<table><caption>Table 7</caption><thead><tr><td>γ</td><td>C<sub>max</sub></td><td>T<sub>u</sub>/T<sub>r</sub></td></tr></thead><tbody><tr><td>1.1</td><td>2.9E6</td><td>1.2803</td></tr><tr><td>1.2</td><td>1.3E6</td><td>.6197</td></tr><tr><td>1.3</td><td>5.7E5</td><td>.3301</td></tr><tr><td>1.4</td><td>2.7E5</td><td>.1876</td></tr><tr><td>1.5</td><td>1.4E5</td><td>.1110</td></tr><tr><td>1.6</td><td>7.3E4</td><td>.0673</td></tr></tbody></table>

Note: The values of T<sub>u</sub>/T<sub>r</sub> were calculated by Eq. 23 from Harper (2010b): T<sub>u</sub>/T<sub>r</sub> = (a<sup>(1-γ)</sup> - 1)/(1 - C<sub>0</sub>(γ-1)), where a = C<sub>max</sub>/C<sub>0</sub>, and C<sub>0</sub> = 100.

It can be seen that as γ decreases the proportion of the urbanized population increases. Note that C<sub>max</sub> had to be computed for each γ, and note also that the above table is meant to be a numerical example in which γ was varied over its observed range. This is further represented in Fig. 28 in which γ is plotted against T<sub>u</sub>/T<sub>r</sub> shows a rapid decline of the urbanized population with respect to increasing γ.

However, the reverse of this trend should actually be considered, as the urbanization process is associated with decreasing γ. The non-linearity of this process implies a very rapid increase in the proportion of the urbanized population as suggested by the power relation,

$$T_u/T_r = 2.81\gamma^{-8.41}, \qquad (\text{Eq. 34})$$

where very rapid urbanization can be expected with smaller and smaller γ. It is my contention that both instances of rapid urbanization followed shortly by rapid de-urbanization, that of the latter part of the last millennium BCE and the 300 years represented by the period of time from 200 CE to 500 CE and also the 13th and 14th centuries CE, are consequences not only of this rapid urbanization but of the consequences of that urbanization process exceeding some as yet to be defined threshold regarding system wide sustainability. This may well be the process of overshoot and its consequences referred to in the book of the same title *Overshoot: The Ecological Basis of Revolutionary Change* by William R. Catton, Jr.
<figure><img src="image_58.png" /><figcaption>**Fig. 39.** The relationship between $\gamma$ and $T_u/T_r$ is shown to be inverse and non-linear, the implication being that as urbanization increases it does so at an ever increasing rate with respect to decreasing $\gamma$</figcaption></figure>

Movement of the system, whether as a consequence of over-shoot, as explained previously, or simply as a result of the more normal processes of world system development, is associated with the distribution of the urbanized population and as such can be characterized by maximum urban area, by $\gamma$, and by the total population of the system itself. Further, it was previously shown that the relationship between identical maximum urban areas, $\gamma$, and $\ln T$ is linear. In other words, if maximum urban area can be predicted, the position of the world system can also be predicted as all points for the world system having a given maximum urban area will fall on the same straight line, an iso-urban line. This fact then further limits the position of the world system and can be used as a potential predictor of the position of the system.

Using these iso-urban lines as a base from which to track the movement of the world system through time allows for a polar representation of the world system trajectory. When this polar plot is inspected the change in the trajectory over time is limited to either a counter-clockwise and ever expanding (with respect to the origin of the plot) new position or a linear change in position without change in $\Psi$, that is a change in which the plot has the appearance of proceeding out of the plane of the page. These limitations are again another way of representing imposed constraints on the system, and they represent a means of prediction of the future state of the system, noting of course that the future state of the system can be viewed from any previous state of the system, that is that the future can be in the past.

Associated with the process of representing the world system trajectory in polar coordinates is the ability to represent the relationship between the pa-
rameters, H and Ψ themselves, and also to represent the relationship between
these parameters individually over time. In all three cases, the relationships can
be represented by a linear regression of the data, which implies the ability to
predict in relatively specific terms. It is interesting, though, to recognize that
while a linear representation of each of the relationships represents a good deal
of the variability in the data, there are non-linearities, either due to phase
changes of the system or periodic changes in the variables, S and Ψ. While
there are several two-step phase changes represented in Fig. 6, in fact four, one
beginning at 2500 BCE, one at 2000 BCE, one at 1000 BCE, and a final one
beginning at 900 CE, and while the temporal position of these phase changes is
suggestive of an exponential sequence, 500 years separating the first from the
beginning of the trajectory, 500 years to the next, then 1000 years to the next,
and finally 1900 years or almost 2000 years to the beginning of the final phase
change, it is the aforementioned periodicities that will be discussed next.

Finally, the relationship between the observed and idealized values for
maximum urban area size over time will be considered, as will the relationship
between observed and expected theoretical world system space. It was shown
that the graph of this data over the 5000 year history of the world system repre-
sented two distinct sets of data on urbanization, distinct in that they gave differ-
ent linear regressions, but only by y-intercept, not by slope. This would seem
to indicate a similar over-all process of urbanization which was simply shifted to
a higher level on the graph with the beginning of the existence of the Roman Em-
pire and shortly after that of the Han Empire. Also, when the natural logarithm of
the length of the regression segment was divided into the natural logarithm of the
total (abstract) distance traveled by the world system in each 2500 year section of
time, the quotient, in other words the fractal dimension, of each was effectively
the same. This indicates a very strong potential for prediction, since per 2500 year
period the fractal dimension appears to be almost identical.

When a fractal analysis was undertaken for the relationship between ob-
served and expected world system theoretical space, quite different results were
arrived at. First, the relationship between the linear regression of the data for
each 2500 year section of world system history and the entire 5000 years of that
history and the actual distance traveled were considered, all the fractal dimen-
sions were approximately 1. Second, given that this is the case, then the trajec-
tory of the world system as represented by this ratio, that is lnD/lnR, is linear,
which implies that at this scale of inspection the world system trajectory is
highly constrained.

Beyond fractal analysis when the log-transformed parallel trajectory of lnT
and lnC<sub>max</sub> is considered, the relationship between these two variables seems
strong and allows for further generalized prediction. First, although the vari-
ability of lnT – lnC<sub>max</sub> ranges from approximately 5 to approximately 6.5,
the regressed value is approximately 5.9. Using this average value, it is easy to extrapolate into the future. If regression yields

$$ \ln T - \ln C_{\max} = 5.9, \qquad (\text{Eq. 35}) $$

then maintaining the 100 year interval that the world system history is divided by permits prediction from any position on the regressed trajectory to the next position on the trajectory and also beyond the current last position of the trajectory, 2000 CE (see Fig. 40). This is not a particularly satisfactory predictive tool however, because, as was mentioned previously, there is variability in the difference, lnT – lnCmax. However, if the data on lnT and lnCmax are considered specifically, a better predictive procedure, but one that still yields approximate results, emerges. This better predictive model, let us call it the ‘abstract square model’, is represented in Figs 41a and 41b.

<figure><img src="image_59.png" /><figcaption>Fig. 40. lnT is represented on the x-axis, and lnCmax is represented on the y-axis. The points used to generate this regression are sets of lnT, lnCmax in 500 year increments. The regressed equation is: lnCmax = 1.1680lnT – 9.0269 (Eq. 34), R² = .9736. If this line is extrapolated over the next 100 years the values of lnT and lnCmax are easily predictable</figcaption></figure>

Note: lnT – lnCmax = Z, or lnCmax = lnT – 5.9, which is clearly an approximated version of the regression equation. Note that Z = any value between 5.0647 and 6.6846, the range of observed values of lnT – lnCmax.

Here the linear regression represented in Fig. 40 is combined with the observed limits of the system. In other words, a rectangle is created with a point representing the position of the world system as a reference. Then the range that the next generation of lnT values is determined by

$$ \ln T = \ln C_{\max} + [5.0646 \rightarrow 6.6846] \qquad (\text{Eq. 36}) $$

and by

$$ \ln C_{\max} = \ln T - [6.6846 \rightarrow 5.0646]. \qquad (\text{Eq. 37}) $$
This gives a square with the dimensions, 1.6199 × 1.6199, in which it is predicted the next generation's world system position can potentially be found. Sadly, this square has within an infinite number of points, which is hardly helpful. Can probability be used to reduce the possible number of points? Possibly. Note that this square can be subdivided into four different sections, and the sections vary in area suggesting that the probability of the position of the world system falling in any of the subsections is proportional to the area of the subsection. This is helpful but only in a general way, since each of these rectangular figures has within it an infinite number of points. If the position of the world system is calculated per century with respect to the context of this square, the position of the world system is observed to change, and since this change falls within the zero sum limits of the value, 1.6199, for both axes, then only one variable is necessary to characterize the position of the world system. Specifically, the reference of a zero sum relationship between the position of the world system within the boundaries of the square model imply that if the difference between the position of the world system and the maximum boundary of the square is known, then the other three differences between the other three boundaries are explicitly predictable, because all relationships are dependent on $\ln T - \ln C_{max} = [6.6846 - 5.0647]$.

<figure><img src="image_60.png" /><figcaption>**Fig. 41a.** This is a simple representation of the general trend of the world system with respect to lnT on the x-axis and lnCmax on the y-axis. In broad terms, the predictability of the future state of the system is simply a matter of following the trend of the line. However, when the range of values between lnT and lnCmax are imposed the number of future positions of the world system becomes more varied as will be seen in Fig. 41b.</figcaption></figure>
<figure><img src="image_61.png" /><figcaption>**Fig. 41b.** The box in the upper right hand corner of this graph represents the space delimited by the maximum and minimum values for the difference between lnT and lnCmax of all possible values that the world system position can have in 100 years from the present. Note that the position of the asterisk, the current position of the world system changes with respect to the boundaries of the square</figcaption></figure>

Data for the position of lnCmax with respect to the maximum value of lnCmax as determined by lnCmax = lnT - [6.6846 → 5.0646] were used to construct the graph in Fig. 42. There are several unique features of this graph. First, the reader should understand that a vertical step representation was chosen so that the change in the difference of the observed value of lnCmax and its maximum, Z, could be represented. This plot reveals little change in the domain of Z over time, that is a linear regression would be expected to give a slope close to zero, and, in fact, the slope is .0027, very close to zero. Further, although the graph is punctuated by a number of peaks and troughs, that there is very little visual regularity to their occurrence. If peaks or maxima are defined as any increase over a previous minimum of .2 or greater on the y-axis scale of Fig. 42 then there are thirteen such maxima occurring at 2800 BCE, 2300 BCE, 2100 BCE, 1800 BCE, 1200 BCE, 900 BCE, 600 BCE, 100 BCE, 200 CE, 600 CE, 1000 CE, 1300 CE, and 2000 CE and doing so in a somewhat irregular way. It is also disconcerting to note that, while increases on the y-axis values are done incrementally and in a stepwise fashion, the decent from twelve of the thirteen maxima is done so precipitously; the decent from the thirteenth maximum has yet to occur and all of these descents may refer to what William Catton refers to as overshoot, or rather the consequences of overshoot (Catton 1982). Superficially, this data appear not to contribute much to prediction with the previous statement about overshoot excepted, however, there is some light at the end of this particular tunnel.
<figure><img src="image_62.png" /><figcaption>**Fig. 42.** Time is represented on the x-axis, and the computation, $[\ln C_{\max} + 6.6846 - \ln T]/1.6199$, is represented on the y-axis. This computation is proportional to the position of the world system within the phase space defined by the maxima and minima of $\ln T - \ln C_{\max}$. The regression, having a slope, $m = .003$, indicates that over the 5000 years of world system history investigated here these changes in the position of the world system with respect to the maximum value of $\ln C_{\max}$ changes and does so episodically</figcaption></figure>

If focus is brought to bear on the changes in y-axis values across time, and, in fact, their absolute value, a size frequency distribution can be produced as represented in Fig. 43. This distribution and the curve fit to this distribution clearly represent a pattern of exponential decay, which can be characterized by a power function with a negative exponent, e.g., $y = ax^{-b}$, or an exponential function such as, $F = F_0 + ae^{-b}$. With regard to the specific data used to create the graph in Fig. 43 and using the actual values for the exponential form of this equation, the equation becomes,

$$F = 48.58881e^{-r/.4609} + 3.6212, \qquad (\text{Eq. 38})$$

where 'r' is the rank of each frequency. The natural log transformation of the frequency data gives the following linear equation,

$$\ln F = 3.9135 - 1.6999r, \qquad (\text{Eq. 39})$$

the equation of a straight line as represented in Fig. 44. If the natural log transformed frequency data are plotted against class size, the linear distribution of points, as represented in Fig. 45, is the result.
<figure><img src="image_63.png" /><figcaption>**Fig. 43.** Class size is represented on the x-axis, and frequency is represented on the y-axis. The regression curve is described by the equation of the form, $F = F_0 + Ae^{-x/t}$, where $F_0 = 3.6212$, $A = 48.5888$, and $t = 0.4609.R^2 = 0.9667$</figcaption></figure>

These equations and the facts that it has been demonstrated that the world system is a non-equilibrium system and that the world system is a large, complex system both suggest that the world system exhibits self-organized criticality, SOC (Bak 2003 and else where). A random distribution of numbers over the same range was generated and coupled with the data in Fig. 43 was subjected to a two-sample t-test. The P-value of this test was P = 1.8176E-5. In other words, the probability of these two data sets being related was approximately 18 in 1,000,000, the implication being that the data showing SOC for the world system are non-random. Further and obviously, if the frequency data for Fig. 43 are natural-log transformed, a linear distribution is produced as represented in Fig. 44. Here the distribution is unquestionably linear and implies continuity of change over the range of the data but also implies the consequences of SOC, which will be discussed briefly in the following paragraph.
<figure><img src="image_64.png" /><figcaption>**Fig. 44.** Class size is represented on the x-axis, and lnF is represented on the y-axis. lnF = 3.9135 - 1.6999r, where r is the rank of the frequency (Eq. 38). R² = .9716</figcaption></figure>

The consequences of a system exhibiting SOC are significant. First, periods of rapid urbanization and de-urbanization are punctuated by periods of relative stasis. This pattern is also exhibited in the second section of this paper discussing the polar plot representation of the world system, specifically in Figs 12 and 13. Second, the pattern of systems exhibiting SOC can be represented by a simple power function or exponential function as is the case here. Third, this pattern is continuous, as is clearly represented in both Figs 44 and 45, and consequently there is no difference in the factors that cause small events of urbanization and those that cause major events of urbanization. Fourth, the timing of these events individually is not predictable, either with regard to increased or decreased urbanization. This was suggested and only suggested by the temporal distribution of maxima in Fig. 42. While these data then are suggestive of regularity, they are not suggestive of explicit temporal predictability, however, the inference that the world system exhibits SOC is itself a prediction in terms of the behavior of the system.

In conclusion, what are the actual implications of this section for predictability? First, the original trajectory of the world system in its natural log-transformed state yields a relatively linear regression with some significant dissimilarities from linearity as have already been mentioned. So, in general, the extension of the regression gives an approximate prediction of the future of the system, and the same holds true for postdictions. However, if one were making a prediction for the future of the system in 500 BCE or, say, 1300 CE, in terms of linearity the prediction would be wildly wrong. In both instances very rapid urbanization occurs in the face of very little or no increase in lnT, the consequence for the trajectory being that it takes very sharp right turns at both 500 BCE and 1300 BCE, clearly events that do not fit the trend of the linear model. So, the linear model is of limited use.
A more detailed study of the trajectory reveals that iso-urban lines exist, in other words, that regarding the graph of $\gamma$ v. lnT points of identical maximum urban area magnitude align linearly. This in itself is of course a prediction. If the current state of the system were to revert to a maximum urban area size of 1,000,000, then the position of the system would fall somewhere on the iso-urban line with $m = .0910$ and $b = -.4430$. Consulting Fig. 4 will allow the reader to estimate the current position of the world system if this reversion in maximum urban area size were to occur with no change in lnT. Again, any prediction using iso-urban lines would be far from explicit.

In turn, the iso-urban lines were used as a basis for constructing a polar plot of the world system trajectory, an ever expanding spiral subject to the changes in both $X = \text{Scos}\Psi$ and $Y = \text{Ssin}\Psi$, the parametric equations for the plot. A three dimensional polar plot reveals a relative degree of regularity in the system. Given a couple of two-dimensional perspectives, it is quite clear that a relatively linear increase in maxima occurs, and the same may be stated for minima. Further, when both $X$ and $Y$ are plotted against time their maxima occur in a predictable fashion and, in general, so do the minima. If $S$ and $\Psi$ are plotted against one another, a near-linear plot is achieved, however, there are clear punctuations in this graph in which $S$ changes rapidly while $\Psi$ does not change at all. This behavior of the world system represents punctuations in change alternating with relative stasis and is characteristic of a number of biological systems. In itself, this characteristic of the world system is predictive of general, over-all prediction but not explicit prediction.

When maximum urban area size is compared with optimal urban area size a clear trend is revealed with decreasing $\gamma$, in that the two values approach one another. The ratio of these two values, $C_{max}/C_{max}(\gamma + 1)^2$, when plotted against time clearly reveals a disjunct graph, one in which the Ancient World is separated by a phase change in maximum urban area magnitude from the Classical and Modern Worlds. This phase change occurs during a period of time that roughly coincides with Karl Jasper's Axial Age, but the graph and the data behind the graph do not explain why this phase change occurred when it did. It is interesting to note here that the world system may be entering another period of phase change, however, aside from the periodicity of these two events being approximately 2500 years in length, there is little reliance at present that can be placed on a data set of only two events. It is interesting, however, that when a simple fractal analysis is applied to this data that the fractal dimensions of both are nearly identical. This is, in one sense, intellectually comforting, but again does not lend itself to explicit prediction.

When the separate trajectories of both lnT and $\ln C_{max}$ are compared they appear nearly linear and parallel to one another. This is confirmed by calculating the differences between the linear regressions of both trajectories. However, the observed data vary in the difference of their magnitude by 1.6199, a signifi-
cant variance when one deals with log-transformed data. While the general re-
lationship between lnT and lnCmax is linear, when the variability between lnT
and lnCmax makes the prediction within that range of variability for both
lnT and lnCmax less possible (see Fig. 41b). Over time the position of the world
system varies with respect to the boundaries of the variability. This variability
opens the door to a new perspective on the behavior of the world system and
the predictability of that behavior.

When this variance in position of the world system with respect to the
boundaries of the variance in the difference between lnT and lnCmax is plotted
against time and is represented as a vertical series of steps, it is quite clear that
the average slope of this graph (Fig. 42.) is nearly zero. But, when a size fre-
quency distribution of the absolute values of the vertical steps is constructed,
the result is a curve exhibiting decay, which can be represented by either a power
function or an exponential function. Given that the world system is a large, com-
plex, non-equilibrium system, this result implies that the world system exhibits
self-organized criticality. There are three important consequences of this impli-
cation. First, the factors that both increase and decrease rates of urbanization
are similar for all magnitudes of urbanization. Second, it should be expected
that periods of urbanization are episodic. Third, these periods of episodic ur-
banization appear not to be temporally predictable.

This research paper closes with two concerns: First, somewhat conflicting
data have been presented with regard to the predictability of the world system
trajectory as it is understood over the last 5000 years of its history. Unques-
tionably, much more research is required to resolve this disparity, however,
personally my intuition tells me that further study of the potential for the world
system to exhibit SOC, self-organized critically, will be quite productive. Sec-
ond, Fig. 43 reveals a pattern of change in which increase in urbanization with
respect to the total population of the world system is for the most part done
incrementally. However, change in the opposite direction is not, it occurs pre-
cipitously. If these data are correct there are two further consequences, that the
timing of these down turns is episodic and may not be predictable, and that
the magnitudes of the down turns is quite large.

Summary

1. The intent of this paper is to show, first, that the trajectory of the world system is highly constrained, and, second, that these constraints lead to the possibility of prediction, that is that the position of the world system at any point on its trajectory is potentially predictable based on the nature of the constraints analysed.

2. The organization of the world system was described in terms of the rela-
tionship between γ, a parameter that generalizes the distribution of urban areas for
any given maximum urban area and the total population of the system.
3. Several types of constraint on the world system trajectory were recognized. Specifically, the overall trend of the system and the existence of iso-urban lines were discussed.

4. The trajectory of the world system was reconfigured in polar dimensions, the morphology of this plot was described, and the changes over time with respect to the polar parameters were noted, and any non-linearities, either of a punctuated or periodic nature were analysed.

5. A standard, the idealized maximum urban area, was established and a ratio was generated with the observed maximum urban area divided by the standard. This allowed the recognition of two distinct phases of urbanization and, further, on generating separate regressions for each phase of urbanization it was shown that the fractal dimension of each was essentially the same.

6. As in #5 a standard was established for total potential area of the world system and the actual potential area of the system at each point in time could then be used to generate a ratio of the standard to the actual so that any significant trends in world system activity could be represented. Fractal analysis was performed, and it was shown that the fractal dimension for both the 2500 year periods and the entire extent of world system history did not vary significantly from unity. This fact has significance with regard to prediction of the world system trajectory into the future.

