1. 1 Eurasian city system dynamics in the last millennium Complex Dynamics of Distributional Change Doug White SASci/SCCR meeting San Antonio 2007

2. 2 Abstract A 25 period historical scaling of city sizes in regions of Eurasia shows both rises and falls of what are unstable city systems, and the effects of the early urban rise in China on the Middle East and Europe. Other elements of historical population dynamics (structural demography and periods of scarcity with rising sociopolitical violence) figure into the observed city system dynamics. Considering these instabilities, the further course of city systems also needs to consider global warming and 45- 250 foot rises in ocean levels, largest caused by the energetic inefficiencies to scale of the larger cities. city systems in the last millennium

3. 3 Zipf’s law? Population at rank r M the largest city and α=1 Chandler Rank-Size City Data (semilog) for Eurasia (Europe, China, Mid-Asia) city systems in the last millennium city rank Zipfian=top curve

4. 4 Zipf’s law? Population at rank r M the largest city and α=1 city systems in the last millennium city rank Take a closer look: Lots of variation from a Zipfian norm

5. 5 Michael Batty (Nature, Dec 2006:592), using some of the same data as do we for historical cities (Chandler 1987), states (and cites) the case made here (in a previous article, 2005) for city system instability: Batty shows legions of cities in the top echelons of city rank being swept away as they are replaced by competitors, largely from other regions. “It is now clear that the evident macro-stability in such distributions” as urban rank-size hierarchies at different times “can mask a volatile and often turbulent micro-dynamics, in which objects can change their position or rank-order rapidly while their aggregate distribution appears quite stable….” Further, “Our results destroy any notion that rank-size scaling is universal… [they] show cities and civilizations rising and falling in size at many times and on many scales.” city systems in the last millennium

6. 6 City Size Distributions for Measuring Departures from Zipf construct and measure the shapes of cumulative city size distributions for the n largest cities from 1st rank size S 1 to the smallest of size S n as a total population distribution T r for all people in cities of size S r or greater, where r=1,n is city rank Rank size power law M~S 1 Empirical cumulative city- population distribution

7. 7 city systems in the last millennium For the top 10 cities, fit the standard Pareto Distribution slope parameter, beta (β) P β (X ≥ x) = x -β (= 1/x β )(1) To capture the curvature of the entire city population, fit the Pareto II Distribution shape and scale parameters theta and sigma (Ө,σ) to curve, let shape q=1+1/Ө. P Ө,σ (X ≥ x) = (1 + x/σ) -Ө (2)

8. 8 Probability distribution q shapes for a person being in a city with at least population x (fitted by MLE estimation) Pareto Type II city systems in the last millennium Shalizi (2007) right graphs=variant fits

9. 9 Examples of fitted curves for the cumulative distribution Curved fits measured by q shape, log-log tail slopes by β city systems in the last millennium

10. 10 Variations in q and the power-law slope β for 900-1970 in 50 year intervals city systems in the last millennium ChinaEurope Mid-Asia

11. 11 Random walk or Historical Periods? Runs Test Results city systems in the last millennium

12. 12 Fitted q parameters for Europe, Mid-Asia, China, 900-1970CE, 50 year lags. Vertical lines show approximate breaks between Turchin’s secular cycles for China and Europe Downward arrow: Crises of the 14th, 17th, and 20th Centuries city systems in the last millennium

13. 13 city systems in the last millennium Are there inter-region synchronies? Cross-correlations give lag 0 = perfect synchrony lag 1 = state of region A predicts that of B 50 years later lag 2 = state of region A predicts that of B 100 years later lag 3 = state of region A predicts that of B 150 years later etc.

14. 14 city systems in the last millennium Time-lagged cross-correlation effects of Mid-Asian q on China (50 year lagged effect)

15. 15 city systems in the last millennium Time-lagged cross-correlation effects of China q on Europe (100 year lagged effect) (non-MLE result for q)

16. 16 city systems in the last millennium Time-lagged cross-correlation effects of the Silk Road trade on Europe (50 year lagged effect)

17. 17 city systems in the last millennium Are there synchronies with Turchin et al Historical Dynamics? i.e., Goldstone’s Structural Demography? E.g., Where population growth relative to resources result in sociopolitical instabilities (SPI) and intrasocietal conflicts; precipitating fall in population and settling of conflicts, then followed by a new period of growth. (secular cycles = operating at scale of centuries) Illustrate with an example from Turchin (2005) and then relate to the city system shape dynamics.

