are strangled with a silken chord. As a result, the secular cycles of the 
Ottoman Empire were 200–300 years long. 

To summarize, all Chinggisid dynasties went through typical Ibn Khaldun 
cycles of about a century in period, and all experienced collapse at approximately 
the same time. In China, a native dynasty expelled the Mongols after one cycle, 
while in Russia and Iran the steppe dynasties went through two cycles before 
giving way to native rulers. Incidentally, the central Eurasian steppes continued 
to undergo Ibn Khaldun cycles, until their conquest and division between the 
Russian and the Chinese empires (Barfi eld 1989). What is remarkable is the 
degree of synchrony in the socio-political dynamics of the settled regions ini-
tially conquered by the Mongols in the 13th century. One possible explanation of 
this pattern is that an initial catastrophic event—the Mongol conquest—reset 
all regions to approximately the same initial conditions. Th ereafter, each region 
oscillated as a result of its endogenous dynamics, but because oscillations were 
driven by similar mechanisms, political collapses occurred at about the same 
time. 

The Black Death as a Resetting Catastrophe 

Returning to the fates of Eurasia as a whole, the continent-wide spread of 
Black Death from its endemic region (Central Asia) may have been another 
resetting catastrophe. Th e Black Death pandemic is widely credited to the 
Mongol conquest, and the resulting density and speed of traffi  c, trade, raids, 
and communications across Central Asia—for which the Mongols are widely 
famous. Th e increase in traffi  c made it possible for various vectors to survive 
to spread various pathogens, notably the plague bacteria, over large distances 



Peter Turchin & Th omas D. Hall56 Spatial Synchrony Among and Within World-Systems 57

shocks, global in their eff ect on most of Eurasian polities, that caused secular 
oscillations across the continent to get in phase. Th e repeated nature of these 
shocks, and especially that they happened to be three centuries apart (leading 
to a potential resonance eff ect) may go a long way to explaining the remarkable 
degree of Eurasia-wide synchrony during the last millenium.4

Spread of Pathogens, Ideas, and People

Th e above discussion has already brought in the disease as one potentially 
synchronizing factor. Th e Black Death, however, was a rather unsual episode in 
the history of epidemics, because of its global (within Eurasia) eff ect. It was not 
a unique occurrence (for example, the fl u pandemic of 1911 was even more global 
in its eff ect), but most diseases tend to spread in a more local fashion. Recent 
research on measles epidemics during the 20th century (when we have excel-
lent data sets, e.g. for England, see Grenfell et al. 2001) has traced how disease 
spreads from town to town. In general, we would expect that epidemics would be 
an important synchronizing factor within world-systems, but except for unusual 
circumstances they will not spread between world-systems. One such exception, 
as noted above, would be the rapid spread of the Black Death within Eurasia 
during the 1330s and 40s (McNeill 1976). 

Cultural infl uences, innovations, and fads could also spread in a manner 
similar to epidemics. A dramatic example is the wave of revolutions that spread 
through western and central Europe in 1848–1849. Other potential examples 
include the spread of agricultural innovations (which elevate the carrying capac-
ity) and birth-control practices (which reduce population growth rate). 

Finally, actual population movements between agrarian polities are prob-
ably too slow to synchronize them, although within a polity they should play 
an important role (e.g. migration to urban centers at the end of population 
increase phase). We can evaluate the rate of migration by considering histori-
cal instances of colonization movement, such as the Iberian Reconquista or the 
colonization of European steppe by the Russians. Incidentally, both of these 
examples involved interpolity migration. Th e Reconquista resulted in a major 
transplantation of Spaniards from the north into the reconquered south, but 
also in massive movements of the French settlers into the north (Bartlett 1993:

(McNeill 1976).³ Th e Mongol conquest, however, was largely complete by mid-
13th century, while the Black Death struck a hundred years later. Why was there 
such a delay? We do not know, but one hypothesis may explain it: that disease 
tends to spread particularly rapidly during the decentralization phase of the 
secular cycle (this was mentioned above). If this hypothesis is correct, then it was 
not the fact of Mongol unifi cation per se, but that simultaneous disntegration of 
various Mongol polities that threw the Great Steppe in turmoil, causing large 
numbers of people to move back and forth, and thus spread the Black Death to 
both ends of the continent. Th at is, as suggested earlier, these social processes 
transformed what might have been an exogenous-global mechanism in to an 
endogenous-global mechanism.

Th e Black Death caused Eurasia-wide turmoil simply by its terrifying 
impact on populations. But it also probably had an additional eff ect that tended 
to bring distant polities in phase with each other. Epidemics generally infl ict 
a higher mortality on lower strata of society, while the elites tend to escape 
relatively lightly. A side eff ect of an epidemic, therefore, is to increase imbalance 
between the productive strata and elites. According to demographic-structural 
theory, excessive elite numbers are a highly destabilizing factor for any society. 
Th us, polities experiencing a severe epidemic should be more likely to go into a 
collapse than polities avoiding such a fate. Note that the logic of this argument is 
similar to the hypothesized connection between climate change and sociopoliti-
cal stability made above: both disease and climate are assumed to act indirectly, 
by aff ecting social structure. 

