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1
Human Survival and Complex Network Dynamics at Continental Scales
Complex Dynamics of Distributional Size, Networks, and Spatial Scales
Douglas R. WhiteUC Irvine
50 minutes+ discussion, 54 slidesUC Campus Complexity Videoconference April 20, 2007
This pdf available athttp://eclectic.ss.uci.edu/~drwhite/center/cac.html#White4
http://tinyurl.com/279ejp
2
Abstract. Two projects on macrosocial systems are examined: food collecting societies varying through time and space in harshness of environmental conditions; and regional city systems networked by trade and war with coordination problems and interregional competition. Both involve complex network dynamics that support human survival. In each case, severe external conditions, competition, and instability often cause create system crashes. A first question in each case concerns the instability of complex systems and the role of networks in resilient outcomes and recovery from system crashes. A second question concerns system dynamics of rise and fall, and problems of coordination. My focus is on how, through network and population dynamics, different but related forms of resilience develop to solve (and hopefully solve in the future) problems of human survival. These problems are particularly acute since we now face potentially catastrophic consequences of global warming; population collapse in many parts of the world; and a climate of fear and preemptive panic in the grab for resources that are more and more limited relative to urban system demands and pressures to solve resource pressures through warfare rather than adaptive innovation.
3
Problems addressed:
Two projects on macrosocial systems are examined. Both involve complex network dynamics that support human survival:
(1) food collecting societies varying through time and space in harshness of environmental conditions;
(2) regional city systems networked by trade and war with coordination problems and interregional competition.
In each case, severe external conditions, competition, and instability create system crashes.
The first question in each case concerns the instability of complex systems and the role of networks in resilient outcomes and recovery from system crashes.
The second question concerns system dynamics of rise and fall, and problems of coordination.
4
My focus is on how, through network and population dynamics, different but related forms of resilience develop to solve (and hopefully solve in the future) problems of human survival.
These problems are particularly acute since we now face: Potentially catastrophic consequences of global warming;
Population collapse in many parts of the world;
A climate of fear and preemptive panic in the grab for resources that are more and more limited relative to urban system demands and pressures to solve resource pressures through warfare rather than adaptive innovation.
5
forager systems
Foragers radiate to fill habitats and operate relatively autonomously at low densities and relatively small language groups, e.g., with populations <500 in each language group.
Problem: how as “isolated small populations” they can survive stochastic demographic variations, consequences of genetic drift and inbreeding depression?
city systems
Cities begin as networks of productive complementarity networked by trade and competition needed for their survival.
They extend trade networks and colonize new regions, forming (1) greater %ages of the worlds population at (2) accelerating growth rates leading to (3) system crashes and (4) problems of resilience.
(to elucidate aspects of complex network dynamics)Different but parallel problems
6
Data - Generally accepted views that are contradictory
• Birdsell, from ethnographic data, estimates that the populations of Indigenous Australian language groups were consistently small, averaging perhaps 500 people each.
• Marriage rules are taken by ethnographers to imply endogamous marriage as both a norm and a logical requirement.
• Social dynamics, by these paradoxical assumptions, would seem to be the opposite of urban systems.
7
• Dousset (2005:91) "rapid diffusion [of section terms] was most probably linked to the strong networks that local groups in the Western Desert maintained among themselves, with frequent ceremonial exchanges and intermariages"
• yet fairly consistent ethnographer reports of strict endogamy
The Australian Paradox 1
8
• Paleodemographers argue that small reproductively closed human populations are doomed due to stochastic variations in birth rates and sex ratios, and inbreeding depression.
• If both the population estimates and the models
are right, how did these small closed societies avoid extinction and indeed persist in Australia for 40,000 years and more?
The Australian Paradox 2
9
In the 19th century, anecdotal discussions of intergroup marriages may have over-reported them because of a naïve assumption that “group marriage” was ubiquitous and intergroup marriage was seen as its logical extension.
But the 20th century, in reaction, saw dismissive assumptions that intergroup marriages were byproducts of colonization and concomitant detribalization rather than of longstanding traditions. Hence authentic cases of intergroup marriage probably were under-reported.
Much potentially valuable data on intergroup marriages is thus defective or missing, biased by different assumptions at different times, with the end result being a paucity of modern understanding of intergroup marriages among Indigenous Australians. — D. White and W.W.Denham 2007. Dousset (2005) upsets this whole applecart.
BIAS IN PERSPECTIVES ON INTERGROUP MARRIAGES
10
11
Australian forager systems
Coast, desert, rivers 12000 BCE-2000 CE
Paradox of extinction risk in closed systems (Bocquet-Appel and Masset 1982). Crises of underpopulation.