7. The parallel trajectories of the world system population as a whole and that of maximum urban areas of that system was analysed, and it was shown that the difference between the natural log-transformed values for both variables falls within a range of values the difference of which is 1.6199.

8. The data on the parallel trajectories of both the natural log-transformed world system population and maximum urban area sizes exhibit properties of self-organized criticality. The consequences of complex systems exhibiting SOC are discussed.

9. The potential of using these constraints and conditions to predict past, present, and future positions of the world system was noted in terms of each of the constraints analysed and each constraint was assessed for its particular contribution to understanding the (future) state of the system.

## References

*Anderson P. W. 1972.* More is Different. *Science* 177: 393–396.

*Arrighi G. 1994.* *The Long Twentieth Century: Money, Power, and the Origins of Our Times*. New York: Verso.

*Bak P. 1996.* *How Nature Works*. New York: Copernicus Springer-Verlag.

*Bak P., Tang C., and Wiesenfeld K. 1987.* *Self-Organized Criticality: An Explanation of 1/f Noise*. *Physical Review Letters* 59: 381–384.

*Catton W. R. Jr. 1982.* *Overshoot: The Ecological Basis of Revolutionary Change*. Chicago, IL: University of Illinois Press.
**Cohen J. 1995.** *How Many People Can the Earth Support?* New York: W. W. Norton and Company.

**von Forester H., Mora P. M., and Amiot L. W. 1960.** Doomsday: Friday 13th, November, A.D. 2026. *Science* 134(3436): 1291–1295.

**Grinin L. 2012.** *Macrohistory and Globalization*. Volgograd: Uchitel Publishing House.

**Grinin L., and Korotayev A. 2006.** Political Development of the World System: A Formal Quantitative Analysis. *History and Mathematics. Historical Dynamics and Development of Complex Societies* / Ed. by P. Turchin, L. Grinin, A. Korotayev, V. de Munck, pp. 115–153. Moscow: KomKniga/URSS.

**Harper T. 2010a.** The Macropattern of Urbanization over the Course of the Last 5000 Years of World-System History. *Social Evolution & History* 9(1): 115–133.

**Harper T. 2010b.** The Trajectory of the World System over the Last 5000 Years. *History and Mathematics: Processes and Models of Global Dynamics* / Ed. by L. Grinin, P. Herrmann, A. Korotayev, and A. Tausch, pp. 13–63. Volgograd: Uchitel.

**Hutchinson G. E. 1978.** *An Introduction to Population Ecology*. New Haven, CT: Yale University Press.

**Korotayev A. 2010.** Globalization and Mathematical Modeling of Global Development. *Hierarchy and Power: Political Aspects of Modernity* / Ed. by L. Grinin, D. Beliaev, and A. Korotayev, pp. 225–240. Moscow: LIBROCOM/URSS.

**Korotayev A., and Grinin L. 2006.** Urbanization and Political Development of the World System: A Comparative Quantitative Analysis. *History and Mathematics: Historical Dynamics and Development of Complex Societies* / Ed. by P. Turchin, L. Grinin, V. de Munck, and A. Korotayev, pp. 115–153. Moscow: KomKniga.

**Korotayev A., and Grinin L. 2013.** Urbanization and Political Development of the World System. *Entelequia* 5: 197–254.

**Korotayev A., Malkov A., and Khaltourina D. 2006a.** *Introduction to Social Macro-dynamics: Compact Macromodels of the World System Growth*. Moscow: URSS.

**Korotayev A., Malkov A., and Khaltourina D. 2006b.** *Introduction to Social Macro-dynamics: Secular Cycles and Millennial Trends*. Moscow: URSS.

**Korotayev A., Malkov A., and Khaltourina D. 2006c.** *Introduction to Social Macro-dynamics: Secular Cycles and Millennial Trends in Africa*. Moscow: URSS.

**Li C. C. 1955.** *Population Genetics*. Chicago, IL: University of Chicago Press.

**Malthus T. H. 1798.** An Essay on the Principle of Population. *The Project Gutenberg*. URL: http://www.gutenberg.org/.

**Mayr E. 1988.** *Toward a New Philosophy of Biology: Observations of an Evolutionist*. Cambridge: Belknap Press of Harvard University Press.

**Modelski G. 2003.** *World Cities: –3000 to 2000*. Cheshire, CT: Faros 2000.

**Stavrianos L. S. 1976.** *The Promise of the Coming Dark Age*. San Francisco: W. H. Freeman and Company.
**Mathematical Appendix**

The Derivation of $T/C_{max} = (C_{max}^{\gamma-1} - 1)/(\gamma - 1)$.

From Eq. 2, $C_{max}^{\gamma} - C_{max} = (\gamma - 1)T = 0$, it can be seen that $C_{max}^{\gamma} - C_{max} = (\gamma - 1)T$, and that $T = (C_{max}^{\gamma} - C_{max})/(\gamma - 1)$. If $C_{max}$ is factored out of the numerator and both sides of the equation are divided by $C_{max}$, this will yield: $T/C_{max} = (C_{max}^{\gamma-1} - 1)/(\gamma - 1)$.

The Derivation of $[e^{5.9-.0078t} - 1]/[\gamma e^{5.9-.0078t} - C_{max}^{\gamma-1}] = 1$.

The linear regressions of lnT and lnCmax yield respectively, lnT = 16.1681 – .0826t and lnCmax = 10.2681 – .0904t. Consequently, lnT – lnCmax = 5.9 – .0078t, and, further, $T/C_{max} = e^{5.9-.0078t}$. As a result $e^{5.9-.0078t} = [C_{max}^{\gamma-1} - 1]/[\gamma - 1]$ and $[\gamma - 1]e^{5.9-.0078t} = [C_{max}^{\gamma-1} - 1]$. Rearrangement gives: $\gamma e^{5.9-.0078t} - C_{max}^{\gamma-1} = e^{5.9-.0078t} - 1$, and dividing both sides by $\gamma e^{5.9-.0078t} - C_{max}^{\gamma-1}$ yields: $[e^{5.9-.0078t} - 1]/[\gamma e^{5.9-.0078t} - C_{max}^{\gamma-1}] = 1$. The expected value of this ratio is clearly 1.0, and the observed value at each 100 year increment can be calculated using appropriate values substituted for each variable of the ratio.
3

Another, Simpler Look:
Was Wealth Really Determined
in 8000 BCE, 1000 BCE, 0 CE,
or Even 1500 CE?

William R. Thompson and Kentaro Sakuwa

**Abstract**

Olsson and Hibbs (2005) and Comin, Easterly, and Gong (2010) make persua-
sive theoretical and empirical cases for the persistence of early biogeographi-
cal and technological advantages in predicting the distribution of national eco-
nomic wealth. However, these results are challenged with an examination of
sixteen observations on economic complexity, GDP per capita, and city size
spanning as much as ten millennia and eight to eleven regions. The regional
complexity / wealth hierarchies are relatively stable only for finite intervals.
Early advantages, thus, have some persistence but do not linger indefinitely.
The rich do not always get richer or even stay rich, and the poor sometimes
improve their standings in the world pecking order dramatically. Early advan-
tages are important but need to be balanced with the periodic potential for
overriding them.

**Keywords:** economic growth, early advantage, biogeographical advantage, technological advantage, city size, societal complexity.

**Introduction**

We live in an era fraught with the potential for tectonic changes in relative eco-
nomic positioning. The United States, long the leader in technological innova-
tion and economic growth, is combating symptoms of relative decline and
an increasingly visible challenge from China, a state emerging rapidly from
a long period of relative underdevelopment. Japan, thought to be the most like-
ly economic challenger to the United States less than two decades ago, is mired
in relative stagnant growth and facing a serious population aging problem. Rus-
sia, once a challenger to the United States, experienced an economic meltdown
when the Soviet Union fragmented. But Russia is re-emerging as an economic
competitor of sorts by exploiting the sale of raw materials. A state adjacent to
China, India, equally populous, seeks to catch up and surpass China. The region
that the United States once overtook, Western Europe, remains affluent but is
confronted currently with the prospect of the world's one successful regional integration experiment breaking up. Throughout all of these potential changes in the making, a large number of states remain poor and have few prospects for any change in the near, or perhaps distant, future.

It is hardly surprising, then, that the question of how economies grow fast and slow and why some economies get ahead of others while others fall back is popular.<fnref n="1" /> Many of the arguments that have surfaced focus on more recent developments and yet many of these remain untested empirically. Olsson and Hibbs (2005) and Comin, Easterly, and Gong (2010) are remarkable exceptions to these generalizations. Not only do their studies encompass thousands of years, they go to some lengths to test their perspective on long-term economic growth. Olsson and Hibbs find that Diamond's (1997) argument, predicated on the technological advantages associated with diffusion possibilities linked to continental axes and the distribution of edible plants and large mammals prior to the advent of agriculture, predict well to current national incomes. The strong implication is that the world's distribution of income was determined even before the advent of agriculture. Comin, Easterly, and Gong find that technological adoption in 1500 CE predicts well to national income in the current period and that knowing about the distribution of technology in 1000 BCE and 0 CE predict respectively to technological distributions in 0 CE and 1500 CE. They conclude that the world's distribution of technology has been quite persistent. Wealth distributions, to the extent that they are predicated on technological attainments, were not strictly determined in 1000 BCE but the extent of path dependency is quite strong. Areas that have been technologically ahead in the past tend to continue to be technologically ahead in the present.

Ambitious and largely unprecedented analyses, however, are likely to be characterized by various empirical and design problems. Attempting to capture changes in economic development over thousands of years is never easy or straightforward. Assuming then that there will always be some problems, the question is whether the problems appear to strongly influence the outcome. In this case, the answer is that assumptions made in the research design appear to have biased the conclusions significantly. We do not dispute Olsson and Hibbs (2005) and Comin et al.'s (2010) specific findings as much as what we should make of them. If the central question is whether technological differences persist over long periods and the answer lies in the affirmative, there are at least several major caveats that need to be advanced based on the long-term analysis of uneven economic development. By more than tripling the length of the Comin et al.'s examination (from three millennia to ten millennia), expanding the number of observations (to sixteen across the ten millennia), changing the unit of analysis (from contemporary states to regions), and simplifying the indi-

<footnote n="1">¹ In the past decade or so, Diamond (1997), Wong (1997), Frank (1998), Landes (1998), Pomeranz (2000), Maddison (2001), Clark (2007), Findlay and O'Rourke (2007), Morris (2010, 2013), Galor (2011), Parthasarathi (2011), Rosenthal and Wong (2011), among others, have appeared.</footnote>
cators relied upon (substituting a different index of complexity for prehistorical
times and gross domestic product per capita and city size for historical times),
a more comprehensive picture of long-term development emerges. The persis-
tence of earlier technological advantages does not disappear. On the contrary, it
is quite evident. But so too are major departures from persistence. We should
not emphasize one dimension over the other. Instead, we should strive to inte-
grate both dimensions in understanding long-term changes.

The Persistence Analyses

Our problems with the two earlier studies differ by study. The Olsson and Hibbs (2005) study develops, elaborates, and operationalizes Diamond's (1997) argument well.<fnref n="2" /> Fig. 1 summarizes their theory and empirical model. Favorable climate, larger continental size, and an east-west axis that permits diffusion of seeds, animals, and technology increases the availability of plants and animals that are suitable for agriculture. The greater is the availability of plants and animals, the greater is the opportunity to experiment with agrarian techniques. Agrarian and industrial revolutions should occur earlier in such areas than in less favored regions. The earlier is the timing of agrarian and industrial revolutions, the greater should be the contemporary level of income per capita.

<figure><img src="image_65.png" /><figcaption>Fig. 1. Logical structure of Olsson and Hibbs' theory (2005: 928)</figcaption></figure>

<footnote n="2">² The analyses of Chanda and Putterman (2005, 2007), Putterman (2008), and Bleaney and Dimico (2011) reinforce Olsson and Hibbs' finding that an earlier start on agriculture is beneficial to income levels much later.</footnote>
One can balk at various aspects of the Diamond argument or not but our main criticism of the Olsson and Hibbs examination is that the tested argument relies on one set of observations.<fnref n="3" /> Areas favored by geographical size, climate, continental axes that do not block pan-continental diffusion, more large mammals that can be domesticated, and more plants that can be cultivated and consumed will develop earlier. This argument implies that Eurasia will be favored over Africa, Australia, and the Americas – a quite reasonable starting point for economic growth analyses.<fnref n="4" /> It helps to explain, for instance and with some substantial help from the spread of European diseases to the Americas, why Spanish conquistadors could defeat the Aztecs and Incas.<fnref n="5" /> It does not really specify why different parts of Eurasia have fared much differently on economic development criteria – a topic on which Diamond (1997) waffles.<fnref n="6" /> Nor does it explain why Eurasia writ large has not linearly developed faster than Africa, Australia, and the Americas. Thus, if we use observations based on ten thousand years ago to predict to the present, we skip much of what happened (or may have happened) in between.<fnref n="7" />

The Comin *et al.'s* analysis (2010) looks at some of the things that happened in between the advent of agriculture and the contemporary period but there are at least six problematic sources of bias. The first problem is ignored almost entirely by the 2010 analysis. From the most macroscopic vantage point conceivable, economic development was first manifested most spectacularly in Sumer, and, later, Egypt and the eastern Mediterranean. The structural axis of Eurasian growth then was transformed into a 'dumb-bell' shape with the Mediterranean on one end and China on the other. Both dumb-bell ends went into

<footnote n="3">³ See Acemoglu and Johnson (2012: 51–56), among others, for a critique of the Diamond argument. Olsson and Paik (2012) develop and test a very interesting argument about the timing of agriculture that substantially modifies the idea of early biogeographical advantages. Basically, the idea is that the earliest adopters of agriculture tended also to adopt highly autocratic political systems which subsequently led to poor or poorer than might otherwise have been anticipated economic performance. Later adopters tended to develop different, less extractive, institutions and, therefore, enjoyed better economic development.</footnote>

<footnote n="4">⁴ See Turchin and Hall (2006) for an extension of the argument to imperial development.</footnote>

<footnote n="5">⁵ There is no question that Eurasia is the largest populated continent and that it encompasses more plants and large mammals that can be used for economic development purposes. Unlike the north-south alignment of Americas and Africa with major, mid-continental blockages to diffusion, it is not only possible for plants, animals, and technological innovations in one end of Eurasia to travel to the other; it is difficult to account for Eurasian development without tracking the diffusions. Parts of Eurasia certainly experienced earlier agricultural and industrial revolutions than elsewhere.</footnote>

<footnote n="6">⁶ At one point, Diamond (1997) suggests that any part of Eurasia might have seized the development lead but later suggests that western Eurasia was favored over eastern Eurasia.</footnote>

<footnote n="7">⁷ Actually, Olsson and Hibbs (2005) say that their initial observations are based on 11,000 BCE because it is around this time that unequal levels of development began to emerge due to population migrations that had started in Africa some 70,000 years earlier and climate change that melted glaciers thereby making agriculture possible in the northern hemisphere.</footnote>
decline around the same time but China re-emerged more strongly in the Sui/T'ang/Song era (roughly 8th–13th centuries CE) than did the Mediterranean, although the dumb-bell structure was initially rebuilt in terms of exchanges between the now-Islamic Middle East and China. China then stagnated, thanks in large part to the Mongol takeover, but its economic innovations were dif-fused across Eurasia to Europe thereby establishing a foundation for subsequent industrial revolutions that catapulted first Britain and then other parts of Europe into the economic lead after the 18th century CE. More recently, a few areas settled by British and European migrants in large numbers have moved ahead of Europe in terms of technological development and economic wealth.

Most of this story makes some tangential appearance in the Comin *et al.* discussion but it does not figure very prominently in the analysis or conclusions. If technology advantages are persistent, why did the Persian Gulf area (Sumer) not maintain its lead? Why did the Rome-Han exchange between the two most advanced parts of the world collapse? Why did China surge ahead only to stagnate in the same period Europe was catching up and forging ahead? Why was Europe the initial beneficiary of industrial revolution but later eclipsed by the United States? Put differently, why did some European colonies out-perform their one-time metropoles? We have various answers for these questions, although many remain contested areas of inquiry. Comin *et al.* (2010) concentrate primarily on the role of European migration in the post-1500 period which helps to answer one of the questions (the near-contemporary and highly selective, colonial catch up with the metropoles) but do not really address the earlier historical questions.

The problem here is that the European migration to less populated North America and Australia / New Zealand was a fairly unique phenomenon.<fnref n="8" /> We know a fair amount about how and why a few of the colonies attracted a disproportionate share of migrating labor and how that was then parlayed into disproportionate shares of international capital investment and global trade integration, in conjunction with optimal locations (in terms of climate and oceans) and natural endowments.<fnref n="9" /> But while large-scale migrations did occur in earlier periods, they cannot explain the decline of Sumer, Egypt, Rome, Han China in ancient history or the fall of various empires in medieval history.<fnref n="10" />

<footnote n="8">⁸ Perhaps the main exceptions are the ‘out of Africa’ movements 50 to 100, 000 years ago in which our species colonized the world and Greek and Phoenician colonization in the first millennium BCE.</footnote>

<footnote n="9">⁹ See, for instance, the analyses reported in Acemoglu, Johnson, and Robinson (2001, 2002); Sachs, Mellinger, and Gallup (2001); and Krieckhaus (2006).</footnote>

<footnote n="10">¹⁰ In some of these cases, migrations of ‘barbarian’ tribes are part of the decline explanations. However, it is easier to argue that imperial decline or weaknesses attracted the migrations and that because of the decline, the migrations were more difficult to manage than it is to contend that migrations were either the or a principal cause of the decline. Yet many of the countless tribal migrations did not involve individuals with technological skills moving into low-tech environments.</footnote>
The second bias is that the analysis hinges on comparing observations at
only three time points – 1000 BCE, 0, and 1500 CE. If the analysis is to be re-
stricted to three observations, analysts need to be careful that the selected ob-
servations are relatively neutral in their implications for economic growth as-
sessments. The three chosen by Comin *et al.* are not exactly neutral. Towards
the end of the second millennium BCE, the most economically advanced cen-
ters in the world were located in the eastern Mediterranean littoral and China.
The initial observation date, 1000 BCE, encompasses a period of ‘dark age’
depression in the Mediterranean area that had begun around 1200 BCE and
lasted roughly through 800 BCE. The depression in economic and population
growth had been brought on by a combination of extensive drought, massive
migrations, urban destruction, and considerable conflict. China was not in much
better shape. The Western Chou regime in this time period was retreating from
tribal pressures in the west, becoming the Eastern Chou regime in the process,
and initiating a period of fragmentation that led to the Warring States era in the
second half of the first millennium BCE. The year 0 is a bit of a chronological
contrivance but, in marked contrast to 1000 BCE, it captures the high points of
the Roman and Han empires, ostensibly the economic growth leaders of the
ancient world. The third observation point, 1500 CE, of course, passes over
a millennium and a half of interesting developments vis-à-vis relative economic
growth but it also marks more or less the starting point of European oceanic
voyaging. If one of the main indicators of technological growth for this time
period is ships with guns and only one small corner of the world has ships with
guns in 1500, the observation point is hardly neutral.<fnref n="11" /> For example, if the same
indicator had been used in, say, 1400 CE, merely a hundred years earlier, only
China then possessed ships with guns. Europeans were still limited to firing
arrows from their ships at that time.

A third problem is associated with the unit of analysis. Comin *et al.* (2010) carry out most of their analyses examining 104–130 current states and backdat-

<footnote>It was often the other way around although tribal warriors did sometimes possess superior weaponry technology – as illustrated by the Hyksos early second millennium BCE movement into Egypt with chariots and stronger bows. However, exceptions on the order of the Phoenician founding of Carthage certainly occurred.</footnote>

<footnote n="11">¹¹ One of the Comin *et al.* (2010) technology indicators for 1500 is ships with 180+ guns. It seems highly unlikely that any ship in the world carried (or could carry without sinking) 180 guns or cannon as early as 1500. At this time, Portuguese ships were armed with artillery that more closely resembled mortars more than cannons but the naos were fairly small and only a few pieces of artillery could be carried on board ship. On the other hand, if the opposition possessed no maritime artillery, as in the Indian Ocean, a few guns often (but not always) sufficed. Henry VIII of England did have several very large ships constructed in the second decade of the 16th century and at least one (The Great Harry) carried 184 guns. But most of these guns were too small to do damage to ships and were used to repel boarders. The ships proved hard to sail, at least one capsized in part due to the heavy guns carried, and by the 1530s, the surviving ships were carrying fewer guns. See Hogg and Batchelor (1978: 11) and Archer *et al.* (2002: 262–263).</footnote>
ing their attributes based on geographic location. The awkwardness here is that earlier observations are based to some extent on prominent empires. All current states that were once located in the Roman Empire, for instance, receive the same score in the year 0. That means Libya, Syria, Romania, France, and the United Kingdom are scored exactly the same. More generally, empires tended to cover large territories in which some areas were more economically advanced than were others. The Comin et al.'s approach treats imperial peripheries as equivalent to imperial centers. It also implies that imperial technologies persisted. In some senses, they did as exemplified by roads and canals that were modified over the years. In other respects, however, the technologies survive only in the form of scattered ruins that attract curious tourists.