Th e 14th century, therefore, was similar to the 17th century in that much of 
Eurasia was in crisis, and in that it was the century of widespread population 
decline. (Additionally, it was the time of decreasing temperatures, leading to the 
Spoerer minimum). Th is raises the possibility that the crisis in the 17th century 
was simply an echo of the 14th century. A more wholistic view, however, would 
be to consider the Black Death and the two minima of solar activity as repeated 

3. Chase-Dunn and Hall (1997, Chs. 6 and 8) present this argument. Th ey further 
note (p. 116) contra to Goldstone’s claim that there is little or no world-system eff ect 
here, that the Black Death spread precisely along the pathways of trade that formed the 
Afroeurasian-wide world-system. In situations like this where world-systems that were 
either isolated, or only connected at the two widest levels (information and prestige 
goods), begin to merge, the endogenous—exogenous distinction becomes particularly 
muddy. Th is is where a more quantitative (and dynamical) approach is called for. For 
example, we need to obtain numerical estimates of how the spatial scale of information 
and prestige goods exchange fl uctuated during this period.

4. But we should not overstate the observed degree of synchrony. Secular waves do 
not have very regular period of oscillations, so we should expect divergence after just one 
or two cycles after a resetting perturbation. Perhaps that is why the Age of Revolutions 
occurred in Western Europe earlier than in other parts of Eurasia. 



Peter Turchin & Th omas D. Hall58 Spatial Synchrony Among and Within World-Systems 59

179). Populations moving into the European steppe came from Russia, Poland-
Lithuania (Ukrainians and Jews) and even Germany. Both processes were very 
slow, occurring on the time scale of centuries. Iberian Reconquista occurred in 
two main pushes, 1080–1150 and 1212–1265 (Bartlett 1993). Russian colonization 
started with the conquest of Kazan in 1552 and continued after the incorporation 
of Crimea in 1783. 

Nomadic populations, however, may be an altogether diff erent story (see 
Barfi eld 1989 and Frank 1992). McNeill (1963, 1987) suggests that diff ering 
ecological conditions created a “steppe gradient” that tended to encourage move-
ment of Central Asian Steppe nomads to the west whenever events in the east 
disrupted their lifeways.⁵ Such disruptions could be socio-political, for instance 
temporary success of Chinese military campaigns against them, or climatic, in 
quality of grazing, or a sudden growth in population (of animals or people or 
both) that strained the carrying capacity of the local environment (again, these 
in turn might have social and/or climatic sources). Th e net eff ect is one of many 
relatively short-distance movements that create a net westward migration across 
Central Asia toward the west. Because nomads are much more mobile than agri-
culturalists, disturbances at the east end of the Great Steppe can rapidly propa-
gate to the western end, probably on the time scale of years and decades.

Asynchronous South Asia

If we consider the Steppe Gradient, along with Jared Diamond’s (1999) 
observation that absent formidable barriers, east—west movement along similar 
latitudes (and therefore similar climates) is easier than north—south movement 
that must traverse signifi cantly diff erent ecological zones, we can construct one 
explanation for the puzzling fi ndings of Chase-Dunn et al. (2000) that east and 
west Asia synchronize, but not south Asia. Th is is all the more so, since the 
Himalayas are a formidable barrier to contact and exchange. To be sure, there has 
been extensive traffi  c across the Himalayas, but it may not have been suffi  cient 
to synchronize the various systems. Steppe nomads seldom made incursions into 
south Asia. Central-Asian infl uence on India was transmitted indirectly via the 
Iranian plateau (for example, the Moguls, whose name is a corruption of the 
“Mongol,” conquered India from Afghanistan). 

Two additional factors give tangential support to this supposition. First, 
while bulk goods, large populations, and armies rarely moved between South 

and Central Asia, travelers and ideas did so extensively. Th e spread of Buddhism 
and of silk and other luxury goods are familiar examples. Both illustrate the criti-
cal diff erence between the various boundaries of world-system, bulk goods and 
the military-political exchanges on the one hand versus information and luxury 
goods on the other. Second, south Asia had tremendous eff ects on southeast 
Asia. Again there is the spread of Buddhism, but also other cultural features, and 
trade in luxury goods. Yet, if the east—west vs. north—south diff erential is at 
work, there should be some synchrony between south Asia and Southeast Asia, 
and less synchrony between Southeast Asia and east Asia. Unless, of course, the 
somewhat lower barriers between east and southeast Asia did allow suffi  cient 
contact and exchange to promote synchrony. 

Th e second explanation for asynchronous dynamics in South Asia is the 
eff ect of climate. Cold, wet, climate leading to problems in most of Eurasia 
might have been a boon for South Asian agriculturalists. Th e two hypotheses, 
movement (of people, goods, and ideas) and global climate are not mutually 
exclusive. 

A possible third explanation for asynchronous dynamics in South Asia is 
that local, i.e., endogenous, processes may have diff ered signifi cantly between 
south Asia and the rest of Asia. Th is would seem less likely, but it is a possibility 
that warrants consideration. 