Question: was there a dynamic open system interacting with stressors?
Eurasian city systems
Mid-asia, China, Europe as regions; 900-2000 CE
Paradox of power-law growth singularity (Kremer 1993). Crises of overpopulation v. resources
Problem: open system competition interacts with over-growth & collapse.
Contrast of city system with forager dynamics
12
If you are live streaming this talk this slide will show again in 1 minute: note down one of these urls and you can download this pdf for cleaner images
http://eclectic.ss.uci.edu/~drwhite/center/cac.html#White4
http://tinyurl.com/279ejp
13
power-law city growth and world population 'response'
Start Year t k C Up to (following period) Length
-5000 or earlier n.a. exponential Classical Antiquity n.a.
-200 0.26 36000 Medieval Renaissance c.7000
1250 0.175 19000 Industrial Revolution c.1450
1750-1860 0.09 11000 Consumer Economy c.610
Post-1962 ? (log time length linear decr.) c.100?
Kremer data; Fitted Coefficients of Equation Nt = C/(t0
– t)k
1250
Village City
%urbanUnsustainable singularities at t0
Billions of people
14
Start Year k C Up to (following period) Length
-5000 or earlier n.a. exponential Classical Antiquity n.a.
-200 0.26 36000 Medieval Renaissance c.7000
1250 0.175 19000 Industrial Revolution c.1450
1750-1860 0.09 11000 Consumer Economy c.610
Post-1962 ? (log time length linear decr.) c.100?
Kremer data; Fitted Coefficients of Equation Nt = C/(t0
– t)k
Artificial power-law pop growth curves
to match actual world
population 10,000 BCE —
2020 CE0
2000
4000
6000
8000
10000
12000
14000
16000
18000
-12000 -10000 -8000 -6000 -4000 -2000 0 2000
Billions of people (in Millions)
15
If live streaming: note down one of these urls and you can download this
pdf for cleaner images
http://eclectic.ss.uci.edu/~drwhite/center/cac.html#White4
http://tinyurl.com/279ejp
16
Australian forager systems
Is each language group really a closed system? As derived from observations that within these societies everyone is considered a relative, all marriages are considered as between relatives, and that it is only kinship terminology that is extended beyond a group’s boundaries? (for Kariera see Romney and Epling 1958:68, “Kariera is a closed system” ??)
Eurasian city systems
In each regional population, and that of the world, city networks as open systems develop innovations, trade and extract resources that attract and maintain more people at accelerating growth rates that eventually outstrip resources to support them: (will come back to this)
Crisis of growth (Kremer 1993) Singularity paradox of power-law growth
Supposed contrast: Open vs. Closed?
17
The Australian ethnographic confusion is about marriage in terms of
(1).. section categories which are not descent groups with common ancestors but distinctions embodied in kin terms involving extended statuses (adjacent generations and even/odd implicit marriage moieties).
(2).. rules that are more specific as to what classificatory or proper kin one should marry within a given section.
(3).. negotiations as to which specific choices are made among classificatory or proper kin in local groups.
But ethnographers and modelers have incorrectly assumed that the logical closure of (1) entails local closure of (3) to marriage with relatives of the same language group!!! (the abstract logic of (1) entails no such claim!)
18
In the 19th century, anecdotal discussions of intergroup marriages may have over-reported them because of a naïve assumption that “group marriage” was ubiquitous and intergroup marriage was its logical extension.
But the 20th century, in reaction, saw dismissive assumptions that intergroup marriages were byproducts of colonization and concomitant detribalization rather than of longstanding traditions. Hence authentic cases of intergroup marriage probably were under-reported.
Much potentially valuable data on intergroup marriages is thus defective or missing, biased by different assumptions at different times, with the end result being a paucity of modern understanding of intergroup marriages among Indigenous Australians. —D. White & W.W.Denham 2007
BIAS IN PERSPECTIVES ON INTERGROUP MARRIAGES
19
One of the few actual network studies (Denham and White 2005; data from Denham 1971) showed
intergroup marriages firmly integrated into consistent marriage patterns, 98% of 114 local marriages consistent
with section memberships
ARANDA ARANDA-ALYAWARRA ALYAWARRA
slanted marriage tie arrows ≡ age-skewed generations, a possible indicator of reproductive stress on availability of mates
20
Our Hypothesis: Reproductive Stress intergroup formation of marriage networks
• Forager paleodemographics may be steady state at the continental level, but show temporal variations in response to changing reproductive stress levels locally, pressing outward to find mates in adjacent societies.
