6237 SOCIAL SCIENCE HISTORY 24:4

The world-systems perspective was invented for modeling and interpreting the expansion and deepening of the capitalist regional system as it emerged in Europe and incorporated thewhole globe over the past 500 years (Wallerstein 1974; Chase-Dunn 1998; Arrighi 1994). The idea of a core/periphery hierarchy composed of ‘‘advanced’’ economically developed and powerful states dominating and exploiting ‘‘less developed’’ peripheral regions has been a central concept in the world-systems perspective.1 In the last decade the

world-systems approach has been extended to the analysis of earlier and smaller intersocietal systems. Andre Gunder Frank and Barry Gills (1994) have argued that the contemporary global political economy is simply a continuation of a 5,000-year-old world system that emerged with the first states in Mesopotamia. Christopher Chase-Dunn and Thomas Hall (1997) have modified the basic world-systems concepts to make them useful for a comparative study of very different kinds of systems. They include very small intergroup networks composed of sedentary foragers, as well as larger systems containing chiefdoms, early states, agrarian empires, and the contemporary global system in their scope of comparison.
All world systems with at least a chiefdom level of political organization exhibit a pattern of the rise and fall of large polities. Among chiefdoms this pattern has been referred to as ''cycling.'' In state-based systems it is known as the rise and fall of empires. And in the modern system it is called the ''power cycle'' or the ''hegemonic sequence.'' This article reexamines the question of synchronicities of rise and fall in systems linked only by verylong-distance prestige goods trade. Earlier research found that increases and decreases in the territorial sizes of empires and the population sizes of cities were highly correlated in East Asia and West Asia/Mediterranean regions from about 600 b.c.e. to 1500 c.e. (Chase-Dunn and Willard 1993). Though data were somewhat scarce for South Asia, it appeared that Indic civilization did not rise and fall in tandem with the East and the West. In this article we report an improved test of the synchronicity of empire sizes and the different pattern found in India.

World-System Cycles: Rise and Fall and Pulsations
Comparative study reveals that all world systems exhibit cyclical processes of change. Chase-Dunn and Hall (1997) focus on two major cyclical phenomena: the rise and fall of large polities, and pulsations in the spatial extent of interaction networks. What they call ''rise and fall'' corresponds to changes in the centralization of political-military power in a set of polities. They note that all world systems in which there are hierarchical polities experience a cycle in which relatively larger polities grow in power and size and then decline. This applies to interchiefdom systems as well as interstate systems, to sys-tems composed of empires, and to the modern rise and fall of hegemonic core powers (e.g., The Netherlands, Britain, and the United States). Very egalitarian and small-scale systems such as the sedentary foragers of northern California (Chase-Dunn and Mann 1998) do not display this kind of cycle, however.
The unit of analysis for the rise-and-fall process is the political-military network (PMN) or ''polity system,'' a set of polities that are directly (or not too indirectly) interacting with one another. These polities can be bands, tribes, chiefdoms, states, or empires. The terms states system or interstate system are used when states are present, and interchiefdom system indicates a set of polities in which the chiefdoms are present, but not states.
Chase-Dunn and Hall also note that all systems, even very small and egalitarian ones, exhibit cyclical expansions and contractions in the spatial extent of interaction networks. They develop a schema for spatially bounding regional world-systems in which smaller bulk goods networks (BGNs) are contained within larger political-military networks (PMNs), prestige goods networks (PGNs), and information networks (INs). They posit the hypothetical pulsation of BGNs, PMNs, PGNs, and INs. By this they mean that the spatial scale of interaction increases and then decreases at each of these network levels. Interaction densities increase because there is more exchange and events at any single point have consequences over a greater distance.Thus both the amount of interaction and the range of interaction increase and then contract (Chase-Dunn and Hall 1997: Figure 10.

2)
This article is not about pulsation. But pulsation may be systematically related to the phenomenon under study here-the rise and fall of politicalmilitary centralization within systems of polities. The main unit of analysis in this article is the PMN-a political-military network in which states fight and ally with one another. The principal phenomenon we are investigating is the discovery that widely separated PMNs exhibit a curious synchronicity in the rise and fall of large empires. The PMNs under study herethe West Asian/Mediterranean (Central) region, South Asia, and East Asia -were parts of a larger prestige goods network (PGN), but they did not, with a few exceptions, make war on one another directly until recent centuries.