Currently we do not have suffi  cient data to discriminate among these expla-
nations. Still, the arguments and analyses presented here suggest ways these 
issues might be addressed empirically. 

CON LUSIONS A N D DI R E C TIONS FOR F U T U R E R E SE A RC H

Much (if not all) of our discussion of potentially synchronizing factors and 
their interplay with sociopolitical cycles in Eurasia is highly speculative. However, 
these speculations constitute a powerful argument for the relevance and utility 
of further systematic, theoretical and empirical extensions of ecological theories 
to world-systems analysis. Our key conclusion is that this synthesis of these two 
widely separated theoretical traditions can lead to much more rigorous explora-
tion and testing of theories of the processes of world-systemic change.

Our goal in this paper was not to provide answers, but to generate hypoth-
eses that can be subsequently tested with data. Th us, the last topic that we need 
to discuss here is how such empirical testing might be accomplished. 

We argue that explicit mathematical models are necessary ingredients in 
this empirical program. Th e reason is that nonlinear dynamics such as cycles 
are suffi  ciently complex in themselves, but when we add a spatial component, 
the resulting problems become much too diffi  cult to be grasped by the “naked” 

5. However, in the fi rst millennium bce the predominant direction of movement was 
to the east, leading to the spread of Indo-European nomads (see McNeill 1987, pp. 265-
67, especially the map on p. 266).



Peter Turchin & Th omas D. Hall60 Spatial Synchrony Among and Within World-Systems 61

human mind. What is needed is mathematical formalism to be able to state the 
problem precisely—as models—and computers to solve the models. As we men-
tioned in the Introduction, some social scientists might object to mathematical 
models on the grounds that they oversimplify the reality. We seek to understand 
such complex systems by building models systematically, starting with simple 
assumptions and then adding more complex processes, as they are warranted by 
data. 

Th e power of mathematical models is that they make quantitative predictions 
that can be compared to data using standard statistical methods. One statistical 
methodology for investigating spatial synchrony is the autocorrelation analysis. 
Th e correlation coeffi  cients calculated by Chase-Dunn et al (2000) between 
empire sizes in the Central, East Asian, and Indic PMNs was a very useful step 
that has already yielded highly suggestive results, but it can be improved upon. 
First, we can estimate spatial autocorrelation functions (ACF), that is, how the 
correlation coeffi  cient changes with distance between the polities. Diff erent 
synchronizing mechanisms leave diff erent “signatures” in the ACF. Th us, a local 
process should result in an ACF that declines with distance: high correlation 
between territorial dynamics if polities are located near each other, and low or 
no correlation for polities separated by great distances. In other words, the scale 
at which ACF becomes indistinguishable from 0 is related to the spatial scale at 
which a process operates. By contrast, a global mechanism should result in no 
relationship between the correlation coeffi  cient and distance. 

Th e approach sketched above tests a qualitative prediction—the question 
of whether the ACF declines with distance has a binary answer (yes or no). A 
more informative approach would address the quantitative aspects of ACF, such 
as the spatial scale at which it becomes indistinguishable from zero. Th us, an 
even stronger test would be to construct a mathematical model of synchronous 
oscillations, estimate the spatial scale at which the postulated factor operates (for 
example, how fast and how far epidemics spread), and then make quantitative 
predictions about the shape of the ACF. 

Furthermore, spatial autocorrelation analysis is not the only statistical 
approach that could be used. Very useful insights can be obtained by examining 
cross-correlations between two or more factors. For example, we can investigate 
how political dynamics are correlated (in space and time) with disease dynamics. 
Again, qualitative predictions can be made readily (for example, no crosscorrela-
tions between polity size dynamics and disease probably means that these two 
factors are unrelated to each other). However, more progress will be made if we 
can make quantitative predictions using explicit models. 

Th e approach that we are advocating needs several ingredients for success. 
On the empirical side we need a more detailed database of territorial dynamics of 

all polities within the Afroeurasia (omitting, perhaps, ones that are smaller than 
a certain threshold).⁶ We also need data on spatio-temporal dynamics of any 
other variables that may aff ect synchrony, such as epidemics and climate. Some 
databases already exist, e.g. Biraben’s (1975) compilation of places aff ected by the 
Black Death in Europe and the Mediterranean. Certain kinds of data, such as 
climate change, are in the process of being developed in other disciplines and all 
we need to do is wait (e.g., see Mann 2000). Other data will probably need to be 
developed from scratch (here recent developments in historical GIS may be of 
great help). 

On the modeling side we need a better understanding of processes that may 
cause oscillations and synchrony. What would be particularly useful in the study 
of synchrony is estimates of the rates of movement for diff erent “things”—goods, 
pathogens, ideas, and people. 

Th e research program combining mathematical theory with sophisticated 
statistical approaches is costly—it requires a large quantity of data and some 
changes in research practice. However, we think that such an investment is 
warranted. Recent results that suggest sociopolitical cycles and wide-scale syn-
chronicity within the Afroeurasia are “intoxicating,” to use the word of Robert 
Denemark (2000). If there are regular empirical patterns, then history is not just 
a collection of accidents. But unraveling the complex interactions causing the 
empirical regularities will require sophisticated quantitative tools.

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