Relying on the Peregrine (2003) *Atlas of Cultural Evolution* source for coding technology creates a fourth problem.<fnref n="12" /> The *Atlas of Cultural Evolution* (ACE), a database that provides systematic information on societal complexity in all prehistorical areas, is indispensable for places less well known. Yet once an area moves from prehistorical to historical, ACE ceases to code its complexity levels. If one begins an analysis in 1000 BCE, a respectable part of the ancient world has already moved beyond the ACE codings which were designed mainly for earlier, less developed, pre-written history circumstances. Using ACE in the year 0 is even more difficult to defend.

All efforts to enumerate technology run into the problem of filtering what is included and excluded. For instance, more recent efforts to measure the pace of change in industrial innovation, on occasion, have given equal weight to ball point pens as they do to jet engines.<fnref n="13" /> Ball point pens and jet engines do not figure in the Comin et al.'s study but they do abandon ACE for the 1500 CE observation and apply a 24 item scale to measure technological development. However, a fifth source of problems concerns the fact that eight of the twenty-four indicators are military in nature. They include standing army, cavalry, firearms, muskets, field artillery, warfare capable ships, heavy naval guns, and ships with 180+ guns. Are these indicators of technology or military power? If the latter, the more straightforward interpretation, the explanation has been altered substantially. Is it military technology that predicts to contemporary economic wealth? It is not clear, moreover, why some things are double- or triple-counted (two measures of firearms and three measures of naval capability for instance).<fnref n="14" /> Another three indicators in the transportation category capture ships

<footnote n="12">¹² ACE is based on the nine-volume *Encyclopedia of Prehistory* (Peregrine and Embers 2001).</footnote>

<footnote n="13">¹³ See, for instance, the list of innovations examined in van Duijn (1983: 178).</footnote>

<footnote n="14">¹⁴ While there is no reason to spend a great deal of time on a single indicator, the technological significance of cavalry, at least on or after 1500, is questionable. At one point, the adoption of cavalry and, later, the stirrup, reflected significant changes in military technology but in places that had access to horses these changes long preceded 1500 CE. Central Eurasian nomads led the way but did not necessarily create standing cavalries. Assyrians began to emulate their practices</footnote>
capable of crossing the Atlantic, Pacific, and Indian Oceans respectively which means one-fourth of the indicators privilege states with commercial maritime capability. In 1500, there was very little in the way of state navies (Modelski and Thompson 1988: 53). Only a few states such as Venice, Portugal, and England maintained state fleets. Commercial vessels were more likely to be pressed into military service when necessary. One can certainly imagine rationales for giving maritime capability heavy weight in technology measurement but no explicit argument is advanced. Similarly, mixing military with non-military technologies can be viewed as problematic if there exist ongoing arguments about whether it was military technology per se that enabled the Europeans to dominate what used to be called the Third World.<fnref n="15" /> At the same time, all sources agree that the European military advantage in 1500 was very rudimentary.

Finally, there are 14 tables in Comin *et al.'s* work (2010), most of which are devoted to regression analysis involving data pertinent to the three observation points. Perhaps not surprisingly, somewhat different outcomes are associated with each of the tables which complicate summarizing accurately and simply the bottom line of the empirical effort. But putting that issue aside, two tables focusing on descriptive statistics probably deserve more attention than they receive. Table 1 synthesizes the core information of the two tables on average scores for technology adoption in selected continents and civilizations.

<table><caption>**Table 1.** Average overall technology adoption by selected continents and civilizations</caption><thead><tr><th>Continent</th><th>1000 BCE</th><th>0 CE</th><th>1500 CE</th><th>Current</th></tr></thead><tbody><tr><td>Europe</td><td>.66</td><td>.88</td><td>.86</td><td>.63</td></tr><tr><td>W. Europe</td><td>.65</td><td>.96</td><td>.94</td><td>.71</td></tr><tr><td>Africa</td><td>.36</td><td>.77</td><td>.32</td><td>.31</td></tr><tr><td>Asia</td><td>.58</td><td>.88</td><td>.66</td><td>.41</td></tr><tr><td>China</td><td>.90</td><td>1.00</td><td>.88</td><td>.33</td></tr><tr><td>Indian</td><td>.67</td><td>.90</td><td>.70</td><td>.31</td></tr><tr><td>Arab</td><td>.95</td><td>1.00</td><td>.70</td><td>.43</td></tr><tr><td>America</td><td>.24</td><td>.33</td><td>.14</td><td>.47</td></tr><tr><td>Oceania</td><td>.20</td><td>.17</td><td>.12</td><td>.73</td></tr></tbody></table>

*Source:* This table combines and simplifies tables 4 (on continents) and 5 (on civilizations) in Comin *et al.* (2010: 77).

<footnote>early in the first millennium BCE, as did the Chinese some 600 years later. After 1500, the maintenance of large cavalry units in Eurasia were more likely to signify aristocratic and agrarian constraints on technological development. Thus, as a 1500 CE indicator, it really only serves to differentiate places that had horses and those that did not (the Americas, the southern half of Africa, and Australia).</footnote>

<footnote n="15">¹⁵ Compare Parker (1988) and Thompson (1999) on this question.</footnote>
Table 1 demonstrates a simple pattern. All areas indicated a peak in the year 1 and then decline. The Europeans decline least. The Americans and Oceanians make a comeback in the current time period while Africans and Asians are showing as continuing to decline. Whether or not this pattern makes historical sense, it suggests that there are very real limits to the technological persistence argument. If the data are ‘right’, we need to explain what happened to China, India, and the Arabs, all of whom were technological leaders at one time and then far from it at other, later times, especially after 1500. Table 1 suggests that the question should not be one of asking whether technological advantages persist in general, but why are they sometimes lost and sometimes gained.

## A Different Approach and Indices

We prefer to follow up on the tantalizing simplifications of Table 1. We first recreate a Diamond/Olsson-Hibbs index for a very early biogeographical advantage. Using ACE data on development complexity for four observations: 4000 BCE, 3000 BCE, 2000 BCE and 1000 BCE, we then switch to Maddison's data on gross domestic product (GDP) per capita which begins in year 1 CE and continues through 1000 CE, 1500 CE, 1600 CE, 1700 CE, 1820 CE, 1870 CE, 1913 CE, 1950 CE, 1973 CE, and 2003 CE. Sixteen observations should be better than one or three. Rather than attempt to create a different technology scale for each observation, we rely primarily on summary biogeographical and ACE indexes for the BCE period and a standardized index of economic development for the CE era.

Instead of looking at current countries, we use calculations for 8 ‘regions’ (Western Europe, Eastern Europe, the USSR, Asia, Japan, Latin America, Africa, and the Western Offshoots) that remain the same from 8000 BCE to 2003 CE. There is no claim made here that either regions in general or these particular regional identifications are ideal units of analysis. Maddison's aggregations are more than a bit idiosyncratic. Yet using his older data means using his choice of aggregations because dis-aggregated numbers are not made available. They do offer, however, several advantages. Regions could be said to more closely approximate ancient empires than do countries, although there is distortion either way.<fnref n="16" /> Current regions do at least resemble ancient regions with little distortion. Maddison (2007: 382) makes regional GDP per capita data available back to the year 1. One can certainly argue that the data are fabrications but an effort has been made to justify and standardize them as meaningful and systematic fabrications. Moreover, Maddison (1995: 21) raised a similar issue to the present concern by stressing that the regional hierarchy of

<footnote n="16">¹⁶ Switching from states to regions does not eliminate the center-periphery problem but there does seem to be some tendency for regions to become more homogenous over time in terms of existing levels of economic development.</footnote>
economic growth performance changed very little since 1820. The regions that were ahead in 1820 have remained ahead. Similarly, the regions in the hierarchical cellar were still at the bottom nearly 200 years later. This affords us with the opportunity to not only re-address Comin et al.'s persistence question with Maddison's data but to also extend Maddison's version of the persistence question backwards in time to 8000 BCE. If the regional hierarchy has been stable for the past two centuries, can we say the same for the past ten millennia? If the hierarchy is more stable in the 'short-term' (i.e., centuries) than it is in the long-term (millennia), what does that tell us about technological persistence?

One disadvantage of the Maddisonian regional approach is that it does distort ancient history in the sense that the regions with which we are familiar today, and the ones Maddison relied on, were regions before but they were not as important as regions as they have since become. To give full justice to ancient history, we would prefer data on Sumer to the Middle East (also not in Maddison's geographical lexicon), Indus to India, or China to Asia.17 Maddison's regions become more awkward and heterogeneous the farther back in time we go but there is little choice once a decision has been made to utilize Maddison's GDP per capita constructions and wed them with ACE complexity scores in order to encompass ten millennia.18

Switching to GDP per capita also obscures the Comin *et al.'s* emphasis on technology somewhat.19 A more straightforward measure of technology across time would be preferable but hard to imagine. With sixteen observations across ten millennia, one would have to create a new technological complexity scale for each observation. While it might be possible to do that, it seems preferable to simplify the task by relying on ACE indices for the BCE period and Maddison's index for the CE era. Relying on GDP per capita as a crude proxy for technological complexity is certainly not uncommon. Yet these indicator simplifications only suggest that our interpretation of the problem will not be the last word on the subject, any more than was Olsson and Hibbs' (2005) or Comin *et al.'s* (2010).20

At the same time, we can examine this question of path dependency in an entirely different way and one that avoids the problems associated with using Maddison's data. If Maddison's regions are thought to be idiosyncratic and

<footnote n="17">17 Maddison seems to have preferred to ignore the Middle East as much as possible in his data collection efforts. Presumably, that tendency reflects a desire to evade the problems associated with small, oil rich states and, perhaps, poor data for the poorer members of that region. To the extent that he dealt with this region, it is usually considered as a western extension of Asia. He classifies Egypt as an African state.</footnote>

<footnote n="18">18 That is to say that Maddison's older data are not available independent of his regional aggregations.</footnote>

<footnote n="19">19 Yet consider Comin *et al.'s* (2010).</footnote>

<footnote n="20">20 However, see as well the very strong correlations we find between regional GDP per capita and regional technological standings and report in the Appendix.</footnote>
highly heterogeneous and his older GDP per capita estimates are difficult to verify, we can avoid these liabilities by examining city size data regionally aggregated in more discrete geographical aggregations. City size data (Chandler 1987 and Modelski 2003) are available back to the beginning of cities and the assertion that regions with more large cities are/were wealthier and more technologically advanced than regions with fewer large cities seems easy to advance. Networks of cities, after all, have provided the basic infrastructure of the world economy for millennia.<fnref n="21" /> All large cities do not work exactly the same. Some have served as agrarian hubs while others represent coastal, commercial nodes. But economic development historically has been manifested in the urbanized centers of political-economic wealth and power ever since the rise of Sumer and extending to the Pax Britannica and Americana, centered on London and New York, respectively. The only caveat is that this argument can no longer be sustained in the contemporary era due to the emergence of very large third world cities that confuse the issue of what large cities currently represent.

To operationalize this alternative, we isolate the 25 largest cities between 3700 BCE and 1950 CE at 23 points of observation.<fnref n="22" /> Each city is assigned to one of eleven regions; Mesopotamia/Iran, Southern Mediterranean (extending from Constantinople to Morocco), Northern Mediterranean / Western Europe (initially extending from Greece to Spain and later farther north), South Asia (primarily the areas that became Pakistan and India), Central Asia (encompassing states now designated as ‘stans’ except for Pakistan), Eastern Europe (east of Berlin and Vienna and including what became Russia), Southeast Asia (essentially the areas that became Burma/Myanmar to Vietnam and south), East Asia (encompassing China, Korea, and Japan), North America (basically the United States), Central America (basically Mexico), and South America (the continent south of what is now Panama).<fnref n="23" />

Once a city is assigned to a region, its population is aggregated with other cities in the same region.<fnref n="24" /> Each region's relative share of the total population of the top twenty-five cities then serves as an indicator of its relative regional standing. Initially, the Mesopotamian/Iranian region monopolizes the large cit-

<footnote n="21">21 On this subject, see Chase-Dunn and Willard (1994); Chase-Dunn, Manning, and Hall (2000); Chase-Dunn and Manning (2002); Modelski (2003); and Chase-Dunn, Hall and Turchin (2007).</footnote>

<footnote n="22">22 Choosing to look only at the top 25 is arbitrary but in older periods, cities tend to become fairly small as one moves beyond the first 25. Restricting our focus to the top 25 thus reduces some of the noise that might be introduced by casting the net farther down the size line. It also helps that Chandler (1987) provides more locational information for the first 25. However, Chandler identifies sources of imperial control whereas we are focused on geographical location.</footnote>

<footnote n="23">23 There are a small number of large cities that do not fit in any of these regions (for instance, a few cities rise to make the top twenty-five threshold in the Arabian Peninsula) but their relative prominence tends to be too short-lived to expand the number of regions.</footnote>

<footnote n="24">24 Only one city changes its regional location. We code Constantinople as Northern Mediterranean prior to the arrival of the Ottoman Turks and Southern Mediterranean thereafter.</footnote>
ies but urbanization gradually diffuses to the east and west. Some regions, such as East Asia, fluctuate in significance while others attain significance only early or late. Our question is whether knowing something about the relative standing of a region at one point in time is very useful in predicting its standing at successive points in time.

Creating a biogeographical index within the context of Maddison's regions requires some adjustments. To be faithful to the Diamond/Olsson and Hibbs argument, the maximal set of ingredients for such an index should include observations for climate, continental size, continental axis direction, numbers of large mammals and plants that were domesticated, and the onset of agriculture. But if we are differentiating within continents (Maddison has five Eurasian regions: Western Europe, Eastern Europe, the former Soviet Union, Asia, and Japan), continental size is no longer an issue. Climate is another casualty because most regions in our study are characterized by very different climate zones.<fnref n="25" />

Differentiating east-west axes (Eurasia) from north-south axes (Americas, Africa, and Australia) is not difficult.<fnref n="26" /> Olsson and Hibbs (2005) provide information on plants and large mammals for most of the regions, as indicated in Table 2. Dates on the timing of agricultural revolutions in specific areas can be linked to regional locations without too much distortion. The dates in parentheses are estimates based on discussion of the spread of agriculture to areas in which it did not originate (Smith 1995; Imamura 1996; Thomas 1996; Frachetti et al. 2010). To create a single biogeographical index, the binary axis information is scored as 5 points if a region is in the vicinity of the Eurasian east-west axis and 0 points if the region is not located within Eurasia. The distribution of plants and mammals is trichotomized as high (Western and Eastern Europe), medium (Asia and the former Soviet Union), and low (all other regions). High scores were assigned 10 points, the medium scores received 6 points, and low scores were turned into 2 points.<fnref n="27" /> For the agricultural revolution timing,

<footnote n="25">²⁵ Another problem is that some regions have experienced climate changes over the last ten millennia. See, e.g., Burroughs (2005).</footnote>

<footnote n="26">²⁶ A reviewer, contrary to Diamond, has argued that Africa has a long east-west axis stretching across the Sahel to the Horn. We do not find this axis very compelling because of the difficulties in crossing (we know French soldiers had problems making the crossing to set up the 1898 Fahoda crisis) and the limited historical traffic actually traversing it (at best, presumably, small groups of desert nomads). More important, large and urbanized population centers at both ends, which may be the most critical factor in differentiating between east-west and north-south interactions even though it goes beyond the Diamond argument, are missing in the African case. Eurasia's east-west axis was not all that easy to traverse but traders at least had strong profit incentives to make the effort. Just how important people were as carriers to the diffusion of seeds and animals across Eurasia is not entirely clear. Nonetheless, we will check our results to see how critical the presence or absence of an African east-west axis is to the outcome.</footnote>

<footnote n="27">²⁷ We did not give equal weight to the continental axis and plants/mammals indicators because Eurasia already scores relatively highly on the distribution of domesticated flora and fauna. In</footnote>
the regional timing date was first subtracted from the Near Eastern timing of 8000 BCE and then divided by 1000.<fnref n="28" /> An aggregate regional score is then constructed by simply adding the axis, plant-mammal, and agricultural revolution scores – reported in the last column of Table 2.

The biogeographical, rank order outcome puts Eastern Europe (13), Western Europe (12), and Asia (10.5) in the early lead, with Eastern Europe in the first rank largely because agriculture diffused there from the Near East before it reached Western Europe.

<table><caption>**Table 2. Constructing a biogeographical index**</caption><thead><tr><th>Region</th><th>EW Axis Direction</th><th>Plants</th><th>Large Mammals</th><th>Agricultural Revolution</th><th>Score</th></tr></thead><tbody><tr><td>Western Europe</td><td>Yes</td><td>33</td><td>9</td><td>(6000-4000 BCE)</td><td>12.0</td></tr><tr><td>Western Off-shoots</td><td>No</td><td>2-4</td><td>0</td><td>2500 BCE</td><td>-3.5</td></tr><tr><td>Eastern Europe</td><td>Yes</td><td>33</td><td>9</td><td>(6000 BCE)</td><td>13.0</td></tr><tr><td>Former Soviet Union</td><td>Yes</td><td></td><td></td><td>(2200 BCE)</td><td>5.2</td></tr><tr><td>Latin America</td><td>No</td><td>2-5</td><td>0-1</td><td>2600-2500 BCE</td><td>-2.5</td></tr><tr><td>Africa</td><td>No</td><td>4</td><td>0</td><td>2000 BCE</td><td>-2.0</td></tr><tr><td>Asia</td><td>Yes</td><td>6</td><td>7</td><td>5750-6500 BCE</td><td>10.5</td></tr><tr><td>Japan</td><td>Yes</td><td></td><td></td><td>(2500-2400 BCE)</td><td>-0.55</td></tr></tbody></table>

*Note:* Cells left blank by missing data required estimation.

The former Soviet Union (5.2), part European and part Asian, falls in the middle of the regional pack. Lowest ranked are Japan (-0.55), Africa (-2.0), and Latin America (-2.5). The outcome certainly mirrors Diamond's (1997) argument about the advantages of Eurasia over the rest of the world.

To measure complexity in the fourth, third, second and first millennia BCE, we employed the ACE aggregate complexity score for some 289 prehistorical groups which were first assigned to one of Maddison's regions and then averaged.<fnref n="29" /> The complexity score simply adds the sub-scores for 10 indicators:

some respects, the irony is that the super-region or continent that experienced the most diffusion needed it least. The exception to this observation is the much later diffusion of industrial technology from China to Europe in the first half of the second millennium CE. On this point, see, among a number of others, Modelski and Thompson (1996).

<footnote n="28">²⁸ In cases in which the timing is indicated as falling within a range of years, the middle point between the high and low timing dates is used for this calculation.</footnote>

<footnote n="29">²⁹ Ideally, we might have weighted the averaging process by the size of the group but this information, unsurprisingly, is not available.</footnote>
writing, residence, agriculture, urbanization, technology, transportation, money, population density, political integration, and societal stratification. The scales for each indicator are reported in Table 3 to give a better sense of what is involved in this computation.

One of the less expected byproducts of this analysis is that the western end of Eurasia is portrayed as relatively rich in biogeographical and societal complexity terms. Europe is often thought of as a backwater that suddenly became rich and prosperous only in the last half millennium. A longer term perspective suggests otherwise. Keeping in mind that these regional aggregations are heterogeneous and the scores are averages across multiple groups residing within their boundaries, Europe comes across as fairly consistent in its rankings across ten millennia.<fnref n="30" /> The temporary exception is the long period of decline after the fall of the Western Roman Empire.