The period of time we focus on here is the last 2,500 years, but we end our dataset in 1800 c.e. 2 This is because the separate PMNs became merged into a larger, nearly global PMN in recent centuries and because the rise of the modern colonial empires creates a temporal trend in all regions that we wish to avoid in analyzing cycles of rise and fall. The long-term trend toward larger polities is important, but it is not our main focus here.

Qualitative Differences in Rise and Fall
Close examination reveals that rise and fall has different characteristics and different causes in distinct types of world systems. The rise and fall of chiefdoms is analytically similar to the rise and fall of empires and the rise and fall of hegemonic core powers. All of these processes are related to the stability of institutions for extracting resources from distant regions. But there are also important differences, in addition to the obvious difference of scale. David G. Anderson's (1994) study of the rise and fall of Mississippian chiefdoms in the Savannah River valley provides an excellent and comprehensive review of the anthropological and sociological literature about ''cycling,'' the processes by which a chiefly polity extends its control over adjacent chiefdoms and erects a two-tiered hierarchy of administration over the tops of local communities. At a later point these regionally centralized chiefly polities disintegrate back toward a system of smaller and less hierarchical polities.
Chiefdoms rely more completely on hierarchical kinship relations, control of ritual hierarchies, and control of prestige goods imports than do the rulers of true states. States have specialized organizations for extracting resources that chiefdoms lack. And states and empires in the tributary worldsystems were more dependent on the projection of armed force over great distances than the modern hegemonic core states have been. The development of commodity production and mechanisms of financial control as well as further development of bureaucratic ''techniques of power'' have allowed modern hegemons to extract resources from faraway places with much less overhead cost.
The development of techniques of power have made core/periphery relations ever more important in competition among core powers and have altered the way the rise-and-fall process works in other respects. One big difference between the rise and fall of empires and the rise and fall of modern hegemons is in the degree of centralization achieved within the core. Tributary systems alternate back and forth between a structure of multiple and competing core states, on the one hand, and corewide (or nearly corewide) empires, on the other. The modern interstate system experiences the rise and fall of hegemons, but these never take over the other core states to form a corewide empire, because modern hegemons are pursuing a capitalist rather than territorialist form of accumulation.

Previous Findings
While examining the relationships within PMNs of urban growth and decline, Chase-Dunn and Alice Willard (1993) accidentally discovered that city growth and changes in city size distributions seemed to occur synchronously in the Central (West Asian and Mediterranean) and East Asian PMNs. 3 Chase-Dunn and Hall further confirmed this interesting synchronicity by studying growth and decline periods of empires in East Asia and the West Asian region between 600 b.c.e. and 1800 c.e. (Chase-Dunn and Hall 1997: Figures 10.7-9). Chase-Dunn and Hall used the data on the territorial sizes of empires coded by Rein Taagepera (1978aTaagepera ( , 1978bTaagepera ( , 1979Taagepera ( , 1986Taagepera ( , 1997.Taagepera used historical atlases and histories to estimate the territorial sizes of empires from 3000 b.c.e. to the present. Chase-Dunn and Hall noted that the correlation between the Central and East Asian empire sizes is somewhat inflated by the fact that both were temporarily united by the Mongol Empire in the thirteenth century. This correlation is also more positive because there is a general upward trend in the sizes of empires over time. When the time trend was statistically controlled (by computing a partial correlation that controls for year) and when the Mongol Empire was removed from the calculation, the correlation of Central and East Asian empire sizes remained quite positive (Pearson's r = .61) and statistically significant (Chase-Dunn and Hall 1997: 218).
These findings suggest the possibility of systemness in the Afro-Eurasian system far earlier than most historians would imagine. This is a hypothesis strongly argued by Frank and Gills (1994). But the 400-year cycles of growth and decline posited by Frank (1993) are not well supported by the data on city and empire growth (Chase-Dunn and Hall 1997: Figures 10.5-6). It was also found that the intermediate Indic PMN did not experience a similar sequence of growth and decline phases in city populations (Chase-Dunn and Hall 1997: Figure 10.11). The causality of these synchronous cycles in distant PMNs is not well understood. We also examined changes in city and empire sizes for the Mesopotamian and Egyptian PMNs in order to see if these revealed synchronicity. Like East and West Asia, these were separate PMNs linked by a larger PGN. But we found no synchronicity between Egypt and Mesopotamia (Chase-Dunn and Hall 2000). Both PMNs experienced cycles of rise and fall, but these cycles were not in phase with one another, despite having been linked into a larger PGN.