18. 18 Chinese phase diagram Turchin 2005: Dynamical Feedbacks in Structural Demography Key: Innovation

19. 19 Turchin 2005 validates statistically the interactive prediction versus the inertial prediction for England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000)interactive prediction

20. 20 city systems in the last millennium J. S. Lee measure of SPI for China region (internecine wars )

21. 21 city systems in the last millennium Interpretation: SPI conflict correlates with low β, a thin tail of elite cities (people migrate out of cities to smaller cities or zones of safety), with a more normal β restored in 150 years. Shows the effect of internecine wars in China on city size distributions

22. 22 city systems in the last millennium Interpretation: SPI conflict correlates with a higher ratio of q to (low) β, but as β recovers slightly in the next 50 years instead of the q/β ratio going down q goes up relative to β as migrations re-shape the smaller city sizes, perhaps seeking refuge in mid-size cities.

23. 23 Before concluding, I want to thank those who contributed to this project Laurent Tambayong, UC Irvine (co-author on the paper, statistical fits) Nataša Kejžar, U Ljubljana (co-author on the paper, initial modeling, statistics) Constantino Tsallis, Ernesto Borges, Centro Brasileiro de Pesquisas Fısicas, Rio de Janeiro (q-exponential models) Cosma Shalizi (the MLE statistical estimation programs in R: Pareto, Pareto II, and a new MLE procedure for fitting q-exponential models) Peter Turchin, U Conn (contributed data and suggestions) Céline Rozenblat, U Zurich (initial dataset, Chandler and Fox 1974) Chris Chase-Dunn, UC Riverside (final dataset, Chandler 1987) Numerous ISCOM project and members, including Denise Pumain, Sander v.d. Leeuw, Luis Bettencourt (EU Project, Information Society as a Complex System) Commentators Michael Batty, William Thompson, George Modelski (suggestions and critiques) European Complex System Conference organizers (invitation to give the initial version of these findings as a plenary address in Paris; numerous suggestions) Santa Fe Institute (invitation to work with Nataša Kejžar and Laurent Tambayong at SFI, opportunities to collaborate with Tsallis and Borges, invitation to give a later version of these findings at the annual Science Board meeting). city systems in the last millennium

24. 24 Conclusions: city systems in the last millennium City systems unstable; have historical periods of rise and fall over hundreds of years; exhibit collapse. Better to reject the “Zipf’s law” of cities in favor of studying deviations from the Zipfian distribution, which can nevertheless be retained as a norm for comparison. It represents an equipartition of population over city sizes that differ by constant orders of magnitude, BUT ONLY FOR LARGER CITIES. Deviations from Zipf occur in two ways: (1) change in the log-log slope (β) of the power-law tail of city sizes (2) change in the curve away from a constant slope (q), also in where this change occurs (not presented here). TAILS AND BODIES OF CITY-SIZE DISTRIBUTIONS VARY INDEPENDENTLY. Both deviations are dynamically related to the structural demographic historical dynamics (SDHD). The SPI conflicts (e.g., internecine wars or periods of social unrest and violence) that interact in SDHD processes with population pressure on resources are major predictors of city-shape (β,q) changes that are indicators of city-system crisis or decline. City system growth periods in one region, which are periods of innovation, have time-lagged effects on less developed regions if there are active trade routes between them. NETWORKS AFFECT DEVELOPMENT.

25. 25 –Batty, Michael. 2006. Rank Clocks. Nature (Letters) 444:592-596. –Chandler, Tertius. 1987. Four Thousand Years of Urban Growth: An Historical Census. Lewiston, N.Y.: Edwin Mellon Press. –Goldstone, Jack. 2003. The English Revolution: A Structural-Demographic Approach. In, Jack A. Goldstone, ed., Revolutions - Theoretical, Comparative, and Historical Studies. Berkeley: University of California Press. –Lee, J.S. 1931. The periodic recurrence of internecine wars in China. The China Journal (March-April) 111-163. –Shalizi, Cosma. 2007. "Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions", math.ST/0701854 http://arxiv.org/abs/math.ST/0701854 –Tsallis, Constantino. 1988. Possible generalization of Boltzmann-Gibbs statistics, J.Stat.Phys. 52, 479. (q-exponential) –Turchin, Peter. 2003. Historical Dynamics. Cambridge U Press. –Turchin, Peter. 2005. Dynamical Feedbacks between Population Growth and Sociopolitical Instability in Agrarian States. Structure and Dynamics 1(1):Art2. http://repositories.cdlib.org/imbs/socdyn/sdeas/ –White, Douglas R. Natasa Kejzar, Constantino Tsallis, Doyne Farmer, and Scott White. 2005. A generative model for feedback networks. Physical Review E 73, 016119:1-8 http://arxiv.org/abs/cond-mat/0508028 –White, Douglas R., Natasa Keyzar, Constantino Tsallis and Celine Rozenblat. 2005. Ms. Generative Historical Model of City Size Hierarchies: 430 BCE – 2005. Santa Fe Institute. References city systems in the last millennium

26. 26 TAILS AND BODIES OF CITY-SIZE DISTRIBUTIONS VARY INDEPENDENTLY