<table><caption>**Table 3.** The ACE complexity score components</caption><thead><tr><th></th><th>Indicator</th><th>Scale</th></tr></thead><tbody><tr><td>1</td><td>Writing and Records</td><td>1 = none, 2 = mnemonic or non-written records, 3 = true writing</td></tr><tr><td>2</td><td>Residence Fixity</td><td>1 = nomadic, 2 = seminomadic, 3 = sedentary</td></tr><tr><td>3</td><td>Agriculture</td><td>1 = none, 2 = 10% or more but secondary, 3 = primary</td></tr><tr><td>4</td><td>Urbanization (largest settlement)</td><td>1 = fewer than 100 persons, 2 = 100–399 persons, 3 = 400+ persons</td></tr><tr><td>5</td><td>Technological Specialization</td><td>1 = none, 2 = pottery, 3 = metalwork (alloys, forging, casting)</td></tr><tr><td>6</td><td>Land Transport</td><td>1 = human only, 2 = pack or draft animals, 3 = vehicles</td></tr><tr><td>7</td><td>Money</td><td>1 = none, 2 = domestically usable articles, 3 = currency</td></tr><tr><td>8</td><td>Population Density</td><td>1 = less than 1 person per square mile, 2 = 1–25 persons per square mile, 3 = 26+ persons per square mile</td></tr><tr><td>9</td><td>Political Integration</td><td>1 = autonomous local communities, 2 = 1 or 2 levels above local communities, 3 = 3 or more levels above community</td></tr><tr><td>10</td><td>Societal Stratification</td><td>1 = egalitarian, 2 = 2 social classes, 3 = 3 or more classes or castes</td></tr></tbody></table>

The main results of our multiple observation approach to the long-term persistence question are reported in Tables 4 through 8.<fnref n="31" /> Table 4 reports the actual biogeographical, ACE and average GDP per capita scores for the eight Maddi-

<footnote n="30">³⁰ Olsson and Paik's (2012) argument and findings, for example, suggest differentiating Southern from Northern Europe in terms of the timing of adopting agriculture and its implications.</footnote>

<footnote n="31">³¹ Space considerations preclude reporting the full correlation matrices. Thus, only significant correlations are shown. The full matrices are available from the authors on request.</footnote>
sonian regions. Biogeographical advantage puts Western Europe, Eastern Europe, and East Asia in the earliest lead. In 4000 BCE, all five Eurasian regions are scored as about equally complex, with Japan lagging slightly behind. In the next several millennia, the European region scores steadily improve. The two Asian regions fluctuate and fall behind both their European and South American / African counterparts. The other parts of the world register consistent gains in average complexity, with North America and Australia / New Zealand (the Western Offshoots) showing only marginal improvements.

<table><caption>**Table 4.** Biogeographical advantage / complexity / GDP per capita averages (dates BCE are in italics)</caption><thead><tr><th>Date</th><th>Western Europe</th><th>Eastern Europe</th><th>Former USSR</th><th>Western Off-shoots</th><th>Latin America</th><th>Asia</th><th>Japan</th><th>Africa</th></tr></thead><tbody><tr><td>8000</td><td>12.0</td><td>11.1</td><td>5.2</td><td>-3.5</td><td>-2.5</td><td>10.5</td><td>-0.6</td><td>-2.0</td></tr><tr><td>4000</td><td>18.5</td><td>18.5</td><td>18.5</td><td>11.4</td><td>13.0</td><td>18.3</td><td>17.1</td><td>13.7</td></tr><tr><td>3000</td><td>22.3</td><td>22.3</td><td>22.3</td><td>12.0</td><td>16.2</td><td>19.6</td><td>16.1</td><td>14.1</td></tr><tr><td>2000</td><td>27.8</td><td>27.8</td><td>27.8</td><td>12.9</td><td>17.8</td><td>20.1</td><td>17.3</td><td>15.7</td></tr><tr><td>1000</td><td>50.0</td><td>50.0</td><td>50.0</td><td>13.0</td><td>19.4</td><td>15.5</td><td>13.0</td><td>20.3</td></tr><tr><td>1</td><td>576</td><td>412</td><td>400</td><td>400</td><td>400</td><td>457</td><td>400</td><td>472</td></tr><tr><td>1000</td><td>427</td><td>400</td><td>400</td><td>400</td><td>400</td><td>466</td><td>425</td><td>425</td></tr><tr><td>1500</td><td>771</td><td>496</td><td>499</td><td>400</td><td>416</td><td>572</td><td>500</td><td>414</td></tr><tr><td>1600</td><td>889</td><td>548</td><td>552</td><td>400</td><td>438</td><td>576</td><td>520</td><td>422</td></tr><tr><td>1700</td><td>997</td><td>606</td><td>610</td><td>476</td><td>527</td><td>572</td><td>570</td><td>421</td></tr><tr><td>1820</td><td>1202</td><td>683</td><td>688</td><td>1202</td><td>691</td><td>577</td><td>669</td><td>420</td></tr><tr><td>1870</td><td>1960</td><td>937</td><td>993</td><td>2419</td><td>676</td><td>548</td><td>737</td><td>500</td></tr><tr><td>1913</td><td>3457</td><td>1695</td><td>1488</td><td>5233</td><td>1493</td><td>658</td><td>1387</td><td>637</td></tr><tr><td>1950</td><td>4578</td><td>2111</td><td>2841</td><td>9668</td><td>2503</td><td>639</td><td>1921</td><td>890</td></tr><tr><td>1973</td><td>11417</td><td>4988</td><td>6059</td><td>16179</td><td>4513</td><td>1225</td><td>11434</td><td>1410</td></tr><tr><td>2003</td><td>19912</td><td>6476</td><td>5397</td><td>28039</td><td>5786</td><td>3842</td><td>21218</td><td>1549</td></tr></tbody></table>

Switching to the GDP per capita measure indicates a different story that suggests that ACE complexity scores probably cannot necessarily be translated directly into GDP per capita terms. On the other hand, 1000 years have passed between 1000 BCE and 1 CE. In the West, the Greek city state complex had given way to the Roman Empire. In the East, Chinese fragmentation had been reversed by the rise of the Qin/Han Dynasties. In the year 1, accordingly, Western Europe and Asia are in the lead, Africa is third, and the other regions are rated as roughly equal. In 1000 CE, Asia retains its former lead, followed by Western Europe, Japan and Africa (all three with near-identical averages), with all other regions scoring at the 1 year minimum.

By 1500 CE, however, Maddison's data have Western Europe once more in the lead with Asia a distant second. The USSR, Japan, and Eastern Europe fall in the middle of the regional hierarchy. Latin America demonstrates some
slight gain while Africa manifests steady decline. North America and Austra-
lia's position and wealth/technology level is shown as remaining unchanged for
1500 years. Then the scores change dramatically. The western European GDP
per capita almost doubles by 1820. The Western Offshoots (North America and
Australia / New Zealand) are not far behind. Eastern Europe, the USSR, and
Latin America have made some progress with development levels that are
about half those of the leaders. Average 1820 Asian and African GDP per cap-
ita are little changed from their 1500 levels. By the end of the 20th century, the
Western Offshoots, Western Europe, and Japan have created strong leads. Latin
America and the USSR are in the middle of the hierarchy but considerably be-
hind the leaders. Eastern Europe, Asia, and Africa occupy the bottom of the
regional hierarchy.

Table 5 reports the same data in regional rank order. The long-term out-
come encompasses several significant shifts in relative standing. Western Eu-
rope is an early leader but falters in the Medieval Era before rising to the lead
after the industrial revolution – a lead it does not maintain beyond the 19th cen-
tury. The Western Offshoots remain in the technology/growth cellar throughout
most of the ten millennia period studied before seizing the lead in the last cen-
tury. Asia begins in the middle, rises to the lead in the first millennium CE, and
then falls back toward the bottom. Japan's position oscillates – initially middle,
then falling back to low, then to high, back to the middle, and then back to
high. Eastern Europe and the USSR begin relatively high and decline to the
middle. Latin America starts low and never exceeds a middle ranking. Africa
tends to stay near the bottom except in the first millennium CE.

Scanning rank orders is one thing. We can improve on this form of data in-
spection by calculating Spearman Rank Order coefficients from observation to
observation, as is done in Tables 6 and 7. Table 6 reports significant coeffi-
cients without any modification of the rank orders. Table 7 corrects for the
more recent European migrations, following a technique utilized by Comin
et al. (2010).<fnref n="32" /> In Table 6, there are basically four clusters of coefficients.

<footnote n="32">³² Comin *et al.* (2010) utilize Putterman and Weil's (2009) matrix on post-1500 migrations to correct 1500 and onward outcomes by the proportion of national population that has migrated into the country. We do the same for regional aggregations. Putterman and Weil's original migration matrix includes information of the migration from 1500 to 2000 for 165 countries. This state-level matrix was converted to a regional-level matrix, so that the modified matrix gives the proportions of each region's population in the year of 2000 that resided in its own and other regions in 1500. As in Comin *et al.*, pre-1500 regional rankings were generated by pre-multiplying the 'raw' vectors of wealth/technology scores by the modified (regional) migration matrix. The resulting historical rankings thus reflect the post-1500 migration on the regional basis. For details of the migration matrix, see Putterman and Weil (2009, 2010).</footnote>
<table><caption>**Table 5.** Regional rank orders</caption><thead><tr><th>Date</th><th>Western Europe</th><th>Eastern Europe</th><th>Former USSR</th><th>Western Off-shoots</th><th>Latin America</th><th>Asia</th><th>Japan</th><th>Africa</th></tr></thead><tbody><tr><td>8000</td><td>2</td><td>1</td><td>4</td><td>8</td><td>7</td><td>3</td><td>5</td><td>6</td></tr><tr><td>4000</td><td>1</td><td>1</td><td>1</td><td>8</td><td>7</td><td>4</td><td>5</td><td>6</td></tr><tr><td>3000</td><td>1</td><td>1</td><td>1</td><td>8</td><td>5</td><td>4</td><td>6</td><td>7</td></tr><tr><td>2000</td><td>1</td><td>1</td><td>1</td><td>8</td><td>5</td><td>4</td><td>6</td><td>7</td></tr><tr><td>1000</td><td>1</td><td>1</td><td>1</td><td>7</td><td>5</td><td>6</td><td>7</td><td>4</td></tr><tr><td>1</td><td>1</td><td>4</td><td>5</td><td>5</td><td>5</td><td>3</td><td>5</td><td>2</td></tr><tr><td>1000</td><td>2</td><td>4</td><td>4</td><td>4</td><td>4</td><td>1</td><td>3</td><td>3</td></tr><tr><td>1500</td><td>1</td><td>5</td><td>4</td><td>8</td><td>6</td><td>2</td><td>3</td><td>7</td></tr><tr><td>1600</td><td>1</td><td>4</td><td>3</td><td>8</td><td>6</td><td>2</td><td>5</td><td>7</td></tr><tr><td>1700</td><td>1</td><td>3</td><td>2</td><td>7</td><td>6</td><td>4</td><td>5</td><td>8</td></tr><tr><td>1820</td><td>1</td><td>5</td><td>4</td><td>1</td><td>3</td><td>7</td><td>6</td><td>8</td></tr><tr><td>1870</td><td>2</td><td>4</td><td>3</td><td>1</td><td>6</td><td>7</td><td>5</td><td>8</td></tr><tr><td>1913</td><td>2</td><td>3</td><td>5</td><td>1</td><td>4</td><td>7</td><td>6</td><td>8</td></tr><tr><td>1950</td><td>2</td><td>5</td><td>3</td><td>1</td><td>4</td><td>8</td><td>6</td><td>7</td></tr><tr><td>1973</td><td>3</td><td>5</td><td>4</td><td>1</td><td>6</td><td>8</td><td>2</td><td>7</td></tr><tr><td>2003</td><td>3</td><td>4</td><td>6</td><td>1</td><td>5</td><td>7</td><td>2</td><td>8</td></tr></tbody></table>

<table><caption>**Table 6.** Significant Spearman rank order coefficients (only entries with *P* < 0.05 are shown; column numbers correspond to row numbers)</caption><thead><tr><th>Date</th><th>1</th><th>2</th><th>3</th><th>4</th><th>-</th><th>8</th><th>9</th><th>-</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th></tr></thead><tbody><tr><td>8000</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>4000</td><td>2</td><td>.93</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3000</td><td>3</td><td>.85</td><td>.93</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2000</td><td>4</td><td>.85</td><td>.93</td><td>1.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1000</td><td>5</td><td></td><td>.77</td><td>.81</td><td>.81</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1</td><td>6</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1000</td><td>7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1500</td><td>8</td><td></td><td>.71</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1600</td><td>9</td><td></td><td>.85</td><td>.85</td><td>.85</td><td>.93</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1700</td><td>10</td><td></td><td>.90</td><td>.93</td><td>.93</td><td>.79</td><td>.91</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1820</td><td>11</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1870</td><td>12</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.85</td><td></td><td></td><td></td><td></td></tr><tr><td>1913</td><td>13</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.92</td><td>.88</td><td></td><td></td><td></td></tr><tr><td>1950</td><td>14</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.95</td><td>.91</td><td>.88</td><td></td><td></td></tr><tr><td>1973</td><td>15</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.83</td><td></td><td>.74</td><td></td><td></td></tr><tr><td>2003</td><td>16</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.76</td><td>.76</td><td></td><td>.91</td><td></td></tr></tbody></table>
The first cluster encompasses coefficients in the BCE era and indicates that the rank orders were similar between 8000 and 1000 BCE.<fnref n="33" /> A second cluster suggests significant similarity in the rank orders between 4000 to 2000 BCE and 1500–1700 CE. The third cluster indicates little change in the rank orders between 1500 and 1700 CE. Finally, the fourth cluster singles out the period between 1820 and 2003 CE as roughly similar in terms of rankings.

If we control for the well-known impact of the early modern and modern European migrations, not too much changes. Table 7 still shows an early cluster in the BCE era and the second cluster of similarity linking the BCE era to the second period spanning from 1600 to 1913.<fnref n="34" /> The third cluster, focusing on 1500–1700 CE in Table 4, disappears in Table 7. The modern fourth cluster, however, remains evident.

<table><caption>**Table 7.** Significant Spearman rank order coefficients adjusted for migration (only entries with *P* < 0.05 are shown; column numbers correspond to row numbers)</caption><thead><tr><th>Date</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>-</th><th>-</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th></tr></thead><tbody><tr><td>8000</td><td>1</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>4000</td><td>2</td><td>.74</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3000</td><td>3</td><td>.83</td><td>.86</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2000</td><td>4</td><td>.76</td><td></td><td>.93</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1000</td><td>5</td><td></td><td></td><td>.81</td><td>.93</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1</td><td>6</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1000</td><td>7</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1500</td><td>8</td><td></td><td></td><td></td><td></td><td>.74</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1600</td><td>9</td><td></td><td>.91</td><td>.74</td><td>.85</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1700</td><td>10</td><td></td><td>.88</td><td>.88</td><td>.76</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1820</td><td>11</td><td></td><td></td><td></td><td>.73</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1870</td><td>12</td><td></td><td></td><td></td><td>.76</td><td></td><td></td><td></td><td></td><td>.85</td><td></td><td></td><td></td><td></td></tr><tr><td>1913</td><td>13</td><td></td><td></td><td></td><td>.76</td><td>.71</td><td></td><td></td><td></td><td>.92</td><td>.88</td><td></td><td></td><td></td></tr><tr><td>1950</td><td>14</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.95</td><td>.91</td><td>.88</td><td></td><td></td></tr><tr><td>1973</td><td>15</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.83</td><td></td><td>.74</td><td></td><td></td></tr><tr><td>2003</td><td>16</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.76</td><td>.76</td><td>.91</td><td></td><td></td></tr></tbody></table>

Whatever these data represent, they do not support an argument for unmitigated technological and economic wealth persistence. To put it another way, it is rather hard to argue that in general national wealth was determined in 8000 BCE. The unadjusted regional rank order correlation in that year is -.143 (with the migration adjustment, the correlation is still only .286. The first-ranked region

<footnote n="33">³³ This first cluster is much diminished in terms of the number and size of the coefficients if Africa is coded as possessing an east-west axis.</footnote>

<footnote n="34">³⁴ The first cluster almost disappears when provision is made for an east-west axis in Africa. The second and third clusters remain roughly the same.</footnote>
in 8000 BCE has slipped to number three ten thousand years later. The lowest-ranked region has climbed to number one. One thousand BCE is no more determinative (the unadjusted spearman coefficient is -.356 and .214 with an adjustment for migration). As in 8000 BCE, the two lowest ranking regions in 1000 BCE were in the lead by 2003. Africa, in the middle in 1000 BCE, has been at the bottom of the hierarchy for the past 500 years. Eastern Europe and the USSR, once among the ACE leaders, have struggled to stay in the middle of the rankings. Only the Asian and Latin American positions in 2003 closely resemble their 1000 BCE rankings.

What if we shift our focus to the year 1? The ability to predict from 1 to 2003 is about the same as when we use 8000 or 1000 BCE. The Spearman coefficient is -.380 if unadjusted and .262 if corrected for migration. Western Europe, Eastern Europe, the USSR, and Latin America have similar rankings at the end of the 20th century that they held in the year 1. Asia, Japan, Africa, and the Western Offshoots do not. Shifting to a predictive base in 1500 yields a better outcome. Although the unadjusted rank order coefficient is -.238, the adjusted correlation is .619. All but Asia and the Western Offshoots have similar rankings in 2003 that they held in 1500. What is missed, however, is that the mis-predicted regions include the most populous (Asia) and the richest (Western Offshoots) groups. Focusing on rank orders also downplays the size of the gap between the leaders and followers in 1500 and 2003. In 1500, the West European lead represented about a 2:1 lead over the lowest average GDP per capita in Africa and the Western Offshoots (then, of course, far less western and more indigenous North American and Australian). In 2003, the Western Offshoots lead is 19 times as large as the lowest regional GDP per capita (Africa).

But Comin *et al.* (2010) also encountered problems in using 1000 BCE and 0 CE data to predict to the current period. What about earlier shorter predictive capability? Between 4000 BCE and 1000 BCE, as noted earlier, there are few changes in the regional complexity hierarchy. All of the positions are not identical but they are very close. Between 1000 BCE to 1 CE, five regions retain similar positions, while three (Eastern Europe and the USSR decline, Asia vaults to a leading position) change their respective rankings. In the transition from 1 CE to 1500 CE, there is again little change. Only Africa falls substantially in the rankings.

Thus, the Maddisonian regional rankings are fairly stable in what might be called the 'short' or intermediate long-term, if we permit what is considered short to become shorter over time since the observations are not equally spaced. With sixteen observations over ten millennia, the rankings tend not to change all that much when one moves three observations forward in time. Attempts to predict beyond three observations, especially very long forecasts, work less well. That would suggest that technology and wealth distributions persist to
some extent, but not indefinitely. With the partial exception of Latin America, none of the regions examined occupies a roughly similar position across all sixteen observations. Nor does it preclude substantial deviations from the persistence expectation. Asia was once very high in the hierarchy and then very low. Conceivably, it might be very high again, as demonstrated in the case of Japan (and perhaps China sometime in the future). The western offshoots, once at the bottom of the hierarchy for a very long term, eventually took the lead. Even if the offshoots should lose that lead, they are likely to remain near the top of the hierarchy for some time to come. Granted, the western offshoots generated their remarkable shift in the growth hierarchy initially through a combination of technological borrowing and endowment, their subsequent growth was due in part to the development of new technologies. Technological persistence, according to the Maddisonian data, is not destiny.

But what if we put the debatable Maddisonian data aside and look only at the city size data which are grouped in more defensible aggregations and which represent something more than one analyst's best retrospective guesstimate. The correlation pattern that emerges in these data (see Table 8) is both different and more simple than the one generated by Maddisonian GDP per capita figures. Yet, substantively, it leads to similar conclusions.

Three clusters are prominent. The first cluster encompasses 3700 BCE to 2000 BCE and represents the most ancient Mesopotamian concentration of cities. A second cluster began to emerge half way through the first millennium BCE and persists through 1800 CE. We might call this cluster the Silk Road grouping of cities stretching from the Mediterranean through South Asia to East Asia. The names and precise locations of the cities in each region that are most prominent in any given year vary but the regions retain their relative standings more or less, as demonstrated in Fig. 2.

The third cluster has a short life span (1900 and 1950). It represents the ascendance of the West and the technological leadership of Britain (London, Birmingham, Glasgow) and the United States (New York, Boston, Chicago, Detroit, Philadelphia, and Los Angeles). However, even by 1950, the large third world cities such as Calcutta and Bombay are also entering the top twenty-five cities in the world.

So, Table 8 demonstrates persistence as well. The first cluster predominated for 2000 years and then disintegrated, largely due to an inability to feed its expanded population with declining grain productivity. The second cluster of cities stretching from the Mediterranean to East Asia persisted for another 2000 years as the central armature of the world economy but was eventually overtaken by technological changes that had first traveled the Silk Roads but became concentrated in northwestern Europe and North America.
<table><caption>**Table 8.** City size correlations across time</caption><thead><tr><th></th><th>3700</th><th>3000</th><th>2000</th><th>1000</th><th>430</th><th>200</th><th>100</th><th>361</th><th>500</th><th>622</th><th>800</th><th>900</th><th>1000</th><th>1100</th><th>1200</th><th>1300</th><th>1400</th><th>1500</th><th>1600</th><th>1700</th><th>1800</th><th>1900</th></tr></thead><tbody><tr><th>3000</th><td>975</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>2000</th><td>982</td><td>975</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1000</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>430</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>200</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>100</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>361</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>500</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>622</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>800</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>900</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1000</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1100</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1200</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1300</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1400</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1500</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1600</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1700</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1800</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1900</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1950</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody><tfoot><tr><td colspan="21">Note: Only entries with P < 0.05 are shown. Pairwise, year-to-year, correlation coefficients are obtained based on the analysis of each region's share of city population. Years BCE in italics.</td></tr></tfoot></table>

<figure><img src="image_66.png" /><figcaption>**Fig. 2.** Northern Mediterranean / West European and East Asian regional city share scores</figcaption></figure>

The third cluster seems unlikely to retain its prominence for another 2000 years. If nothing else, city size is no longer a reliable instrument for capturing wealth and technological leadership as it once was. But the diffusion of wealth and technology is taking place faster than it once did (Comin and Hobijn 2010). The persistence of relative regional standings, as a consequence, must also be expected to change to varying extents as some once low ranking areas rise in the rankings. Yet there is also no reason to assume that all low-ranking regions
will rise equally. In that respect, some mixture of persistence and change
should be anticipated.