We will discuss possible explanations of the indicated synchronicity in the last part of this article. But the main task here is to improve upon the analysis of the Taagepera data in order to confirm or disconfirm the indicated synchronicity and to further investigate Indic exceptionalism. To do this we reworked and fine-tuned our analysis of the Taaegepera data specifically to test for synchronicity. In the original analysis presented in Chase-Dunn and Hall (1997) we used the information contained in Taagepera's published and unpublished articles to create a dataset with empire sizes at 50-year intervals. This involved interpolating from the years given in Taagepera to the closest 50-year time points, a possible source of error. It is possible that this kind of error might have produced an apparent synchronicity: any two systems that are oscillating might appear to be in sync with one another if the time measurement is too crude.
To gain a more exact estimation of the timing of events that changed empire sizes, we created a new dataset with 10-year intervals. This allowed us to code the Taagepera years with much less error. We still have a great deal of interpolation, but the real numbers are much closer to the actual years in which historical events occurred. This provides a much stronger test of the hypothesis of synchronicity.
We also made another change to improve our ability to test the synchronicity hypothesis. We note that the Afro-Eurasian world system came together in a series of spasms, rather than in an abrupt expansion or a long slow expansion (Chase-Dunn and Hall 1997: chap. 8 and Figure 10.2). The bestknown spasm was the Mongol Empire, which briefly united the East Asian and Central PMNs from c.e. 1210 to c.e. 1300.When we include empires that encompass more than one of our PMNs, we are building in a correlation of empire sizes because the same empire is included in more than one PMN. In order to eliminate this possible source of specious temporal correlation, we created variables that removed the empires that extended into more than one of the PMNs under study, substituting the largest nonshared empire in each region for the shared empire.
The earlier results were based on examining the sizes of the largest empires in each PMN. In this reanalysis we also coded the second largest empire in each PMN in order to see if these also exhibit synchronicity and to calculate a two-empire size distribution measure. This latter is the ratio of the size of the largest empire to the sum of the largest and second largest. This is supposed to indicate the relative centrality of a local system using empire sizes as an indicator. It is analogous to a city size distribution. It would have been desirable to have also third and fourth largest empires to calculate an empire size distribution, but these data are available for only a few time periods. We settled for a two-empire measure of the empire size distribution. A sample from our dataset is provided in Table 1. This table shows the first 15 time points and the empire sizes for the largest and second largest empires in the Central PMN. 4 It should be noted that several other states or polities are always present in each PMN, but we do not have estimates of their territorial sizes. We are not claiming that only one or two states exist; rather, we are using the data we have on the largest states as a window on the PMN.
In addition to improving our data, we also decided to use stronger tests of synchronicity and better methods for detrending. As mentioned above, the long-term trend toward larger empires builds in a degree of correlation over Figure 1 Largest empires in the Central PMN Sources: Taagepera 1978bTaagepera , 1979Taagepera , 1986 time. The method used by Chase-Dunn and Hall to remove the trend was to calculate a partial correlation controlling for year. In the present analysis we use two additional techniques for detrending.We calculate first differences change scores by subtracting the value in the year before the current year. This reduces autocorrelation. And we also detrend by regressing our empire size variables on year and then computing the correlations of the residuals.

Results of the Reanalysis
First we will discuss the three PMNs separately. Figure 1 shows the rise and fall of the largest empires in the interstate system that was located in Western Asia and the Mediterranean. We follow David Wilkinson in calling this the ''Central System'' because it developed states first and eventually enveloped all the other systems. Figure 1 labels only a few of the largest empires, but all of the largest empires were plotted in this graph. Both the long-term upward trend in empire size and the sequential rise and fall can be seen. As with Figure 2 Largest two empires in the Central PMN Sources: Taagepera 1978bTaagepera , 1979Taagepera , 1986 many ''social cycles,'' the rise and fall phenomenon does not approximate a sine wave; rather, it is an irregular oscillation with a varying period and magnitude. The size and duration aspects of empires are analyzed and discussed in Taagepera's articles.