• These reproductive stresses, and the mechanisms for responding to them, constitute the motive force that “powers” our model, entailing as a consequence that:
• Each language group will form a local cluster within a connected “small world” in a large space of continent-wide connections.
• If so, then the universality of section systems in Australia would be explained by selective pressure on institutional mechanisms – shared inter-cultural understandings – that would allow local societies to integrate, not unlike city networks!
(common factors in complex network dynamics)
21
Much Diffusional Evidence for Reproductively Open Systems
Dousset (2005): Western Desert diffusion of section names implies: exogamous alignments
Trade + travel networks, dreaming tracks, ritual interactions at boundaries
Ubiquitous generation and descent moieties underlie region-wide relational system: source, direction, onset, rate, process of alignment, outcomes
22
The answer to the paradox is thus: what appeared to ethnographers as “closed” section systems with local marriage rules are a means of broader institutional integration creating a continental “small world” of intermarriages and exchange
Diffusion of sections (and intermarriage)
The new data here is on the Western Desert, from Dousset 2005:87
Trade Routes as they relate to
23
Dreaming Tracks as they relate to Diffusion of sections (and intermarriage)
… the new data from Dousset 2005:88, etcetera
24
A Counter-Intuitive Hypothesis as to why sections facilitate integration• Widespread restrictions on marriages may
reduce choices locally, but facilitate integration of populations globally by forcing people to marry outside their own local group. Local restrictions encourage the dispersion of marriages. When mates are scarce this may help to promote links outside the language group.
• And … sections as a logic of extension of recognized social ties, are abstract (for cities, much like universal civil rights). If you marry an outsider, they and their relatives become classificatory kin.
(This deals with factors of cohesion in complex network dynamics)
25
Australian forager systems
Virtually all Australian marriage models assumed these societies were endogamous (H. White, Bush, Kemeny, Hammel), except perhaps for Levi-Strauss (1971:219-220).
Our model and evidence, along with Dousset (2005), shows open marriage networks.
Key to resilience: actual open system, dynamic interaction, with stressors.
Eurasian city systems
Gibrat: Can city growth be stable independent of size?
That would contradict the actual demographic growth curves in each region and the world. It might be true on average but what about dynamics?
Key to resilience? Actual open system, dynamic interaction, with stressors?
(we begin now to see parallels in complex network dynamics)
26
World cities and thus world population tend to grow proportional to their size over long periods.
This abnormal growth is sustained by migration into cities and, eventually, increases in longevity, adding those urban populations that are rapidly expanding before demographic transitions occur.
Obviously populations cannot and do not continue to grow proportional to their size, which is power-law growth.
Does expected population growth overall follow Gibrat, while the micro-dynamics of growth is volatile and unstable?
Eurasia, Cities, and World Population
27
Michael Batty (Nature, Dec 2006:592), using some of the same data as do we for historical cities (Chandler 1987), cites the case made here and in our 2005 article 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
28city systems in the last millennium
Color key: Red to Blue in time of the rank clock are early to late city entries: Rank 1 is at the center. Low rank Blues, latest in time, rise quick to the top, displacing older yellow cities and ancient red.
The world system & Eurasia are the most volatile. Big shifts occur in the classical era until around 1000 CE. Gradual reduction in shifts until the Industrial Revolution. US shift lower, largest 1830-90. UK similar, with a 1950-60 suburbanization shift
RANK CLOCK Slide from Michael Batty, Nature 2006
29
To see how city system rise and fall plays out regionally we fit log-log slopes for the cumulative city size distribution tail
measured by β and a curve-shape q=1+1/Ө to the body
Maximum likelihood estimation (MLE) procedures provided by Cosma Shalizi
Pβ (X ≥ x) = (x/xmin)-β
(top ten cities)
PӨ,σ (X ≥ x) = (1 + x/σ)-Ө
30
Variations in q and the power-law slope β for 900-1970 CE in 50 year intervals
city systems in the last millennium
1970
1950
1925
1900
1875
1850
1825
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1750
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1950
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1950
1925
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1750
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1250
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1150