Since the patterns that emerge vary by indicator, do we need to pick and
choose which one seems to have the greatest validity? The city size data dem-
onstrate what we earlier described as largely missing from the earlier analyses
of Olsson and Hibbs (2005) and Comin, Easterly, and Gong (2010). The city
data isolate the Sumerian starting point for relatively large cities and underscore
the ‘dumb-bell’ interaction between the Mediterranean and East Asia across
Diamond's east-west axis. They also capture the post-1800 shift in cities due to
industrialization. In these respects, the city size data most clearly conform to
our understanding of the major shifts in, and evolution of, world history. Yet as
long as all our indicators underline the limitations of persistence, there is really
no reason to focus on one index alone. Multiple indicators show roughly similar
mixtures of persistence and abrupt change.

**Conclusion**

Our point throughout has been that there are important limitations on path de-
pendencies in historical economic growth patterns. Diamond's argument about
east-west axis and the number of plants and large mammals certainly helps ex-
plain Eurasia's advantages over Africa and the Americas. It does not tell us too
much about what happened within Eurasia after the creation of the world's con-
tinents. Whether we use biogeographical, societal complexity, GDP per capita,
or city size indicators, there are very clear limits on the ability to predict in the
long term who will be ahead in one year. Some places have been advantaged
over others but not to the extent of predetermining economic growth well into
the future. We cannot predict who precisely within Eurasia will get ahead based
on Eurasia's initial advantage. Nor could we have predicted how long any Eura-
sian advantage might persist, except to say that it did not last forever. Using our
indicators, we cannot predict who will be on ‘first base’ in 1 CE based on in-
formation in 1000 BCE. We cannot predict who will be ahead in 1950 or 1998
based on information in 1500. These prediction failures are not based on vola-
tility in the data. There is substantial persistence across selected intervals. But
there are also substantial shifts due ostensibly to leads and lags in technological
leadership, demographic differentials, migration, climate change, disease, and
warfare.

If we grant that human existence on planet Earth is characterized by some
tendencies toward the stickiness of wealth and technological persistence subject
to strong temporal limitations, the most interesting questions involve why these
persistence tendencies fail to bar very substantial changes in regional and na-
tional rankings in economic wealth. We probably understand the reasons for
technological and wealth persistence best. We do less well explaining how
these characteristics are overwhelmed or in predicting how they may change in
the future. It is conceivable, but by no means guaranteed, that an emphasis on
very long-term shifts in technology and wealth will give us a better perspective
on why the rich do not always get richer (or even stay rich) and why the poor
sometimes improve their standings in the world pecking order.

References

**Acemoglu D., and Johnson S. 2012.** *Why Nations Fail: The Origins of Power, Prosperity and Poverty*. New York: Crown.

**Acemoglu D., Johnson S., and Robinson J. A. 2001.** The Colonial Origins of Comparative Development: An Empirical Investigation. *American Economic Review* 91: 1369–1401.

**Acemoglu D., Johnson S., and Robinson J. A. 2002.** Reversal of Fortune: Geography and Institutions in the Making of the Modern World Income Distribution. *Quarterly Journal of Economics* 117: 1231–1294.

**Archer C. I., Ferris J. R., Herwig H. H., and Travers T. H. E. 2002.** *World History of Warfare*. Lincoln, NE: University of Nebraska Press.

**Bleaney M., and Dimico A. 2011.** Biogeographical Conditions, the Transition to Agriculture, and Long-Run Growth. *European Economic Review* 55 (7): 943–954.

**Burroughs W. J. 2005.** *Climate Change in Prehistory: The End of the Reign of Chaos*. Cambridge: Cambridge University Press.

**Chanda A., and Putterman L. 2005.** State Effectiveness, Economic Growth, and the Age of States. *States and Development: Historical Antecedents of Stagnation and Advance* / Ed. by M. Lange, and D. Rueschemeyer, pp. 69–91. London: Palgrave Macmillan.

**Chanda A., and Putterman L. 2007.** Early States, Reversals and Catch-up in the Process of Economic Development. *Scandinavian Journal of Economics* 109: 387–413.

**Chandler T. 1987.** *Four Thousand Years of Urban Growth: An Historical Census*. Lewiston, NY – Queenston: St. David's University Press.

**Chase-Dunn C., and Willard A. 1994.** Cities in the Central Political-Military Network since CE 1200. *Comparative Civilizations Review* 30: 104–132.

**Chase-Dunn C., Manning S., and Hall T. D. 2000.** Rise and Fall: East-West Synchro-nicity and Indic Exceptionalism Reexamined. *Social Science History* 24(4): 721–748.

**Chase-Dunn C., and Manning S. 2002.** City Systems and World Systems: Four Mil-lennia of City Growth and Decline. *Cross-Cultural Research* 36(4): 379–398.

**Chase-Dunn C., Hall T., and Turchin P. 2007.** World-Systems in the Biogeosphere: Urbanized State Formation, and Climate Change since the Iron Age. *The World System and the Earth System: Global Socioenvironmental Change and Sustainability Since the Neolithic* / Ed. by A. Hornbrog, and C. C. Crumley, pp. 132–148. Walnut Creek, CA: Left Coast Books.

**Clark G. 2007.** *A Farewell to Alms: A Brief Economic History of the World*. Princeton, NJ: Princeton University Press.
**Comin D., Easterly W., and Gong E. 2010.** Was the Wealth of Nations Determined in 1000 BC? *American Economic Journal: Macroeconomics* 2: 65–97.

**Comin D., and Hobijn B. 2010.** An Exploration of Technology Diffusion. *American Economic Review* 100: 2031–2059.

**Diamond J. 1997.** *Guns, Germs and Steel: The Fate of Human Societies*. New York: W.W. Norton.

**Duijn J. J. van 1983.** *The Long Wave in Economic Life*. London: George Allen and Unwin.

**Findlay R., and O'Rourke K. H. 2007.** *Power and Plenty: Trade, War and the World Economy in the Second Millennium*. Princeton, NJ: Princeton University Press.

**Frachetti M. D., Spengler R. N., Fritz G. J., and Mar'yashev A. N. 2010.** Earliest Direct Evidence for Broomcorn Millet and Wheat in the Central Eurasian Steppe Region. *Antiquity* 84: 993–1010.

**Frank A. G. 1998.** *ReOrient: Global Economy in the Asian Age*. Berkeley, CA: University of California Press.

**Galor O. 2011.** *Unified Growth Theory*. Princeton, NJ: Princeton University Press.

**Hogg I., and Batchelor J. 1978.** *Naval Gun*. Poole: Blandford Press.

**Imamura K. 1996.** Jomon and Yayoi: The Transition to Agriculture in Japanese Prehistory. *The Origins and Spread of Agriculture and Pastoralism in Eurasia* / Ed. by D. R. Harris, pp. 442–464. Washington: Smithsonian Institution Press.

**Krieckhaus J. 2006.** *Dictating Development: How Europe Shaped the Global Periphery*. Pittsburgh, PA: University of Pittsburgh Press.

**Landes D. S. 1998.** *The Wealth and Poverty of Nations: Why Some Are So Rich and Some Are So Poor*. New York: W.W. Norton.

**Maddison A. 1995.** *Monitoring the World Economy, 1820–1992*. Paris: OECD.

**Maddison A. 2001.** *The World Economy: A Millennial Perspective*. Paris: OECD.

**Maddison A. 2007.** *Contours of the World Economy, 1–2030 AD: Essays in Macroeconomic History*. Oxford: Oxford University Press.

**Modelski G. 2003.** *World Cities: –3000 to 2000*. Washington: Faros 2000.

**Modelski G., and Thompson W. R. 1988.** *Sea Power in Global Politics, 1494–1993*. London: Macmillan.

**Modelski G., and Thompson W. R. 1996.** *Leading Sectors and World Powers: The Coevolution of Global Politics and Economics*. Columbia, SC: University of South Carolina Press.

**Morris I. 2010.** *Why the West Rules – For Now: The Patterns of History, and What They Reveal about the Future*. New York: Farrar, Straus and Giroux.

**Morris I. 2013.** *The Measure of Civilization: How Social Development Decides the Fate of Nations*. Princeton, NJ: Princeton University Press.

**Olsson O., and Hibbs D. A. Jr. 2005.** *Biogeography and Long-Run Economic Development. European Economic Review* 49: 909–938.
Olsson O., and Paik C. 2013. *A Western Reversal since the Neolithic? The Long-Run Impact of Early Agriculture*. Working Papers in Economics 552, University of Gothenburg, Department of Economics. URL: https://gupea.ub.gu.se/bitstream/ 2077/32052/1/gupea_2077_32052.1.pdf.

Parker G. 1988. *The Military Revolution: Military Innovation and the Rise of the West, 1500–1800*. Cambridge: Cambridge University Press.

Parthasarathi P. 2011. *Why Europe Grew Rich and Asia Did Not: Global Economic Divergence, 1600–1850*. Cambridge: Cambridge University Press.

Peregrine P. N. 2003. *Atlas of Cultural Evolution*. *World Cultures* 14(1): 1–75.

Peregrine P. N., and Embers M. (Eds.) 2001. *Encyclopedia of Prehistory*. 9 vols. New York: Kluwer Academic/Plenum Publishers.

Pomeranz K. 2000. *The Great Divergence: China, Europe and the Making of the Modern World Economy*. Princeton, NJ: Princeton University Press.

Putterman L. 2008. *Agriculture, Diffusion and Development: Ripple Effects of the Neolithic Revolution*. *Economica* 75: 729–748.

Putterman L., and Weil D. 2009. *Main Appendix to World Migration Matrix, 1500–2000*, version 1.1. Brown University Department of Economics. URL: http://www.econ.brown.edu/fac/louis_putterman/world%20migration%20matrix.htm.

Putterman L., and Weil D. 2010. *Post-1500 Population Flows and the Long Run Determinants of Economic Growth and Inequality*. *The Quarterly Journal of Economics* 125(4): 1627–1682.

Rosenthal J.-L., and Wong R. B. 2011. *Before and Beyond Divergence: The Politics of Economic Change in China and Europe*. Cambridge, MA: Harvard University Press.

Sachs J., Mellinger A. D., and Gallup J. L. 2001. *The Geography of Poverty and Wealth*. *Scientific American* 284(3): 71–75.

Singer J. D., Bremer S., and Stuckey J. 2010 [1972]. *Capability Distribution, Uncertainty, and Major Power War, 1820–1965*. *Peace, War, and Numbers* / Ed. by B. Russett, pp. 19–48. Beverly Hills, CA: Sage.

Smith B. D. 1995. *The Emergence of Agriculture*. New York: Scientific American Library.

Thomas J. 1996. *The Cultural Context of the First Use of Domesticates in Continental Central and Northwest Europe*. *The Origins and Spread of Agriculture and Pastoralism in Eurasia* / Ed. by D. R. Harris, pp. 310–322. Washington: Smithsonian Institution Press.

Thompson W. R. 1999. *The Military Superiority Thesis and the Ascendancy of Western Eurasia in the World System*. *Journal of World History* 10: 143–178.

Turchin P., Adams J. M., and Hall T. D. 2006. *East-West Orientation of Historical Empires and Modern States*. *Journal of World-Systems Research* 12(2): 218–229.

Wong R. B. 1997. *China Transformed: Historical Change and the Limits of European Experience*. Ithaca, NY: Cornell University Press.
**Validation Appendix**

Any examination of behavior over multiple millennia is apt to rely on question-
able assumptions and data. There are at least four possible threats to the validity
of our results. One is that the Maddison data, especially for the earlier periods, are
not very accurate. The problem, however, is that we lack alternative estimates of
a similar nature to be able to assess Maddison's guesstimates about GDP per cap-
ita. Whether we will ever have alternative data, other than the city size data, en-
compassing the same period remains to be seen. In the interim, we have utilized
what is available. Better estimates in the future would of course be very welcome.
Similarly, using Maddison's older data forces us to use his regions as well. That is
the way the data are made available. Would we like to experiment with different
regional identifications? Certainly, but, again, we cannot at this time do so with-
out abandon the GDP per capita scheme altogether.

However, there are two other debatable assumptions that we can assess.
We use gross domestic product (GDP) per capita data to assess a question that
is framed by Comin *et al*. as a matter of technological development. If we move
away from indicators of technology per se, either in terms of societal complex-
ity in the BCE era or GDP per capita in the CE era, have we modified substan-
tially the argument at stake? We cannot do much more with the BCE era but there
is a way to assess the relationship between GDP per capita and technological de-
velopment in the more recent CE era. Less substantively perhaps, we also rely on
rank orders to evaluate regional movement. Rank ordering in this case loses in-
formation by imposing an ordinal hierarchy on raw interval data. Why not just
look at the raw interval data? The answer is that rank ordering simplifies the pres-
tentation of the findings. But it is worthwhile to check whether this simplification
makes any meaningful difference to the analytical outcome.

We can make use of the Cross-Country Historical Adoption of Technology (CHAT) dataset developed by Comin and Hobijn (2010) and available at http://www.nber.org/data/chat. This data set focuses on the annual development of over 100 technologies in over 150 countries since 1800. We extracted a sample of some of the more important technologies of the past two centuries: steam ships, passenger trains, telegraph, telephone, electric power, cars, passenger planes, cellphones, and computers to create an overall technology score based on average, standardized scores on these nine technology foci. To pre-clude possible problems in interpreting the data, we also calculated scores based on the same data without technologies that had been introduced more than 100 years earlier. We also computed the relationship between overall technology scores and GDP per capita at the country and regional level, as shown in Table A1.<fnref n="35" />

<footnote n="35"><sup>35</sup> The 1870–1998 interval is dictated by the absence of much earlier and more recent information in CHAT. In addition, one has to be careful in using CHAT data because there are some problems</footnote>
The overall technology level is calculated in the following procedure. First, we take ‘raw’ technology indicators from the CHAT dataset which includes quantities such as the number of cars registered. We then normalized the raw values to population in order to obtain per capita indicators for the nine technology foci. Population data are taken from the National Material Capabilities dataset version 4 (Singer, Bremer and Stuckey 1972 [2010]). Second, the standardized score of each technology item *k* for country *i* is obtained as $Z_{ik} = (X_{ik} - \bar{X}_{k})/\sigma_{k}$, where $\bar{X}_{k}$ is the mean value. Finally, overall technology level of country *i* is calculated by averaging $Z_{ik}$ over all *k*'s.

<table><caption>**Table A1. Technology-GDP per capita correlations**</caption><thead><tr><th rowspan="2"></th><th colspan="2">Country-level</th><th colspan="2">Regional-level</th></tr><tr><th>Original</th><th>Adjusted</th><th>Original</th><th>Adjusted</th></tr></thead><tbody><tr><td>1870</td><td>0.840</td><td>0.840</td><td>0.867*</td><td>0.867*</td></tr><tr><td>1913</td><td>0.850</td><td>0.850</td><td>0.954</td><td>0.954</td></tr><tr><td>1950</td><td>0.798</td><td>0.854</td><td>0.949</td><td>0.953</td></tr><tr><td>1973</td><td>0.760</td><td>0.778</td><td>0.940</td><td>0.884</td></tr><tr><td>1990</td><td>0.898</td><td>0.884</td><td>0.918</td><td>0.896</td></tr><tr><td>1998</td><td>0.910</td><td>0.915</td><td>0.991</td><td>0.994</td></tr></tbody></table>

*Note:* The adjustment involves removing technology that is older than 100 years from the calculation. Statistical significance is < 0.05 except for the two correlations with asterisks where $p = <.10$.

The outcome is that since 1870 at least, the general relationship between technological development and GDP per capita is quite high, especially at the regional level. It does not seem to matter if we control for old technology, the outcomes are quite similar. The possession of a high gross domestic product per capita indicates a high technological development score and vice versa. Of course, we do not find these relationships surprising in the contemporary period. The correlations do not test our assumption that a similar linkage between technological development and wealth holds over the long term but they do buttress our ability to make the assumption.

When we replace rank ordering with the raw scores suitably standardized, Table A2 summarizes the statistically significant correlations over time. The outcome looks much like the outcome reported in Table 6 using rank orders. There are some clusters of stability in the regional hierarchy, most notably demonstrated in the BCE era and in the post-1870 era. In between, there is not all that much correlation outside of the 1500–1700 CE period. It would appear that our finding that there are strong constraints on regional hierarchical stabil-

<footnote>with data listed in non-equivalent units that can be traced back directly to the sources that were utilized. We attempted to correct these problems prior to the analysis.</footnote>
ity in the really long term is not due to using rank ordered data. Similar outcomes emerge from the raw data as well.

<table><caption>Table A2. Regional hierarchy correlations over time with adjustment</caption><thead><tr><th></th><th>-8</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th><th>1</th></tr><tr><th></th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th></tr><tr><th></th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th></tr><tr><th></th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th><th>0</th></tr></thead><tbody><tr><th>-8000</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>-4000</th><td>.853</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>-3000</th><td>.888</td><td>.903</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>-2000</th><td>.835</td><td>.835</td><td>.977</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>-1000</th><td>.695</td><td>.636</td><td>.849</td><td>.941</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1000</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1500</th><td>.743</td><td></td><td></td><td></td><td>.815</td><td></td><td></td><td>.989</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1600</th><td>.741</td><td></td><td>.718</td><td>.707</td><td>.804</td><td></td><td>.947</td><td>.978</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1700</th><td></td><td></td><td></td><td></td><td>.744</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1800</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1820</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th>1870</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.964</td><td></td><td></td><td></td><td></td></tr><tr><th>1913</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.941</td><td>.984</td><td></td><td></td><td></td></tr><tr><th>1950</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.875</td><td>.943</td><td>.980</td><td></td><td></td></tr><tr><th>1973</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.845</td><td>.847</td><td>.873</td><td>.851</td><td></td></tr><tr><th>2003</th><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>.818</td><td>.811</td><td>.835</td><td>.796</td><td>.976</td></tr></tbody></table>

Note: Only correlations significant at the < .05 level are reported.
## II. CYCLICAL PROCESSES IN PRE-INDUSTRIAL SOCIETIES

### 4 Cycling in the Complexity of Early Societies

Sergey Gavrillets, David G. Anderson, and Peter Turchin

**Abstract**

Warfare is commonly viewed as a driving force of the process of aggregation of initially independent villages into larger and more complex political units that started several thousand years ago and quickly led to the appearance of chiefdoms, states, and empires. Here we build on extensions and generalizations of Carneiro's (1970) argument to develop a spatially explicit agent-based model of the emergence of early complex societies via warfare. In our model polities are represented as hierarchically structured networks of villages whose size, power, and complexity change as a result of conquest, secession, internal reorganization (via promotion and linearization), and resource dynamics. A general prediction of our model is continuous stochastic cycling in which the growth of individual polities in size, wealth/power, and complexity is interrupted by their quick collapse. The model dynamics are mostly controlled by two parameters, one of which scales the relative advantage of wealthier polities in between- and within-polity conflicts, and the other is the chief's expected time in power. Our results demonstrate that the stability of large and complex polities is strongly promoted if the outcomes of the conflicts are mostly determined by the polities' wealth/power, if there exist well-defined and accepted means of succession, and if control mechanisms are internally specialized.

**Keywords:** modeling, warfare, state, territory, rebellion.

**Introduction**

For most of humanity's existence people lived in small egalitarian bands or villages that were politically autonomous. However, a qualitative change happened roughly 10,000 years ago when villages began aggregating into larger and more complex, hierarchically-structured *polities* (a general term that includes not only states and empires but also smaller-scale independent political
units, such as chiefdoms, acephalous tribes, and autonomous villages, see, e.g.,
Ferguson and Mansbach 1996). This process of aggregation first took place in
Mesopotamia, East Asia, South America, and Mesoamerica, followed by sec-
ondary developments elsewhere (Service 1975). The process of aggregation
led, over time, to the emergence of chiefdoms, states, and empires. Once estab-
lished, these complex societies rose and fell over time, with centers of power
and authority shifting from one location to another over the landscape, a proc-
ess that has been described as *cycling* (Wright 1977, 1984; Cordy 1981; Kirch
1984; Marcus 1992, 1998; Anderson 1994, 1996; Earle 1997; Cioffi-Revilla
and Landman 1999; Junker 1999; Hall 2001). The causes of this process have
fascinated scholars and been the subject of speculation for centuries (Engels
1884; Lenin 1918; Childe 1950; Wittfogel 1957; Adams 1966; Fried 1967;
Flannery 1972; Webster 1975; Wright 1977, 1984, 1986; Service 1975, 1978;
Ferguson and Mansbach 1996; Earle 1997; Trigger 2003; Cioffi-Revilla 2005;
Drennan and Peterson 2006; Turchin and Gavrilets 2009; Spencer 2010).