Generally, empires that rise fast also decline fast and do not last long. It is notable that all the largest empires, and the ones that establish new size records, are dynasties that came from semiperipheral regions.This is the phenomenon of semiperipheral marcher states, discussed by Chase-Dunn and Hall (1997: chap. 5). Wilkinson (1991) notices another interesting patternthat of the ''forerunner.'' Often a semiperipheral conquering state will make a grand attempt that fails, while an immediately subsequent attempt by a different empire-builder succeeds. Figure 2 shows the territorial sizes of the two largest empires in the Central PMN. It appears to the eye that the two largest empires rise and fall together, and indeed this is supported by the correlation of .62 between these empires. Rather than empire sizes being a zero-sum game, it would appear that empires get larger and smaller together. The temporal relationships between the largest and the second largest empires in the East Asian and the Figure 3 Largest empires in the East Asian PMN Sources: Taagepera 1978bTaagepera , 1979Taagepera , 1986 Indic PMNs are not as positive (Pearson's r = .26 and .35), but neither are they negative.
The East Asian PMN shows a similar pattern of long-term upward trend and shorter rises and falls ( Figure 3). Note that the Mongol Empire appears in both Figures 1 and 3 because the Mongols brought East and West Asia temporarily into the same PMN.
The Turks that appear in Figure 3 are the Uighurs, another Central Asian group that became famous in China long before their entrance into the Central PMN as the Ottoman Empire. The Indic PMN looks visually quite different from the Central and East Asian PMNs (Figure 4). The early emergence of states in the Indus River valley is not included because there is no reliable way to estimate the territorial sizes of those states. The emergence of states in the valley of the Ganges in the seventh century b.c.e. is what appears first in Figure 4.
The Mauryan Empire was large even by the standards of the other Figure 4 Largest empires in the Indic PMN Sources: Taagepera 1978bTaagepera , 1979Taagepera , 1986 PMNs. In addition to the question of synchronicity (discussed below), there are two striking differences between the Indic system and the Central and East Asian PMNs. The first is that there is no long-term upward trend of empire sizes in the Indic system. The Mauryan Empire of the fourth century b.c.e. was nearly as large as the Mogul Empire of eighteenth century c.e. Indeed, the mean size of states in the Indic system was only 1.5 square megameters, while for the East Asian PMN the mean was 3.4, and for the Central PMN it was 4.0. We may suppose that this is a function of the size and isolation of the South Asian subcontinent. But while Indic empires never expanded outside of the subcontinent, empires from both the East and the West did occasionally expand into India. The second difference is that there were several long periods in which the largest states in the Indic system were very small. These general conclusions will probably stand even after the data on empire sizes in South Asia has been improved. 5 We should note that Taagepera's data often provides territorial size estimates for only one state in this  Taagepera 1978bTaagepera , 1979Taagepera , 1986 region. In order to compute our two-empire indicator of the empire size distribution, we simply assumed that the second state was small and estimated its size as .1 square megameter. 6

Synchronicity
How does our improved method for investigating the finding of synchronous empire growth and decline reinforce or undermine previous conclusions? The first thing we will discuss is the periodization of synchronicity between the Central and East Asian systems. Recall that we have no estimates of empire sizes in South Asia before the seventh century b.c.e. Figure 5 focuses on the period from 1500 b.c.e. to 250 b.c.e. During this period we can see that there is little East-West synchronicity. For this period the Pearson's r correlation coefficient for the sizes of the largest empires in the Central and East Asian PMNs is −.20. The period of the huge Achaemenid (Persian) Empire occurred during the end of the warring states period in China, when several small states competed and allied with one another in an interstate system. The synchronicity between East and West began with Figure 6 Largest empires in the Central, East Asian, and Indic PMNs (complete) Sources: Taagepera 1978b, 1979, 1986 the rise of the Han and Roman Empires. The simultaneities of Roman and Chinese events documented by Frederick Teggart (1939) support the notion that systemic forces had emerged that were causing East and West to march to the same drummer. Figure 5 demonstrates that the growth of Chinese and Gangetic states track closely from the seventh to the third centuries b.c.e. Indeed, the correlation coefficient for these 35 time points is .80, but this relationship does not extend to the larger time period that we shall examine next. Now let us consider the entire span of time from 1500 b.c.e. to 1800 c.e. Rather than exclude the years considered above, we shall retain them despite the negative relationship shown above between Eastern and Western empire sizes. We want to provide the strongest test possible of the synchronicity hypothesis. Figure 6 graphs the sizes of the largest empires in the Central, Indic, and East Asian PMNs. The correlation coefficients among the three regions are shown in Table 2.
There is a large and statistically significant correlation between the East Asian and Central empire sizes.This is a replication of the finding reported in Chase-Dunn and Hall 1997: chap. 10. The shift from 50-year to 10-year intervals did not obliterate the finding of East-West synchronicity. 7 The correla-

Figure 7
Largest Central, East Asian, and Indic Empires (excluding shared ones) Sources: Taagepera 1978bTaagepera , 1979Taagepera , 1986 tion of .24 between the Indic and Central systems is shown to be statistically significant, but it is possible that autocorrelation and interpolation could be artificially inflating the level of statistical significance. In order to reduce error due to the temporal trend, we need to examine first differences. The small positive relationship may indeed exist between Indic and Central cycles but might also be due to chance alone in two systems that are oscillating. The next step is to test the relationship between East and West after the shared empires (such as the Mongol) have been removed from the data. Figure 7 graphs the largest empires in each PMN after the shared empires have been removed. When an empire is removed, it is replaced by the second largest empire in a region. This results in somewhat different patterns than those produced in Figure 6. The correlation coefficients among the variables in Figure 7 have also changed to some extent (see Table 3). The correlation between the East Asian and Central empires is reduced from .82 to .68 when the Mongol Empire is removed. This is still a high correlation and demonstrates that the East-West synchronicity is independent of the Mongol conquest. The correlation of the Indic empire sizes with the other PMNs increases when shared empires are removed. This would seem to be logically impossible, but we can offer an explanation. Though the removal of shared empires does reduce the Indic correlation with the other PMNs, the removal of the Mongol Empire, which did not conquer India, increases the correlation because its gigantic relative size was a major source of the difference between India and the other regions. The net effect is to increase the correlation between the Indic system and the others when shared empires are removed. Should we now conclude that Indic exceptionalism should be rejected? We think not, because the positive relationship is still much smaller than that between the Eastern and Western PMNs.
We also investigated the possibility that synchronicity might be revealed in the correlation of changes in the sizes of the second largest empires in the different regions. The resulting correlation coefficients were very small (from .05 to −.09), and none were statistically significant.
To further test the East-West synchronicity, we examined the correlations across PMNs of our two-empire measures of empire size distributions. The hypothesis here is that inequalities in the sizes of empires within regions might rise and fall simultaneously across regions. Recall that we did find an East-West correspondence in changes in city size distributions (Chase-Dunn and Hall 1997: Table 10.7). Table 4 shows the resulting correlations when the examined variables are two-empire measures of size distribution.
There is no East-West synchronicity in empire size distributions, despite the large positive relationship when we study changes in the size of the largest empires alone. But the Indic empire size distributions have small but significant positive correlations with both the Central and the East Asian PMNs.  This indicates some small level of correspondence in processes of rise and fall between the Indic and other regions, but the lack of any East-West relationship simply adds another conundrum to the complex mystery of Afro-Eurasian patterns of social change.
As Chase-Dunn and Hall (1997) have done, we examine the extent to which the apparent synchronicity between East and West is due to the longrun upward trend in empire sizes. Chase-Dunn and Hall calculated a partial correlation controlling for time.When we replicate this partial correlation using our refined dataset on the largest empires in each PMN, we produce the results shown in Table 5. This implies that the East-West synchronicity is not due solely to the long-term upward trend in empire sizes. The correlation between East and West remains quite high. And the correlation between Indic and Central empire sizes is still statistically significant, though it is not large.
A stronger test of the East-West synchronicity of largest empire sizes is provided by the study of first differences. First differences are change scores computed by subtracting the value of a variable at Time 0 from its value at Time 1. Change scores show the amount and the direction of change over the period between the two time points. These change scores have the advantage that they have a great deal less autocorrelation (each score is not highly correlated with scores before and after it in the time series), so synchronicity uninfluenced by the overall trend toward larger empires is estimable. The results  of correlating first differences on the complete variables (including shared empires such as the Mongols) are shown in Table 6. Interestingly, the East-West correlation for the complete (shared) set of largest empires is slightly larger with first differences than it is straight up. The other correlations are smaller. In fact, they are so near zero that one might infer that there are no real synchronicities between Indic empire sizes and the other regions. When we compute the first difference correlations for the variables that do not include shared empires, we obtain the results shown in Table 7. Without autocorrelation and without the Mongols the East-West relationship is reduced, but it is still present. The relationship between Indic and East Asia is still statistically significant.