Here we are concerned with a set of influential theories that put special
emphasis on warfare between different polities (starting with villages). When
warfare first occurred in human (pre)history is controversial, although it is as-
sumed to have been relatively small in scale and consequence until complex
and presumably multicommunity societies emerged (Ferguson 1984; Haas
2004; Trigger 2003; but see Keeley 1997; Cioffi-Revilla 2000). Besides war-
fare, there are of course a number of additional prerequisites for the evolution
of social complexity. One requirement, emphasized by Carneiro, is circum-
scription (environmental, due to the resource concentration, or social, due to the
presence of other human groups nearby; see Carneiro 1970, 1981). Circum-
scription was the factor that precluded losing communities from moving away
and thus separating themselves spatially and politically from victors. Other pre-
requisites include existence of agricultural potential capable of generating sur-
pluses and significant variation in productive and/or demographic potential
among local communities (Webster 1975). Equally important was ability to
designate power and the invention of hierarchically structured control mecha-
nisms in which each superior directly controlled only a limited number of sub-
ordinates (Flannery 1972; Wright 1977, 1984; Turchin and Gavrilets 2009).
The latter was also important for the subsequent growth of polities given what
has been called ‘scalar stress’, a decrease in the ability of leaders to process
information and maintain efficient control over subordinates as their number
(herein, the number of subordinate villages) increased (Johnson 1982).
The outcome of these processes and factors was the emergence of simple chief-
doms (Steponaitis 1978, 1981; Wright 1984) in which one village controlled
(and received tribute from) several subordinate villages. More complex polities
were characterized by greater numbers of subordinate levels, with complex
chiefdoms, paramount chiefdoms, and state societies typically defined as those
polities with two, three, and four or more administrative levels above the local or primary community, respectively (Flannery 1972; Wright and Johnson 1975; Steponaitis 1978; Wright 1984; Anderson 1994).

The paramount chief delegated power over a subset of his villages to somebody else (a subchief), often a relative (e.g., Cordy 1981). Sometimes the chiefs of vanquished groups were permitted to stay in power but had to pay tribute (e.g., Kurella 1998). The hierarchical nature of this organizing principle allows, in theory, for unlimited growth in the size and complexity of chiefdoms. However, in early chiefdoms, constituent communities could exist autonomously. Moreover, in these societies control was vested in one or a few individuals, and such absence of internal specialization meant that subchiefs had almost total control over their subordinate villages (Wright 1977, 1984; Earle 1987). Therefore rebellion and secession by subchiefs had a low cost and was relatively easy to organize, although not always successfully accomplished. As a result, the growth in the size and complexity of chiefdoms was counterbalanced by a tendency to fragment through rebellion and secession.

Although the argument just given is well accepted by anthropologists, historians, and political scientists, many questions remain. These concern the levels of complexity that can be achieved, its dynamic patterns and timescales, and the qualitative and quantitative effects of various parameters and factors. Here we use a stochastic spatially-explicit agent-based mathematical model to shed light on these questions. The analyses that follow encompass developments over large geographic and extended temporal scales, the processes that cause chiefdoms, states, and empires to emerge, persist, and collapse at the scale of decades to centuries, the *longue durée* of human history. Our approach is a generalizing one, sacrificing specific detail for a glimpse of the reasons behind the broad patterns recorded by archaeology and history. At the same time, however, our modeling approach aims to connect these broad processes to the finer scale historical events generating those patterns under examination.

Until recently there has been only a limited amount of modeling work directly addressing the evolution of large-scale polities (Dacey 1969, 1974; Bremer and Mihalka 1977; Cusack and Stoll 1990; Cederman 1997; Spencer 1998; Cioffi-Revilla 2005; Cederman and Girardin 2010). Most of this work has focused exclusively on polity size, was limited to a small number of simulation runs, and was primarily motivated by questions of interest to political scientists. Here, we build on earlier approaches by presenting a dynamic quantitative model exploring the origin and operation of early human complex society, focusing on both the size and complexity of emerging polities as well as their longevity and settlement patterns. We systematically examine the effect of parameters such as system size, the effect of polity power on the probability of winning a conflict, tribute level, variation in productivity between individual villages, span of control, and chief's average time in power. The polities in our
model exhibit a strikingly fluid nature resembling so-called ‘chiefly cycles’. Unexpectedly, the largest effect on results is due to just two parameters: the scaling of the polity power to the probability of winning a conflict, and the chief’s average time in power. At the end of the paper we discuss the implications of our results and some relevant empirical evidence. Some preliminary results of our model were presented in Turchin and Gavrilets (2009).

## The Model

Here we describe the model informally; readers interested in the mathematical details will find them in the Mathematical Appendix. We consider a hexagonal array of initially autonomous local communities (villages), consistent with earlier hex-based models (e.g., Cusack and Stoll 1990; Bremer and Mihalka 1977). Each community is represented by a hexagon and has up to six neighbors (Haggett 1965), reflecting a more natural modeling abstraction than square cells. Time is discrete and the unit of time ('year') is the expected interval between two consecutive 'decisions' made by a community (explained below). Each community $i$ is characterized by a constant base-line resource level $f_{0,i}$ which can be interpreted as a measure of the settlement's catchment size (Steponaitis 1981). The values $f_{0,i}$ are chosen randomly and independently from a (truncated) normal distribution with mean 1 and constant standard deviation $\sigma$. Parameter $\sigma$ represents variation in productive/demographic potential between local communities due to environmental heterogeneity. Each community is also characterized by its actual resource level $f_i$. Initially, for each community the actual resource level is set at the base-line level (i.e., $f_i = f_{0,i}$), but different actions in which the community takes part change its value (explained below).

Each community is a part of a polity (which can consist of a single community). The polities have a hierarchical structure. Each community in a polity except for the one at the top of the hierarchy (the 'chief community') has one superior community and may have up to $L$ subordinate communities, where $L$ is a constant parameter measuring the maximum span of control (i.e. the maximum number of subordinates; see Johnson 1982). Each polity is identified by its chief community (see Fig. 1). Each subordinate community pays tribute by transferring a fixed proportion $\theta$ of its total resources to its superior. The total resources of a community are the sum of the resources $f_i$ it produces and the tribute received from subordinates (Steponaitis 1981). The power (wealth) of a polity $F_i$ is given by the total resources available to its chief community. The complexity of a polity $c_i$ is given by the number of levels of control above the level of individual villages.

Polities are engaged in warfare as a result of decision-making, similar to earlier agent-based models of polity systems. The polities grow, decrease in size, or disappear as a result of conquest, with the winner absorbing (all or a part of) the loser. New polities also appear, and old polities decrease in size, when a subordinate community secedes with all of its subordinates.
<figure><img src="image_67.png" /><figcaption>**Fig. 1.** An example of a system with 37 villages and four polities. a) Spatial view. The arrows indicate the direction of the tribute flow. The circles are proportional to the polity power. The numbers are labels identifying the chief communities. b) A hierarchical representation of the polities. The complexity of polities 3, 26 and 30 is two while that of polity 17 is one</figcaption></figure>

Each chief community and each of their direct subordinates make exactly one decision every year. For the chief community, the decision is whether or not to attack a neighboring polity. For a direct subordinate of a chief community,
the decision is whether or not to attempt to secede. Warfare is modeled as follows. A polity selects its weakest neighbor and calculates the chance of success of an attack upon it (which increase the probability of attack), as well as the attack costs (which decrease the probability). The willingness to attack also decreases as the amount of resources available decreases. An attack of polity *i* on polity *j* succeeds or not with probabilities proportional to $F_i^\alpha$ and $F_j^\alpha$. Parameter *α* characterizes the importance of other factors ('noise') besides the polities' power in controlling the outcome of a conflict, with larger *α* implying less noise and more determinism. For example, let polity *i* be twice as strong as polity *j*. Then with linear scaling (i.e., with *α* = 1), the probabilities of polities *i* and *j* winning the conflict between them are in the ratio 2:1. However with quadratic scaling (i.e., with *α* = 2) this ratio becomes 4:1. That is, as *α* increases, polity strength becomes a better predictor of the outcome of conflict.

The aggressor attempts to conquer communities of the victim, starting with border ones, and proceeding in a series of ‘battles’ until either it suffers a defeat, or until the chief community of the victim polity is conquered. Thus, the aggressor either fails completely, seizes a part of the victim polity, or the whole victim polity is annexed.

Annexing communities may require reorganization of the successful aggressor polity (via linearization and promotion, see Flannery 1972), because of the limit $L$ on the number of subordinates of any community. Thus, if one community is to become a subordinate of another, the latter must have at least one open control slot. When all open slots are exhausted, new ones are created by demoting some communities, that is moving them to a lower level in the hierarchy (Flannery 1972). The winning polity attempts to maximize the flow of tribute to the top, and therefore demotes poorer/smaller communities while keeping wealthier/larger ones at higher levels of the hierarchy.

A community subordinate to the chief polity will secede if it estimates that the attack of its old master will be successfully repelled and is willing to pay the price of rebellion. The chief polity attempts to suppress the rebellion immediately. If a successful rebellion results in spatial separation between different parts of the master state, all communities that become disjointed from their superiors secede as well. To account for a possibility of secession upon the death of the paramount chief as a result of a struggle among subchiefs (which is a major source of instability in chiefdoms, see Anderson 1994; Wright 1984; Cordy 1981; Kirch 1984), we introduce an additional parameter $\tau$, the average time in power of the paramount chief. Upon the death of the paramount chief, a random number of subordinate communities become independent without war.

The cost of warfare is a reduction in the amount of actual resources available to participants, with less likely outcomes being costlier for all participants. Following conflict resolution resources are renewed at a fixed low rate.
Analysis

To develop an intuition about the model's behavior, we ran numerical simula-
tions with all possible permutations of the following six parameters: system
edge size S = 4, 5, and 6 villages (so that the total number of villages is 37, 61,
and 91, respectively); α = 1 and 2 (i.e., linear and quadratic scaling of the polity
power to the probability of a win); variation in productivity σ = 0.3, 0.4, and 0.5
(using data in Steponaitis 1981, σ can be estimated to be between 0.34 and
0.48), tribute θ = 0.1, 0.2, and 0.3 (in Steponaitis 1981 tribute level was esti-
mated to be 0.16–0.22), span of control L = 5, 6, and 7 (Johnson 1982 argued
that the most common value of the span of control is 6), and the chief's average
time in power τ = 5, 10 and 20 years (for all model parameters, see Table 1).
Numerous sources, from Polynesian chiefly genealogies to the so-called ‘king
lists’ of many early states, indicate these are reasonable estimates of τ . Very
few leaders in chiefly or even state-level societies lasted longer than
20–30 years, with most reigns appreciably shorter; rulers who held power for
exceptionally long times are just that, unusual exceptions rather than the rule
(Kamakau 1872; Beckwith 1977; Dodson and Hilto 2004).

Each simulation ran for 1,000 years, and the statistics were evaluated using
the data from the last 800 years. Our focus was on the dynamics of the relative
size of the largest polity $s_{max}$ (Fig. 2a), the mean $\bar{c}$ (Fig. 2b) and maximum $c_{max}$
complexity, and average ‘centrality’ $\bar{\rho}$ (i.e., the ratio of the power of the chief
village and the one immediately below, see Steponaitis 1981) (Fig. 2c). We also
looked (see Supplementary Information) at the relationships between a polity’s
base-line productivity and actual power (Steponaitis 1981) and between settle-
ment power and rank on a log-log scale (Johnson 1980; Wright 1984), and at
the distributions of village power (Wright 1984).

Starting with a system of independent villages, we observe the rapid for-
mation of polities of various size and complexity as a result of warfare.
The system quickly (within 50–100 years) reaches a kind of equilibrium in
which our focal characteristics $s_{max}$, $c$, $c_{max}$ and $\bar{\rho}$ are maintained at ap-
proximately constant values (see e.g., Fig. 2). However, this equilibrium is
stochastic and is characterized by the dynamic instability of individual poli-
ties, with quick collapse characterizing chiefdoms reaching relatively large
size and complexity.
<figure><img src="image_68.png" /><figcaption>**Fig. 2.** Examples of the temporal dynamics of the relative size of the largest polity, the mean complexity, and the mean centrality. Black lines: $S = 5$, $a = 1$, $\sigma = 0.4$, $\theta = 0.2$, $L = 6$, $\tau = 10$; grey lines: the same but with $a = 2$</figcaption></figure>

<table><caption>**Table 1.** Major model parameters and statistics</caption><tr><td>S</td><td>System edge size</td></tr><tr><td>α</td><td>Scaling exponent (of the polity power to the probability of a win)</td></tr><tr><td>σ</td><td>Standard deviation of the baseline resource level</td></tr><tr><td>θ</td><td>Tribute level</td></tr><tr><td>L</td><td>Span of control (the maximum number of subordinate communities)</td></tr><tr><td>τ</td><td>The expected time in power of the paramount chief</td></tr><tr><td>s<sub>max</sub></td><td>Relative size of the largest polity</td></tr><tr><td>c&#773;</td><td>Mean complexity</td></tr><tr><td>c<sub>max</sub></td><td>Maximum complexity</td></tr><tr><td>p&#773;</td><td>Average centrality (i.e. the ratio of the power of the chief village and the one immediately below)</td></tr></table>

To quantify this process, we identified all ‘significant complex chiefdoms’, that is polities with complexity $c \ge 2$ and size $s \ge 10$ villages. Note that only a small proportion of polities reaches this status. Fig. 3, illustrating the dynamics of such polities, shows their rapid growth and collapse.
<figure><img src="image_69.png" /><figcaption>**Fig. 3.** The dynamics of polities that have achieved a size of at least *s* = 10 and complexity *c* = 2. Different curves correspond to different chief villages:</figcaption></figure>

a) $S = 5, a = 1, \sigma = 0.4, \theta = 0.2, L = 6, \tau = 10$;

b) the same but with $a = 2$
<table><caption>**Table 2.** Results of the analysis of variance: the effects of the parameters and of their pairwise interactions on system properties</caption><thead><tr><th>Parameters and their combinations</th><th>s<sub>max</sub></th><th>c&#773;</th><th>c<sub>max</sub></th><th>T</th><th>p&#773;</th></tr></thead><tbody><tr><td>S</td><td>13.2</td><td>0.3</td><td>8.3</td><td>3.4</td><td>0.0</td></tr><tr><td>α</td><td>39.8</td><td>33.6</td><td>34.9</td><td>19.9</td><td>5.4</td></tr><tr><td>σ</td><td>0.8</td><td>1.6</td><td>0.7</td><td>0.7</td><td>25.0</td></tr><tr><td>θ</td><td>1.0</td><td>2.0</td><td>0.5</td><td>8.6</td><td>36.3</td></tr><tr><td>L</td><td>0.0</td><td>0.8</td><td>5.7</td><td>1.0</td><td>1.1</td></tr><tr><td>τ</td><td>33.8</td><td>40.8</td><td>38.9</td><td>55.5</td><td>10.4</td></tr><tr><td>S×α</td><td>0.3</td><td>0.1</td><td>1.5</td><td>0.1</td><td>0.0</td></tr><tr><td>S×σ</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.1</td></tr><tr><td>α×σ</td><td>0.0</td><td>0.2</td><td>0.0</td><td>0.0</td><td>2.0</td></tr><tr><td>S×θ</td><td>0.1</td><td>0.0</td><td>0.2</td><td>0.0</td><td>0.0</td></tr><tr><td>α×θ</td><td>0.2</td><td>0.7</td><td>0.6</td><td>0.2</td><td>0.0</td></tr><tr><td>σ×θ</td><td>0.0</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.3</td></tr><tr><td>S×L</td><td>0.0</td><td>0.0</td><td>0.1</td><td>0.0</td><td>0.1</td></tr><tr><td>α×L</td><td>0.0</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.3</td></tr><tr><td>σ×L</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.1</td><td>0.1</td></tr><tr><td>θ×L</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.2</td><td>0.5</td></tr><tr><td>S×τ</td><td>0.4</td><td>0.1</td><td>1.2</td><td>0.1</td><td>0.1</td></tr><tr><td>α×τ</td><td>7.0</td><td>12.9</td><td>1.8</td><td>0.1</td><td>0.4</td></tr><tr><td>σ×τ</td><td>0.1</td><td>0.3</td><td>0.1</td><td>0.0</td><td>2.1</td></tr><tr><td>θ×τ</td><td>0.3</td><td>0.9</td><td>0.5</td><td>2.5</td><td>0.1</td></tr><tr><td>L×τ</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.6</td><td>0.2</td></tr><tr><td>error</td><td>2.6</td><td>5.2</td><td>4.5</td><td>6.6</td><td>15.3</td></tr><tr><td>total</td><td>100.0</td><td>100.0</td><td>100.0</td><td>100.0</td><td>100.0</td></tr></tbody></table>

We studied the effects of parameters on system properties (see Table 2 and the Supplementary Information). The relative size of the largest polity $s_{max}$ increases most significantly with the success probability exponent $\alpha$ and with the chief's average time in power $\tau$, but decreases with system size $S$ (see Fig. 4 and Supplementary Information). With $\alpha = 2$ (i.e., quadratic scaling of polity power to success probability) we occasionally observe cases when all villages are incorporated into a single polity. Such a state can last for up to 35 % of run time and is most likely with maximum values of both $\tau$ and $\theta$.

Average complexity $\bar{c}$ increases most significantly relative to $\alpha$ and $\tau$. It also increases with system size $S$, but decreases with increasing span of control $L$. Overall, $\bar{c}$ stays below c. 2 and 3.3 for $\alpha = 1$ and 2, respectively. Average centrality $\bar{p}$ increases most significantly with variation in productivity $\sigma$ and with tribute $\theta$; it also increases with $\alpha$, but decreases with $\tau$.
<figure><img src="image_70.png" /><figcaption>**Fig. 4.** The effects of parameters on the relative size $s_{max}$ of the largest polity. Each bar corresponds to a combination of four parameters: $\sigma$, $\theta$, $\tau$ and $L$. The values of $s_{max}$ are simultaneously reflected in the bar's height and in the number shown next to it. Other parameters are $S = 5$, $a = 2$.</figcaption></figure>

Average lifetime of ‘significant complex chiefdoms’, *T*, increases with $\alpha$ and $\tau$ (most dramatically), while growing with tribute $\theta$, but decreasing with system size *S*. Overall, the average lifetime of the ten most significant complex chiefdoms stays below 55 and 68 years for $\alpha = 1$ and 2, respectively.

The rank-size curves describing the distribution of polity sizes (Haggett 1965; Johnson 1980; Wright 1986; Peterson and Drennan 2005; Drennan and Peterson 2006) are always convex (see Fig. 5), as expected; polity power declines approximately linearly with the logarithm of its rank indicating the presence of poorly integrated competing centers. The scatter plots for the relationships between the actual and base-line power of polities (Steponaitis 1981) do not show much clustering, suggesting that they are a poor indicator of the degree of complexity in the system (see Supplementary Information).
<figure><img src="image_71.png" /><figcaption>**Fig. 5.** Rank-size curves. Solid black lines: the time average. Dashed black lines: the time average plus minus one standard deviation. The light grey line gives the lognormal curve. Medium dark lines on top gives the rank-size curve at the final year of simulations. Parameters are as in Fig. 3</figcaption></figure>

**Discussion**

Our model provides theoretical support for a view that the formation of com-
plex polities is ‘a predictable response to certain specific cultural, demographic
and ecological conditions’ (Carneiro 1970). Conditions explicitly accounted by
our model include warfare, circumscription, variation in productivity between different local communities, ability to generate surpluses, ability to delegate power, and restrictions on the growth of polities due to scalar stress. Once these conditions are present within a particular geographic area, the model predicts rapid formation of hierarchically organized competing polities partitioning available space.

A striking feature of the model output is the fluid nature of ‘significant’ polities, which continuously go through stochastic cycles of growth (both in size and complexity) and collapse. Growth is driven by successful warfare whereas collapse results from defeat in warfare, rebellion of subchiefs, or fragmentation following the death of the paramount chief. The lifetime of chiefdoms observed in our simulation – a few generations – is comparable to those identified by archaeological studies (e.g., Anderson 1994; Wright 1984; Earle 1991; Hally 1996; Junker 1999; Blitz and Livingood 2004). The model suggests that the rapid collapse of chiefdoms can occur even without environmental perturbations (e.g., drought) or overpopulation.

While the characteristics of individual polities (such as size, complexity, power, and centrality) undergo continuous change, the average values of these characteristics across the whole system remain relatively stable. We have systematically studied how these characteristics are affected by the following six parameters: variation in productivity between local communities $\sigma$, probability of success in war exponent $\alpha$, span of control $L$, tribute $\theta$, system size $S$, and the average chief's time in power $\tau$. Our results show that most variation in system behavior can be explained just by two parameters: $\alpha$ and $\tau$, with higher values strongly promoting the existence of larger, more complex, and more stable polities. Only in the case of centrality were the effects of $\alpha$ and $\tau$ small, with most variation being explained by $\sigma$ and $\theta$.

The chief's expected time in power $\tau$ is one of the two most important parameters. This finding strongly supports arguments on the crucial importance of having well-defined and legitimate mechanisms of succession for the stability of polities (Anderson 1994; Wright 1984). Creating and maintaining complex polities thus requires effective mechanisms to deal with both internal and external threats. In both cases, leaders (paramount chiefs) must solve collective action problems to overcome challenges. Even a most abbreviated reading of human history shows how difficult this task has been.

The other critical parameter of the model is the probability of success in war (controlled by $\alpha$), which sets the relative effectiveness of stronger (wealthier) polities in internal and inter-polity conflicts. In our model, the stronger of the two polities does not necessarily win a conflict between them. This is reasonable as there are many other factors besides wealth that can affect the outcome of conflict. However increasing $\alpha$ implies a stronger dependence of the outcome of the conflict on the polities' power (wealth). The degree of determin-
ism in the conflict resolution (and thus, parameter $\alpha$) is expected to increase with economic and political development (Carneiro 1970, 1981; Collins 1986). Note that in our simulations, polities conquering the whole simulation domain are observed only with $\alpha = 2$.

Our model shows no qualitative differences between polities with a single level of control above the level of individual villages ('simple chiefdoms') and polities with two or more levels of control ('complex chiefdoms' or 'states'). During each individual run, the number of control levels is not stable but changes dynamically and therefore cannot by itself serve as an indicator of the presence of 'true' states. Our results support Carneiro's (1981: 38) insight that 'the transcending of local sovereignty and the aggregation of previously autonomous villages into chiefdoms was a critical step in political development – probably the most important one ever taken. It crossed a threshold, and once crossed, unlimited further advance in the same direction became possible. The emergence of chiefdoms was a qualitative step. Everything that followed, including the rise of states and empires, was, in a sense merely quantitative'.

In our simulations it was possible for polities to conquer the whole spatial domain, or a significant part of it. However, our analyses also show that such polities are relatively short-lived. A major reason for this is the relative ease of rebellion within larger polities. Additionally, our model explicitly assumes that any 'internal specialization' is absent and that all mechanisms for autonomous existence of a rebellious province are already in place. This model behavior thus further emphasizes, through the effect of its absence, the importance of 'internal specialization' for the emergence of large and stable polities (Flannery 1972; Wright 1977, 1984).

## Implications for Archaeological Research

Due to temporal resolution limitations archaeological analyses of settlement hierarchies typically combine sites occupied over intervals of a half century to, sometimes, hundreds of years. The hierarchies reconstructed by archaeologists are commonly displayed as a series of maps showing site sizes during different periods, often separated by a century or more, or else histograms or rank size plots (Wright and Johnson 1975; Wright 1977, 1984, 1986; Johnson 1980; Hal-ly 1996; McAndrews et al. 1997; Spencer and Redmond 2001; Liu and Chen 2003; Peterson and Drennan 2005; Drennan and Peterson 2006). These recon-structions suggest rigid formal hierarchies and static political landscapes. Our analyses, in contrast, indicate that at a finer temporal scale the various factors that produce these archaeological signatures are much more dynamic. This re-sult is in agreement with written records of historical events (when available; e.g., Earle 1987, 1991).

Our estimates of chiefdom duration are comparable with those based on ar-chaeological evidence. In studying Southeastern Mississippian chiefdoms, Hal-
ly (1993) examined the time periods when occupation and mound construc-
tion occurred at 47 mound centers in central and northern Georgia. He con-
cluded that ‘paramount chiefdoms must have been unstable and short lived’
while ‘simple and complex chiefdoms endured for as much as a century or
more’ (Hally 1993). The actual duration of phases, or periods of occupation
and construction in his analysis (Ibid.: 145), however, could not be resolved
much below 75–100 years. Hally extended this analysis in a second paper
(Hally 1996) examining 45 mound centers, and including episodes of mound
stage construction. Where evidence for numbers of internal mound construc-
tion stages was available, duration of occupation was estimated to be between
75 and 100 years, with the average number of years per stage ranging from 12
to 25 years at the best understood sites (Hally 1996). This span may represent
the duration of a chiefly leader, or generation. At 29 of the 45 mound centers,
only a single period of use is currently known, indicating most ‘chiefdoms’
locally lasted no more than 75–100 years, and perhaps appreciably less (Hally
1996).

In a follow up, Hally (2006: 27) argued that ‘as many as 47 distinct chief-
doms rose and fell’ in 27 locations during the Mississippian period in northern
Georgia (some locations were occupied repeatedly, often with gaps in occupa-
tion of a century or more). The numbers of chiefdoms in his sample fluctuated
between 8 and 17 during the period of 1000–1500 CE (Hally 2006). Many poli-
ties in the sample were single-mound simple chiefdoms (Hally 2006).

Blitz and Livingood (2004) used mound volume as an alternate means of
measuring regional settlement hierarchies, using a sample of sites from across
the southeast USA. For a sample of 35 mounds they recorded a mound volume
index (basal length × basal width × height / 1000), the number of major mound-
construction stages, the duration of mound use in years, and the number of
mounds at the site where the sample mound was found (Ibid.: 293). Their anal-
ysis, while geographically broader than Hally's, yielded generally similar re-
sults, noting average mound center ‘duration of use range is 100–450 years,
with a mean of 183 years and a median of 150 years. Also, there appears to be
a rough periodicity in mound construction: the average occupation span per
construction layer is 25–50 years’ (Ibid.: 296). They were able to demonstrate
that mound stage construction might fall into two cycles, one of c. 12–18 years,
and another of c. 25–50 year spacing (Ibid.: 297).

Our finding that the duration of a chief's reign is a significant parameter
parallels that in the literature on state fiscal organization. In this literature, the
discount rate of rulers (that is, their expected time in office) is shown to be
a major determinant of the kind of taxation system employed, which in turn has
various implications for society, for example, for political stability of the Ro-
man state and Ptolemaic Egypt (Kiser and Kane 2007; Levi 1988; Monson
2007).
In our model individual villages differ only in their base-line productivity and geographic location but otherwise have equal ability to form complex societies. In human history some polities had a headstart, allowing them to achieve large size initially (e.g., San Miguel Mogote or El Mirador in Mesoamerica; Uruk and Susa in Mesopotamia; Aspero in South America; see Service 1975); but the strategies for complex polities buildup and maintenance would have spread quickly in a Darwinian fashion as a result of conquest and imitation. Therefore once chiefdoms appeared, their organizational form would itself have tended to spread, as neighboring societies adopted it for reasons ranging from emulation to self defense (Carneiro 1981; Anderson 1994).

## Conclusion

The dynamics generated by our model, in which hierarchical societies tend to achieve at most medium levels of complexity, and only for relatively short periods of time, resembles the chiefly cycles observed prior to sustained Western contact in eastern North America, southern Central America and northern South America, Oceania, southeast Asia and the Philippines, and across large parts of sub-Saharan Africa (e.g., Wright 1984; Marcus 1992; Earle 1991; Anderson 1994; Cordy 1981; Junker 1999; Drennan and Peterson 2006).

The model developed here can be extended in a number of ways. For example, instead of a simple conquest mechanism, one can consider a more nuanced dynamic in which external threat of conquest (or raiding) induces a greater degree of cooperation between lower-level groups, which results in a more stable higher-level polity. According to Cioffi-Revilla's canonical theory (2005), such a ('fast') process is common for producing stronger institutions of government. One possible direction is to generalize the model to allow for the formation of coalitions between different polities (Carneiro 1998; see Gavrilets et al. 2008 for a possible dynamic approach). Also, to adapt the model for describing larger spatial scales (e.g., as necessary for modeling the origin of states and empires), changes in population densities need to be considered, as well as the propensity for cooperation (and, conversely, conflict) should be allowed to depend on cultural similarity/dissimilarity between the agents.

Over the past several decades mathematical methods and techniques have become very important in life sciences and social sciences (Spencer 1998; Cioffi-Revilla 2002; Bentley and Maschner 2008; Costopoulos 2008; Kohler et al. 2005). In particular, mathematical and computational modeling are powerful tools for better understanding the origins of new species (Gavrilets 2004) and of general rules of biological diversification (Gavrilets and Losos 2009). Agent-based simulation modeling efforts like those advanced here offer fruitful avenues for future research on general patterns in historical dynamics and on the emergence and diversification of human societies (Turchin 2003, 2006, 2009).
References

Adams R. M. 1966. *The Evolution of Urban Society*. Chicago, IL: Aldine Press.

Anderson D. G. 1994. *The Savannah River Chiefdoms: Political Change in the Late Prehistoric Southeast*. Tuscaloosa, AL: University of Alabama Press.

Anderson D. G. 1996. Fluctuations between Simple and Complex Chiefdoms: Cycling in the Late Prehistoric Southeast. *Political Structure and Change in the Prehistoric Southeastern United States* / Ed. by J. F. Scarry, pp. 231–252. Gainesville, FL: University Press of Florida.

Beckwith M. W. 1977. *Hawaiian Mythology*. Honolulu, HI: University of Hawaii Press.

Bentley R. A., and Maschner H. D. G. 2008. Complexity Theory. *Handbook of Archaeological Theories* / Ed. by R. A. Bentley, H. D. G. Maschner, and C. Chippindale, pp. 245–270. Lanham, MD: AltaMira Press.

Blitz J., and Livingood P. 2004. Sociopolitical Implications of Mississippian Mound Volume. *American Antiquity* 69(2): 291–301.

Bremer S. A., and Mihalka M. 1977. Machiavelli in Machina: Or Politics Among Hexagons. *Problems of the World Modeling: Political and Social Implications* / Ed. by K. W. Deutsch, B. Fritsch, H. Jaquaribe, and A. S. Markovits, pp. 303–337. Cambridge: Ballinger Publishing.

Carneiro R. L. 1970. A Theory of the Origin of State. *Science* 169: 733–738.

Carneiro R. L. 1981. The Chiefdom: Precursor of State. *The Transition to Statehood in the New World* / Ed. by G. D. Jones, and R. R. Kautz, pp. 37–79. Cambridge: Cambridge University Press.

Carneiro R. 1998. What Happened at the Flashpoint? Conjectures on Chiefdom Formation at the Very Moment of Conception. *Chiefdoms and Chieftaincy in the Americas* / Ed. by E. M. Redmond, pp. 18–42. Gainesville, FL: University Press of Florida.

Cederman L.-E. 1997. *Emergent Actors in World Politics*. Princeton, NJ: Princeton University Press.

Cederman L.-E., and Girardin L. 2010. Growing Sovereignty: Modeling the Shift from Indirect to Direct Rule. *International Studies Quarterly* 48: 27–48.

Childe V. G. 1950. The Urban Revolution. *The Town Planning Review* 21: 3–17.

Cioffi-Revilla C. 2000. Ancient Warfare: Origins and Systems. *Handbook of War Studies II* / Ed. by M. I. Midlarsky, pp. 59–89. Ann Arbor, MI: University of Michigan Press.

Cioffi-Revilla C. 2002. Invariance and Universality in Social Agent-based Simulations. *Proceedings of the National Academy of Sciences* 99: 7314–7316.

Cioffi-Revilla C. 2005. A Canonical Theory of Origins and Development of Social Complexity. *Journal of Mathematical Sociology* 29: 133–153.

Cioffi-Revilla C., and Landman T. 1999. Evolution of Maya Polities in the Ancient Mesoamerican System. *International Studies Quarterly* 43: 559–598.

Collins R. 1986. *Weberian Sociological Theory*. New York: Cambridge University Press.
Cordy R. H. 1981. *A Study of Prehistoric Social Change. The Development of Complex Societies in the Hawaiian Islands*. New York: Academic Press.

Costopoulos A. 2008. Simulating Society. *Handbook of Archaeological Theories* / Ed. by R. A. Bentley, H. D. G. Maschner, and C. Chippindale, pp. 273–281. Lanhan, MD: AltaMira Press.

Cusack T. R., and Stoll R. J. 1990. *Exploring Realpolitik. Probing International Relations Theory with Computer Simulation*. Boulder, CO: Lynne Rienner Publishers.

Dacey M. F. 1969. *A Probability Model for the Rise and Decline of States*. *Peace Research Society Papers* 14: 147–153.

Dacey M. F. 1974. A Model of Political Integration and Its Use in the Reconstruction of a Historical Situation. *Locational Approaches to Power and Conflict* / Ed. by K. R. Cox, D. R. Reynolds, and S. Rokkan, pp. 213–230. New York: SAGE Publications.

Dodson A., and Hilto D. 2004. *The Complete Royal Families of Ancient Egypt: A Genealogical Sourcebook of the Pharaohs*. New York: Thames and Hudson.

Drennan R. D., and Peterson C. E. 2006. Patterned Variation in Prehistoric Chiefdoms. *Proceedings of the National Academy of Sciences* 103: 3960–3967.

Earle T. K. 1987. Chiefdoms in Archeological and Ethnohistorical Perspective. *Annual Review of Anthropology* 16: 279–308.

Earle T. K. 1991. *Chiefdoms: Power, Economy and Ideology*. New York: Cambridge University Press.

Earle T. K. 1997. *How Chiefs Come to Power*. Stanford, CA: Stanford University Press.

Engels F. 1884. Origins of the Family, Private Property, and the State. *Selected Readings in Two Volumes*. Vol. 2 / Ed. by K. Marx, and F. Engels, pp. 185–326. Moscow: Foreign Languages Press.

Ferguson R. B. 1984. *Warfare, Culture, and Environment*. Orlando, FL: Academic Press.

Ferguson Y. H., and Mansbach R. W. 1996. *Polities: Authority, Identities, and Change*. Columbia, SC: University of South Carolina Press.

Flannery K. V. 1972. The Cultural Evolution of Civilizations. *Annual Review of Ecology and Systematics* 3: 399–426.

Fried M. H. 1967. *The Evolution of Political Society*. New York: Random House.

Gavrilets S. 2004. *Fitness Landscapes and the Origin of Species*. Princeton, NJ: Princeton University Press.

Gavrilets S., Duenez-Guzman E. A., and Vose M. D. 2008. Dynamics of Alliance Formation and the Egalitarian Revolution. *PLOS ONE* 3(10): e3293.

Gavrilets S., and Losos J. 2009. Adaptive Radiation: Contrasting Theory with Data. *Science* 323: 732–737.

Haas J. 2004. *The Anthropology of War*. Cambridge: Cambridge University Press.

Haggett P. 1965. *Locational Analysis in Human Geography*. London: Edward Arnold.

Hall T. D. 2001. Chiefdoms, States, Cycling, and World-Systems Evolution: A Review Essay. *Journal of World-Systems Research* 7: 91–99.
**Hally D. J. 1993.** The Territorial Size of Mississippian Chiefdoms. *Archaeology of Eastern North America Papers in Honor of Stephen Williams*. Archaeological Report No. 25 / Ed. by J. B. Stoltman, pp. 143–168. Jackson, MS: Mississippi Department of Archives and History.

**Hally D. J. 1996.** Platform Mound Construction and the Instability of Mississippian Chiefdoms. *Political Structure and Change in the Prehistoric Southeastern United States* / Ed. by J. F. Scarry, pp. 92–127. Gainesville, FL: University Press of Florida.

**Hally D. J. 2006.** The Nature of Mississippian Regional Systems. *Light on the Path: The Anthropology and History of the Southeastern Indians* / Ed. by T. J. Pluckhahn and R. Ethridge, pp. 26–42. Tuscaloosa, AL: University of Alabama Press.

**Johnson G. A. 1980.** Rank Size Convexity and System Integration. *Economic Geography* 56(3): 234–247.

**Johnson G. A. 1982.** Organizational Structure and Scalar Stress. *Theory and Explanation in Archaeology* / Ed. by C. Renfrew, M. Rowlands, and B. A. Segraves, pp. 389–421. New York: Academic Press.

**Junker L. L. 1999.** *Raiding, Trading, and Feasting: The Political Economy of Philippine Chiefdoms*. Honolulu: University of Hawaii Press.

**Kamakau S. M. 1872.** *Ruling Chiefs of Hawaii*. Honolulu: Kamehameha Schools Press.

**Keely L. H. 1997.** *War before Civilization: The Myth of the Peaceful Savage*. New York, NY: Oxford University Press.

**Kirch P. V. 1984.** *The Evolution of the Polynesian Chiefdoms*. Cambridge: Cambridge University Press.

**Kiser E., and Kane D. 2007.** The Perils of Privatization: How the Characteristics of Principals Affected Tax Farming in the Roman Republic and Empire. *Social Science History* 31(2): 191–212.

**Kohler T., Gumerman G., and Reynolds R. 2005.** Simulating Ancient Societies. *Scientific American* 293(1): 76–82.

**Kurella D. 1998.** The Muisca. Chiefdoms in Transition. *Chiefdoms and Cieftaincy in the Americas* / Ed. by E. M. Redmond, pp. 189–216. Gainesville, FL: University Press of Florida.

**Lenin V. 1918.** The State and Revolution. *Collected Works*. Vol. 25, pp. 381–492. Moscow: Progress Publishers.

**Levi M. 1988.** *Of Rule and Revenue*. Berkeley, CA: University of California Press.

**Liu L., and Chen X. 2003.** *State Formation in Early China*. London: Duckworth.

**Marcus J. 1992.** Political Fluctuations in Mesoamerica. *National Geographic Research and Exploration* 8(4): 392–411.

**Marcus J. 1998.** The Peaks and Valleys of Ancient States an Extension of the Dynamic Model. *Archaic States* / Ed. by G. Feinman and J. Marcus, pp. 59–94. Santa Fe, NM: SAR Press.

**McAndrews T. L., Albarracin-Jordan J., and Bermann M. 1997.** Regional Settlement Patterns in the Tiwanaku Valley of Bolivia. *Journal of Field Archaeology* 24: 67–83.
Monson A. 2007. Rule and Revenue in Egypt and Rome: Political Stability and Fiscal Institutions. *Historical Social Research* 32(4): 252–274.

Peterson C. E., and Drennan R. D. 2005. Communities, Settlements, Sites, and Surveys: Regional-scale Analysis of Prehistoric Human Interaction. *American Antiquity* 70(1): 5–30.

Service E. R. 1975. *Origins of the State and Civilization. The Process of Cultural Evolution*. New York: Norton and Company.

Service E. R. 1978. Classical Theories of the Origin of Government. *Origins of the State* / Ed. by R. Cohen, and E. R. Service, pp. 21–34. Philadelphia, PA: Institute for the Study of Human Issues.

Spencer C. S. 1998. *A Mathematical Model of Primary State Formation*. *Cultural Dynamics* 10(1): 5–20.

Spencer C. S. 2010. Territorial Expansion and Primary State Formation. *Proceedings of the National Academy of Sciences of the United States of America* 107(16): 7119–7126.

Spencer C. S., and Redmond E. M. 2001. Multilevel Selection and Political Evolution in the Valley of Oaxaca, 500–100 B.C. *Journal of Anthropological Archaeology* 20: 195–229.

Steponaitis V. P. 1978. Location Theory and Complex Chiefdoms: A Mississippian Example. *Mississippian Settlement Patterns* / Ed. by B. D. Smith, pp. 417–453. New York: Academic Press.

Steponaitis V. P. 1981. Settlement Hierarchies and Political Complexity in Nonmarket Societies: The Formative Period of the Valley of Mexico. *American Anthropologist* 83: 320–363.

Trigger B. G. 2003. *Understanding Early Civilizations: A Comparative Study*. Cambridge: Cambridge University Press.

Turchin P. 2003. *Historical Dynamics: Why States Rise and Fall*. Princeton, NJ: Princeton University Press.

Turchin P. 2006. *War and Peace and War: The Life Cycles of Imperial Nations*. New York: Pi Press.

Turchin P. 2009. A Theory for Formation of Large Empires. *Journal of Global History* 4: 191–207.

Turchin P., and Gavrilets S. 2009. Evolution of Complex Hierarchical Societies. *Social Evolution and History* 8(2): 167–198.

Webster D. 1975. Warfare and the Evolution of the State: A Reconsideration. *American Antiquity* 40: 464–470.

Wittfogel K. A. 1957. *Oriental Despotism: A Comparative Study of Total Power*. New Haven, CT: Yale University Press.

Wright H. T. 1977. Recent Research on the Origin of the State. *Annual Reviews of Anthropology* 6: 379–397.

Wright H. T. 1984. Prestate Political Formations. *On the Evolution of Complex Societies. Essays in Honor of Harry Hoijer* / Ed. by W. Sander, H. T. Wright, and R. M. Amams, pp. 41–77. Malibu, CA: Undena Press.
Wright H. T. 1986. The Evolution of Civilizations. *American Archeology Past and Future* / Ed. by D. J. Meltzer, pp. 323–365. Washington: Smithsonian Institution Press.