Another strong test for ruling out the effects of the long-term trend is accomplished by regressing year on the empire size measures and then correlating the unstandardized residuals to see if the relationship holds up independent of the long-term upward trend. When we perform this operation on the complete variables (those containing shared empires), we obtain the results shown in Table 8.
Here we see that the East-West synchronicity holds up well and that the correlation between the Indic and Central empire sizes, though much smaller, is still significant. But what about the time residuals when we eliminate the shared empires? These are shown in Table 9. The news here is that the East-West relationship is somewhat reduced but is still substantial. And the Indic relationship with the others is the highest that we have found in all our tests.  This implies that the Indic system does indeed experience a substantial degree of synchronicity with the Central and East Asian PMNs, though it is lower than the East-West relationship.

Causes of Synchronic Rise and Fall
The question remains as to what caused the synchronous growth of cities and empires in the Central and East Asian PMNs. The hypothesis of simultaneous expansions and contractions across a wide region should specify the causal mechanisms credited with causing these synchronicities. It is possible that climate changes explain the similar timing of growth and decline in Western Asia and China. India, at a more equatorial latitude, probably experienced a very different climatic sequence. 8 Climate change can affect urban growth and empire formation through its effects on agricultural productivity (Nix 1985). Periods of flooding may disrupt irrigation systems, and periods of drought also may negatively affect agriculture. Recently acquired evidence indicates that the collapse of Mayan states may have been caused by an extended period of drought. Harvey Weiss and his coauthors (1993) contend that both the expansion and the collapse of the Akkadian Empire were spurred by climate changes. If we should find significant relationships between indicators of climate change and the urban and empire growth/decline sequences, we will want to examine the important issue of the direction of causality. Does climate change cause urban change, or, conversely, does the expansion of agriculture associated with urban growth cause climate change? It is possible that expanded agricultural activity, and/or deforestation due to human exploitation of forest resources, may have effects on local and regional rainfall patterns and groundwater levels. Thus, intense agriculture and forest exploitation related to population density (and thus urbanization) may affect climate change. There is a huge developing literature on the anthropogenic causes of climate change. It is well known that the intensification of productive activities cause environmental degradation and that this process has significantly affected the development of human societies from the very beginning. If urban or empire growth episodes precede climate change or changes in water levels, then causality in the direction of human effects on climate would be supported.
It may be that climate changes are related to growth and decline phases but that these changes do not explain the synchronicities we observe between the Central and East Asian PMNs. Another possible explanation involves the flows of microparasites and their affects on human populations. As trade increases in density and volume, formerly isolated disease pools come into contact, unleashing epidemics-what Alfred Crosby (1972) and others call ''virgin soil epidemics.'' These can produce massive disruptions and, following Jack Goldstone's (1991) argument, can unleash all sorts of social, economic, and political changes. As pathogens and hosts adapt to each other, these diseases become less lethal and populations recover. Trade then resumes and the cycle can repeat as other, formerly isolated disease pools come into contact or as new diseases spread along expanding trade networks.
A more interesting explanation of Central/East Asian synchronicity from the world-systems perspective is  hypothesis of the ''centrality of Central Asia'' as a peripheral region linking both ends of the Eurasian continent. As we have already mentioned, the Mongol Empire briefly linked Western Asia and China into a single polity in the thirteenth century c.e. Owen Lattimore (1940) was the first to observe the tight core/periphery interaction between the horse pastoralists of Central Asia and the agrarian Chinese empires. Thomas Barfield (1989) traces the long-term linkage of the rise and fall of steppe empires with the rise and fall of agrarian empires in China.  contends that processes of peripheral migration and steppe-empire formation and their effects on the long-distance trade carried along the Silk Roads of Central Asia are the explanation of the event simultaneities found by Teggart (1939) and also account for Frank's hypothesized 200-year phases of growth and decline. While our research indicates only mixed support for the timing of expansion and contraction phases as hypothesized by Frank (1993), we do find that the sequences of growth and decline of Western Asian and East Asian PMNs track quite closely.
Perhaps it is Frank's Central Asian linkage that accounts for this. In order to find additional support for this hypothesis, we would need to rule out the climatic hypothesis by gathering data on climate change for the relevant regions and to closely compare the data on long-distance trade, warfare, migrations, and steppe-empire formation to sort out the causes of the synchronicities.We would also need to understand why India was not affected in the same way by these processes.
Frank's Central Asian hypothesis is quite plausible. The spread of the bubonic plague from the Central Asian steppes to both Europe and China by the Mongols is well known (McNeill 1976). But if this is the explanation, why did South Asia (the Indian subcontinent) follow a different sequence? One explanation might be that the tropical and semitropical climates of South Asia followed a different disease regime. It is also likely, given the Himalayan barrier, that climatic cycles in South Asia differed significantly from those in northern Eurasia. The monsoons certainly follow a different rhythm than the weather patterns of northern regions.
A much more plausible explanation can be found in the ways in which South Asia was connected into the Afro-Eurasian PGN. India had multiple connections into the Afro-Eurasian trading networks: overland, either via the Hindu Kush passes to the Silk Roads or through Yunnan and Assam, and by sea. The sea routes are quite old, going back at least two millennia. At first they involved coastal routes, but later sailors mastered the monsoons and were able to sail across the Arabian Sea and the Bay of Bengal (see maps in Chaudhuri 1985 andAbu-Lughod 1989: 172-73, 202, 252). Thus at any given time South Asian tributary states had multiple routes of access to the larger PGN. Disruption of any one route-for whatever reason-could be bypassed by means of alternate routes.
South Asia also had an alternative source of trade in its extensive links with Southeast Asia. 9 At times when the straits of Malacca or Sunda were controlled by pirates who made sea trade very risky, portages across the Malay Peninsula or overland through northern Southeast Asia (what is today northern Myanmar, Thailand, Laos, and Vietnam) were used. Thus, while a large state (e.g., Funan, the Khmer Empires, Srivijaya, or later Siam) could block one or more routes, no single state could control all the paths from India to China.
Indian connections to, and trade with, various Southeast Asian states buffered India from blockages that occurred on other routes. Southeast Asia supplied aromatic woods, spices, and especially gold. When access to northern sources of gold were severed by Bactria and when the Romans sought to curb the export of gold to the east in the first centuries of the current era, India turned to Southeast Asia to fill the gap. As Georges Coedes (1968: 19) notes, this was not the kind of gold rush that occurred in California in 1849, but the region became known as the ''land of gold.'' While it is clear that India had a profound influence on state formation and interstate relations in Southeast Asia, there is little evidence of direct colonization. Since the connection to Southeast Asia was maritime, Indian states did not get bogged down in expensive land wars, as China did from time to time.
Finally, the combination of streams of immigration into Southeast Asia by the Tai peoples from the northeast and by the Burmo-Tibetans from the northwest, along with impacts of China and Indian states, prevented the formation of a single regionwide power in Southeast Asia. Funan, located approximately where modern Cambodia is, came closest in the early centuries of the current era. But even Funan could not control all the routes.
Here we note that Frank's thesis is also bolstered by the consideration of what happened in Southeast Asia. Central Asians played a role, albeit an indirect one, in Indianization of Southeast Asia. The Mongols, especially in the Yuan dynasty under Kublai Khan, triggered major changes in the political organization of Southeast Asia. To avoid prolonged wars and ensure tribute, Kublai supported small states and blocked the formation of large ones. Mongol attacks helped finish the Burmese Empire centered on Pagan, already in decline. Their support of smaller spin-off states in the north among Shans and Thais started the marcher state process that eventuated in the rise of Siam. Finally, China's withdrawal from oceanic trade in the Ming dynasty, in part due to fear of another Mongol invasion, left the southern oceans open to Arab, then European traders (Fitzpatrick 1992).
In short, the states in Southeast Asia played an important role in the con-nections between China and India, and through India to West Asia and the Mediterranean. However, unlike the Central Asian steppe federations, which rose and fell with Chinese empires (Barfield 1989(Barfield , 1991, the states of Southeast Asia waxed and waned countercyclically with the Chinese and Indian Empires. Warfare is an interaction variable that affects both urban growth and the territorial size of empires. The hypothesis that processes of steppe-empire formation and the migration of pastoral nomads out of Central Asia were the key to the synchronous rise and fall of agrarian empires at both ends of the Eurasian landmass can be supported if we find simultaneous increases and decreases in warfare between steppe nomads and agrarian states in both West Asia and East Asia. Thomas Barfield's (1989) Perilous Frontier provides the information for the East Asian region. For West Asia, the approach to data on warfare utilized by the LORANOW project (Cioffi-Revilla 1991Cioffi-Revilla and Lai 1999) can be used to examine this hypothesis. 10

Summary and Conclusions
Formal comparative research on premodern world-system cycles has only begun, and firm conclusions would be unwarranted. Earlier research found only weak support for synchronous changes within PMNs between the political rise-and-fall cycle and economic expansion and contraction as measured by urban growth. Perhaps this should not be surprising. The long business cycles of the modern world system correspond only roughly with the rise and fall of hegemonic core powers. George Modelski and William Thompson's (1996) ''twin peaks'' model postulates that there are two Kondratieff waves 11 per ''power cycle.'' Other researchers (e.g., Goldstein 1988;Arrighi 1994) contend that hegemonic cycles are only roughly related to Kondratieff waves. More research is needed on both the modern and premodern world systems before certain conclusions can be supported.