Wright H. T., and Johnson G. A. 1975. Population, Exchange, and Early State Formation in Southwestern Iran. *American Anthropology* 77: 267–289.

## Mathematical Appendix

Here we provide some additional details on the model and simulations. The model was implemented in the Matlab.

**Attacks.** A polity may attack only its weakest neighbor. The attack of polity *i* on polity *j* is successful with probability

$$P_{ij} = \frac{F_i^{\alpha}}{F_i^{\alpha} + F_j^{\alpha}}, \qquad (\text{Eq. 1})$$

where $F_i$ is the power of polity *i*, and $\alpha$ is the success probability exponent. Polity *i* will attack polity *j* only if it estimates that the attack will be successful, is willing to pay the cost of warfare, and is not too devastated by previous warfare. Specifically, the probability of attack is set to

$$A_{ij} = P_{ij} \exp[-\beta c_{ij}] \frac{F_i}{F_{i,0}}. \qquad (\text{Eq. 2})$$

Here the first term is the probability of winning (estimated by the potential aggressor via ‘scenario building’). The second term accounts for a negative effect of costs of warfare, $c_{ij}$ (defined below), on the willingness to attack; $\beta > 0$ is a parameter. The third term accounts for a reduction in the willingness to attack caused by recent conflicts (and ensuing drop in available resources); $F_{i,0}$ is the maximum possible power of the *i*-th polity (observed at maximum possible level of resources; i.e., if all $f_i = f_{i,0}$). If attack is not successful, a war ends in a draw.

We assume that attacks proceed through one or more stages. At the first stage, the target is the wealthiest border community of the weakest neighbor. The victim repels the attack successfully with probability $Q_{ij} = 1 - P_{ij}$. If the attack was successful, the aggressor proceeds to attack the superior of the target. Now the probability that the victim repels the attack successfully is reduced to $(1 - \gamma)Q_{ij}$, where $0 \le \gamma < 1$ is a parameter characterizing the ‘loser effect’ (e.g., due to demoralization). If the second attack is successful, the aggressor proceeds to attack the superior of the superior of the target and so on. The process stops when an attack is repelled or when the chief community of the victim polity is conquered. In the former case, the aggressor seizes a part of the victim polity that was subordinate to the community attacked at the last successful attack. In the latter case, the whole victim's polity is seized.

**Linearization and promotion.** Polity *i* attempts to maximize the flow of tribute by the processes of linearization and promotion, after Flannery (1972),
subject to geographic restrictions and restrictions on the number of subordinates. If the chief community *i* has an open control slot, it will control polity *j* directly. If there are no open control slots, then the chief community will control directly the *L* wealthiest communities chosen (*i.e.*, promoted) from the set of its *L* subordinates and the newly conquered polity *j*. The remaining (*i.e.*, the poorest) community will be demoted and reattached to its geographically closest neighbor of the higher rank (*i.e.*, by-passed in a process akin to linearization). If this neighbor has already filled all its control slots, further re-arrangements will follow according to the same strategy.

**Costs.** Different actions (*i.e.*, attack, defense, rebellion, or suppression of rebellion) reduce the actual resource level for all participants by a factor (1 − *c*) where the cost *c* of an action is equal to a constant *δ* times the probability of loss for the winner (0 < *δ* ≤ 1). That is, if *P*<sub>*ij*</sub> is the probability that an attack of polity *i* on polity *j* is successful, then the cost of a successful attack is

$$c = \delta(1 - P_{ij}), \qquad (\text{Eq. 3a})$$

whereas the cost of an unsuccessful attack is

$$c = \delta P_{ij}. \qquad (\text{Eq. 3b})$$

This simple model captures the idea that more likely outcomes are less costly to all participants. For attacks involving several stages, costs are combined multiplicatively.

**Resource dynamics.** Each year the actual resource level *f*<sub>*i*,0</sub> grows towards its baseline level *f*<sub>*i,0*</sub> at an exponential rate. Specifically, we define the half-life of resource recovery *r* measured in years so that it takes *r* peaceful years for the resource to grow from 1 − *δ* to 1 − *δ*/2.

**Implementation rules.** We use a ‘parallel’ implementation of the model in which different actions happen simultaneously rather than sequentially. To handle multiple events potentially involving the same polity we use the following rules: 1) A polity that is subject to a rebellion does not attack other polities. 2) A polity that is subject to a rebellion is not attacked by other polities. (The justification: since dealing with the rebellion will make the polity weaker, potential attackers would prefer to wait and attack later.) 3) If there are multiple rebellions within a polity, the polity's power is divided proportionally and multiple suppression attempts occur simultaneously.

## Supplementary Information

1. Sample movies with $\alpha = 1$ and $\alpha = 2$. Other parameters are at the mid-points of the ranges used ($S = 6$, $\sigma = 0.3$, $\theta = 0.2$, $L = 6$, $\tau = 10$).

The movies are currently available at http://neko.bio.utk.edu/~sergey/chiefdoms/chiefdoms.html.

2. Detailed simulation results for $S = 4$, $S = 5$, $S = 6$.
The files are currently available at http://neko.bio.utk.edu/~sergey/chiefdoms/chiefdoms.html.

3. Effects of parameters on the properties of the system.

The files are currently available at http://neko.bio.utk.edu/~sergey/chiefdoms/chiefdoms.html.

**Acknowledgement**

We thank the reviewers for valuable comments and suggestions. This research was supported by a Guggenheim Fellowship (SG) and by the National Science Foundation Grant NSF-HSD SES-0527720 (PT).
# 5
## Demographic-Structural Theory and the Roman Dominate

David C. Baker

### Abstract

This article uses the theory of secular cycles to examine the Eastern and Western Roman Empires in roughly 285–700 CE. The analysis suggests that the Eastern Empire conforms to an almost ‘standard’ cycle during that time. The Western Roman Empire, on the other hand, appears to expand until 350 CE and then decline again, long before the Germanic invasions of the fifth century. This decline may have been due to elite dynamics and the extremely top-heavy social pyramid in the fourth century West. Elite overproduction and infighting may have cut short the West's expansion phase and led to a premature decline. If correct, it is possible that demographic-structural theory explains the decline and fall of the Roman Empire.

**Keywords:** Cliodynamics, Roman Empire, Dominate, population, history.

### Introduction

The work of Peter Turchin over the last decade has shown that population pressure exerts a powerful influence over socio-political instability, historical events, and the ebb and flow of state power (Turchin 2003, 2006; Turchin and Nefedov 2009). The dynamics can be identified in cycles of a few hundred years of expansion and contraction.<fnref n="1" /> One interesting test of theory has recently been done on Pueblo societies by Kohler et al. (2009: 290–291). Here is a rough overview of the theory. When a population is low, there is plenty of food and a labour shortage, and so food prices are low and wages are high. A population enjoys a decent standard of living. This dynamics translates into political stability. As a result, the population tends to grow. This is the expansion phase. Eventually a population approaches its carrying capacity resulting in shortages of food and an oversupply of labour. Prices rise, wages drop, and the standard of living declines. The average person is paid less and has to pay more for the basic essentials. Famines increase in severity, the susceptibility of

<footnote n="1">¹ The average appears to be roughly 300 years for a full cycle, but depends greatly on specific conditions.</footnote>
people to disease also increases, as does the possibility of widespread epidem-
ics. At the same time, it is a ‘golden age’ for the elite. Landowners pay lower
wages and charge higher rents. Middling landowners are forced off their farms
and land is concentrated in the hands of the few. The inequality gap widens.
Elite numbers and appetites grow. This is the ‘stagflation’ phase (Turchin and
Nefedov 2009: 10–13).

Then a society hits a crisis. People starve, social cohesion collapses, the number of people living at subsistence level grows, grain reserves disappear, diseases ravage a malnourished population, there are rural and urban uprisings and, ultimately, the population declines. As the general population shrinks, the elites, cushioned by their status and their wealth, do not die at the same rate. The social pyramid becomes top-heavy. Elites begin to see their incomes shrink. The result is elite infighting and competition for the resources of the state. In this period faction and civil war are prevalent. Thus the first crisis, spurred mainly by demographic causes, is followed by a second crisis or ‘de-pression’ which is largely man-made. The man-made crisis holds recovery down, and this can last for decades. Eventually, however, a population does rebound. Elite numbers are reduced. Low numbers in the general population combined with high wages and low food prices lead to another period of expan-sion, peace, and stability.

In this paper I apply the demographic-structural theory to the period of the
Roman Dominate. First I review the two secular cycles that were experienced
by the Roman Republic and Empire before 285 CE. Next I consider the demo-
graphic-structural trends in the Eastern Empire between 285 and 628 CE. Then
I look at the divergent cycle in the West between 285 and 400 CE and possible
demographic-structural explanations for the downfall of the Western Roman
Empire.

The Republican Cycle (350–30 BCE) and Principate Cycle
(30 BCE – 285 CE)

Rome underwent two previous cycles that have been examined by Peter Tur-
chin and Sergey Nefedov in *Secular Cycles* (2009). There is even a theoretical
case to be made for an even earlier cycle spanning 650 to 350 BCE, seeing ex-
pansion and stagflation for the first 150 years, and crisis and depression falling
around the overthrow of Tarquin the Proud and the establishment of the Repub-
lic. The Republican Cycle entered an expansion phase during which Rome es-
tablished hegemony over the Italian peninsula from c. 350 onward. The popula-
tion losses of the Second Punic War (218–201), an exogenous variable, might
explain the elongated duration of the Republican cycle. Stagflation set in
around 180, and a disintegrative trend began somewhere between 133 and 90,
more likely the latter, and lasted through the wars of Sulla, Caesar, and the Tri-
umvirate until around 30 BCE (Turchin and Nefedov 2009: 176–210).
The following period, the Principate cycle (30 BCE – 285 CE), precedes
the one on which I focus in this article. The Roman Empire experienced growth in the first and second centuries CE, crisis following the Antonine Plague in 165 and lasting until 197, and a secular 'depression' of elite infighting in the Third Century Crisis (197–285).

In general I am in agreement with Turchin's findings, excepting one caveat. Turchin states that the expansion phase (27 BC – 96 CE), which according to the theory should have been stable, was 'somewhat marred' by political instability in the ruling class. He is referring to the violent overthrow of Caligula, Nero, Galba, Otho, Vitellus, and Domitian (Table 1). He dismisses them as mere 'palace coups'. He then plays down the severity of the civil war following Nero's death, 68–69 (Turchin and Nefedov 2009: 211). All this might be taken by some historians of the period as an understatement and perhaps a hasty dismissal of something that might expose a weakness in the theory or necessitate a refinement of the notion of elite dynamics. At any rate, the presence of such sustained elite conflict, to speak nothing of the rising tension at the end of the reign of Tiberius, is a too glaring variable to be quickly passed over.

Yet such a dismissal of the first century unrest is unnecessary even within the theory. Rural settlement patterns show that the population in Italy peaked in the first century CE, unlike in most other provinces of the Empire, which continued to flourish until the second century (Fig. 1). In the second century, while Britain, Belgica, Gaul, and Spain continued to grow, the population of Italy actually fell by 14 per cent. Even Turchin acknowledges this fact in his examination. There is no reason why this fact cannot account for the growing tension among Italian elites at the end of the reign of Tiberius, during the reign of Caligula, and also the periods of violence in the late sixties, and above all the localised nature of a great deal of the first century unrest within Italy.

Nor should Italy's first century peak come as a surprise. Unlike the Social War and the wars between Marius and Sulla in the Republican cycle, also explored by Turchin, the majority of the most brutal campaigning under Caesar, Pompey and later Octavian and Marc Antony, was held outside of Italy, in Spain, Africa, and above all in Greece. Although Italy undoubtedly experienced depopulation, not to mention the elite proscriptions of the second triumvirate, the ravages of actual military campaigning fell elsewhere in the Empire. In 49 CE, Caesar took Rome with ease and hounded Pompey out of Italy, while the most decisive battles of this latter part of the Republican cycle: Pharsalus, Philippi, and Actium took place in Greece. The shortness of Italy's period of expansion (27 BCE – 60 CE) as opposed to the flourishing of the Empire (27 BCE – 165 CE) might therefore be explained by the fact that the later campaigning of the Republican crisis (49–30 BCE) largely spared Italy, unlike the earlier part of the crisis (91–70 BCE). Thus it is conceivable that the Italian population might have recovered earlier than the rest of the Roman Empire.
<table><caption>**Table 1.** Sociopolitical instability in Roman Empire, 0-100 CE (an expanded list following Turchin and Nefedov 2009: 222)</caption><thead><tr><td>Year</td><td>Event</td></tr></thead><tbody><tr><td>15</td><td>Disturbances at Rome</td></tr><tr><td>16</td><td>Revolt of Legions in Pannonia and Germania</td></tr><tr><td>19</td><td>Alleged murder of a rival Germanicus by Piso, supposed acolyte of Tiberius</td></tr><tr><td>23</td><td>Mysterious death of Drusus, who had shared tribunician power with Tiberius</td></tr><tr><td>24</td><td>Rebellion of the slaves in southern Italy</td></tr><tr><td>29</td><td>First minister Sejanus begins purging senatorial class of all opponents</td></tr><tr><td>30</td><td>Sejanus exiles members of imperial family, some of whom die mysteriously</td></tr><tr><td>31</td><td>Sejanus falls from favour and is executed</td></tr><tr><td>37</td><td>Tiberius dies having become unpopular for his informers and treason trials</td></tr><tr><td>37</td><td>After a brief period of popularity, Caligula begins persecuting nobles</td></tr><tr><td>38</td><td>Caligula executes people without full trial</td></tr><tr><td>39</td><td>Famine strikes, Caligula seizes property of the wealthy, executes senators</td></tr><tr><td>41</td><td>Assassination of Caligula; proclamation of Claudius, stability returns</td></tr><tr><td>42</td><td>Conspiracy at Rome (Scribonianus)</td></tr><tr><td>55</td><td>Nero allegedly murdered Britannicus, a rival to the throne</td></tr><tr><td>59</td><td>Disturbances at Pompeii, Nero orders the murder of his mother</td></tr><tr><td>60–61</td><td>British revolt</td></tr><tr><td>62</td><td>Nero executes his ex-wife, Octavia</td></tr><tr><td>62–63</td><td>Persecution of senators for treason</td></tr><tr><td>64</td><td>Fire of Rome and disturbances</td></tr><tr><td>65</td><td>Conspiracy at Rome (Piso)</td></tr><tr><td>66–70</td><td>Jewish revolt</td></tr><tr><td>68</td><td>Uprising against Nero (Vindex and Galba), flight and forced suicide of Nero</td></tr><tr><td>69</td><td>Civil war. Galba destroys several towns, executes senators and knights without trial, murdered by army, Otho succeeds, is beaten by Vitellius, and commits suicide, Vitellius conducts a series of tortures and executions, and is killed by Vespasian's men while attempting to flee</td></tr><tr><td>70</td><td>Uprisings in Egypt, Gaul, and Germania</td></tr><tr><td>70</td><td>Alleged string of ‘false Neros’ and conspiracies against Vespasian</td></tr><tr><td>79–80</td><td>Rebellion of Terentius Maximus</td></tr><tr><td>89</td><td>Revolt of Saturninus</td></tr><tr><td>93–96</td><td>Sharp rise in persecution of dissidents</td></tr><tr><td>95</td><td>Conspiracy at Rome</td></tr><tr><td>96</td><td>Murder of Domitian, accession of Nerva</td></tr></tbody></table>
<figure><img src="image_72.png" /><figcaption>**Fig. 1.** Proportion of rural sites occupied (per cent of the peak value) in Italy compared to the whole of Western Empire (data from Lewit 1991)</figcaption></figure>

## Trends in the Eastern Empire (285–628 CE)

The Dominate cycle developed in different ways in the two major parts of the Roman Empire. The Eastern Empire after 285 enjoyed a period of demographic growth and economic prosperity throughout the fourth and fifth centuries, continuing until the Justinianic plague struck in the mid-sixth. The West also enjoyed a partial recovery after 285 and it lasted until the mid-fourth century, after which there was a sharp decline and eventual collapse.

Settlement patterns in northern Syria show that the population grew to a peak around 540 CE, then stagnated and declined into the eighth century. For example, east of Antioch, villages sprang up in the first century CE, and then there was a decline during the Third Century Crisis, followed by growth in small-scale farming and the development of new fields. Growth came to an end around 550, after which sites were abandoned (Gatier 1994: 17–48). In Greece, there was growth in rural settlements during the fourth, fifth, and sixth centuries. This trend is seen in surveys in Attica and Boeotia. At Corinth in the same period, there was a demographic recovery to a level which had not been seen since the time of Alexander the Great in the fourth century BCE. The same pattern can be seen in Methana, which saw nine sites occupied for the first time around 300 CE, and thereafter site numbers continued to grow (Alcock 1993: 38–48;
Bintliff 1994, 1997). In the eastern desert of Egypt, at Bir Umm Fawakhir, a Byzantine gold mining town developed in the 400s and was occupied for many years until it was abandoned at the end of the 500s (Meyer 1995). At Ephesus, many parts of the city were being redeveloped in the fifth century. All signs point to new buildings being erected as late as 600. Wealthy households on Embolos street were exquisitely decorated during the late 300s or early 400s. In 614, a fire destroyed these buildings. It is telling that they were not rebuilt (Foss 1977). Similar trends can be found all over the Eastern Mediterranean (for a survey, see Chris Wickham 2005: 442–453).

In the prosperous fourth century there was more equality among elites, but few hyper-rich landowners. Most Eastern senators were elites on a provincial level, and could not yet threaten the emperor (Wickham 2009: 37). The 300s were clearly an expansion period. Archaeological evidence from Northern Syria shows that there were many small landholders and very few large estates (Tate 1992). In Egypt tenant leases were short, peasant landholders were numerous (Fig. 2), wage labourers experienced high wages and low prices, and there were no attempts by fourth-century Egyptian landholders to tie their peasants to the land (Bagnall 1993: 110–123, 148–153).

<figure><img src="image_73.png" /><figcaption>**Fig. 2.** Frequency distribution of farms by size: Kanaris, Egypt, the fourth century CE (data from Bagnall 1993)</figcaption></figure>

However, in the 400s one begins to see growth in the number and size of large estates in the East. Landholders began to acquire trans-regional property, rather than holdings in just one province (Sarris 2004). This prosperity was the classic
result of an increase in the availability of labour, a decrease of wages that land-
holders had to pay, a rise in food prices, and consequently a rise in the incomes
of landholders (Turchin and Nefedov 2009: 10–11). In the fifth century, the
East began to acquire more elites at a time when the West was already glutted
with the hyper-rich. An increase in elite numbers and wealth is a symptom of
stagflation. The senatorial order expanded rapidly during the fifth century, par-
ticularly in the reign of Marcian (450–457). Stratification and inequality also
became a problem. Stratification culminated with the highest ranking elites, the
*illustres*, gradually excluding the less wealthy elites, the *spectabiles* and *claris-*
*simi*, from the senate altogether by the reign of Justinian I (527–565) (Haldon
2005: 39).

The problem of intraelite conflict appears in Byzantine history after the death of Marcian in 457. The reign of his successor, Leo I (457–474), was marked by increased tension between the old Byzantine elite and the Isaurian faction, whose new and disproportionate influence they resented. While the reign was generally stable, it was marked by a number of assassination plots between the two camps. Leo I nevertheless ruled for a long time and died of natural causes at a ripe old age. The same could not be said of his grandson, Leo II (474), who ruled for less than a year before dying under suspicious circumstances. His father, Zeno, an Isaurian who had married into the dynasty, became emperor, but was soon overthrown by a revolt that slaughtered many of his Isaurian officers. Zeno fought his way back to the throne, but elite revolts persisted – in stark contrast to the stable fourth and early fifth centuries (Table 2). Elite competition exploded into open conflict in the 490s (Williams and Friell 1999: 171–184). The reigns of Anastasius (491–518), Justin (518–527) and Justinian (527–565) sustained a precarious equilibrium fraught with many court intrigues and noble plots, where the emperor had to constantly remain on his guard. Even the glorious reign of Justinian was witness to the Nika Revolts in 532, in which the senators were heavily involved. Several changes to the senatorial order followed the revolt. Sons of ‘full’ senators, the *illustres*, inherited the rank of *clarissimus* only. The emperor had to be petitioned for higher rank (Haldon 2005: 39). This was an attempt to restrain elite overproduction and to come to grips with the ‘over-mighty subject’.

Nevertheless, the wealthy upper orders of *illustres* continued to multiply and proliferate. The lower *spectabiles* lost a lot of their military and administrative positions to the ever-growing horde of *illustres*. The late 530s saw the creation of ranks higher than that of *illustris*, those of *magnificus*, *gloriosus*, and later, the superlative *gloriossisimus*. The title of *illustris* was further devalued by being held by provincial elites (Ibid.: 40).