In this article we have improved the analysis of Taagepera's data on empire growth/decline sequences for the purpose of testing for synchronicities across regions. We have found rather strong additional evidence of synchronicity of empire rise and fall between the Central (Mediterranean-West Asian) and East Asian PMNs. India did not rise and fall as synchronously with the more distant ends of the Eurasian PGN, but the relationship was more positive than reported earlier. Indeed, the stronger tests of synchronicity increased the size of the relationship with India. While India was not marching to the same drummer, the beat was heard, and there were consequences even in the subcontinent. An earlier investigation of Mesopotamian and Egyptian urban and empire growth/decline phases from 3000 b.c.e. to 1500 b.c.e. failed to find synchronicity (Chase-Dunn and Hall 2000).
More research is needed to further test for synchronicity and to examine possible causes. New information on city population sizes needs to be added to Tertius Chandler's (1987) monumental work to further examine the possible synchronicities of urban growth and decline. Taagepera's empire sizes also need to be extended to cover the smaller South Asian states more thoroughly. Testing different explanations for the observed Central/East Asian synchronicity will require the assembly of data on climate change, warfare, and trade (see Chase-Dunn 1995).

Notes
Christopher Chase-Dunn is a distinguished professor of sociology at University of California-Riverside, E. Susan Manning is a Ph.D. candidate at Johns Hopkins University, and Thomas D. Hall is a professor of sociology at Depauw University. An earlier version of this article was presented at the annual meeting of the International Studies Association held in Minneapolis on 17-21 March 1998. The authors would like to thank David Wilkinson and two anonymous reviewers for helpful comments and criticisms. 1 For a helpful introduction read Shannon 1996. 2 We use the abbreviations b.c.e. (before common era) and c.e. (common era), which have been adopted by world historians who are trying to be less Eurocentric. 3 While looking at separate graphs of changes in city size distributions, Chase-Dunn and Willard noted a similar pattern that was confirmed by holding the sheets of paper up against a window. 4 This dataset (empall7.sav) is available as an SPSS system file from the World-Systems Archive (http://csf.colorado.edu/wsystems/wsarch.html). 5 In an earlier version of this article we included a comparison between Taagepera's Indic data on territorial size and a study in which David Wilkinson (1993) coded the system polarity of the Indic state system.We found only very low positive correlations between Wilkinson's coding and the Taagepera data. 6 This assumes that missing data means that the second largest state was small. For purposes of a rough distinction between flat and primate empire size distributions, this assumption is adequate, but not ideal. Future work should code territorial size estimates of more states in each system.

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The levels of statistical significance may be inflated to some extent because interpolation to decennial time points creates a larger N. But we also found statistically significant relationships based on 50-year time points. We think that our findings are quite robust despite the incredulity of most historians. 8 Climate change patterns occur at local, regional, and global levels, so it is necessary to obtain data on climate change in or near the localities one is studying. 9 This discussion of Southeast Asia is based on the following sources : Cady 1966;Coedes 1966Coedes , 1968Glover et al. 1992;Marr and Milner 1986;andWyatt 1984, 1994. 10 Claudio Cioffi-Revilla's LORANOW project has gathered archaeological and documentary data on 30 early wars: Mesopotamia from 2960 to 2520 b.c.e.; China from 2700 to 722 b.c.e.; and Mesoamerica from 900 b.c.e. to 400 c.e. 11 A Kondratieff wave is a 40-to 60-year business cycle in which economic growth is strong for a 20-to 30-year A-phase and then stagnant or slower for a 20-to 30-year B-phase.