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1000
900
date
3.0
2.5
2.0
1.5
1.0
0.5
0.0
MinQ_BetaBeta10MLEqExtrap
China Europe Mid-Asia
1970
1950
1925
1900
1875
1850
1825
1800
1750
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1600
1575
1550
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1950
1925
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1950
1925
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900
3.0
2.5
2.0
1.5
1.0
0.5
0.0
MinQ_BetaBeta10MLEqExtrap
31
Random walk or Historical Periods? Runs Tests at medians for q and β for Eurasia
Runs Test Results
MLE-q Beta10 Min(q/1.5,
Beta/2) Test Value (Median) 1.51 1.79 .88 Cases < Test Value 35 36 35 Cases >= Test Value 36 37 38 Total Cases 71 73 73 Number of Runs 20 22 22 Z -3.944 -3.653 -3.645 Asymp. Sig. (2-tailed) .0001 .0003 .0003
Runs Test for temporal variations of q in the three regions mle_q Europe mle_q MidAsia mle_q China
Test Value (Median) 1.43 1.45 1.59 Cases < Test Value 9 11 10 Cases >= Test Value 9 11 12 Total Cases 18 22 22 Number of Runs 4 7 7 Z -2.673 -1.966 -1.943 Asymp. Sig. (2 -tailed) .008 .049 .052
32
Mean q~1.5>1~(No) Gibrat stationarity
N Minimum Maximum Mean Std. Deviation Std.Dev/Mean MLEqChinaExtrap 25 .56 1.81 1.5120 .25475 .16849 MLEqEuropeExtrap 23 1.02 1.89 1.4637 .19358 .13225 MLEqMidAsIndia 25 1.00 1.72 1.4300 .16763 .11722
BetaTop10China 23 1.23 2.59 1.9744 .35334 .17896 BetaTop10Eur 23 1.33 2.33 1.6971 .27679 .16310 BetaTop10MidAsia 25 1.09 2.86 1.7022 .35392 .20792
β tail
q body
Mean β<2~Zipfian tails
33city systems in the last millennium
Are there synchronies with Turchin et al Historical Dynamics? i.e., Goldstone’s Structural Demography?
I.E., 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)
An example from Turchin (2005) will illustrate so as to relate to the city system shape dynamics.
34Chinese phase diagram
Turchin 2005:
Dynamical Feedbacks in
Structural Demography
Key:
Innovation
35
Turchin 2005 validates statistically the interactive prediction versus the inertial prediction for England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000)
36
Fitted q parameters for Europe, Mid-Asia, China, 900-1970 CE, 50 year lags. Vertical lines show approximate breaks between Turchin’s secular cycles for China and Europe;
Arrows: Crises of the 14th, 17th, and 20th Centuries
qqq
37city systems in the last millennium
Are there inter-region synchronies? Cross-correlations at successive time lags:
lag 0 = synchronic correlation
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
38
76543210-1-2-3-4-5-6-7
Lag Number
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
mle_MidAsia with mle_China
Lower Confidence Limit
Upper Confidence Limit
Coefficient
Time-lagged cross-correlation effects of Mid-Asia q on China
(1=50 year lagged effect)
city systems in the last millennium
3976543210-1-2-3-4-5-6-7
Lag Number
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
mle_China with mle_Europe
Lower Confidence Limit
Upper Confidence Limit
Coefficient
76543210-1-2-3-4-5-6-7
Lag Number
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
China with Europe4
Lower Confidence Limit
Upper Confidence Limit
Coefficient
(100 year lagged effect)
(non-MLE result for q)
Max.Likelihood: China q predicts Europe q with a 100 year time lag
city systems in the last millennium
40city systems in the last millennium
76543210-1-2-3-4-5-6-7
Lag Number
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
logSilkRoad with EurBeta10
Lower Confidence Limit
Upper Confidence Limit
Coefficient
Time-lagged cross-correlation effects of the Silk Road trade on Europe (50 year lagged effect)
4176543210-1-2-3-4-5-6-7
Lag Number
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
mle_Europe with ParisPercent
Lower Confidence Limit
Upper Confidence Limit
Coefficient
Europe q (max. likelihood) with % French Population in Paris
42city systems in the last millennium
J. S. Lee measure of SPI for China region ≡ (internecine wars )
43
Fitted q parameters for Europe, Mid-Asia, China, 900-1970 CE, 50 year lags. Vertical lines show approximate breaks between Turchin’s secular cycles for China and Europe;
Arrows: Crises of the 14th, 17th, and 20th Centuries
WHAT DO THESE OSCILLATIONS HAVE TO DO WITH NETWORKS OF TRADE AND WAR?
44
Having developed network analytic predictions for growth and decline in city systems and individual cities in Medieval Europe, Laurent Tambayong and I are now looking for patterns in Eurasia, region by region. The following slides represent data for which we are trying to connect, through mathematical models, the changes in inter-city networks & those of power-law tail (β) and q oscillations in the city size distributions.
In consultation with Michael Batty (1976:593; Theil), we can calculate expected growth rate for each region, decomposed into overall growth and change at different spatial scales (information distance), enabling different systems (and types) to be integrated through spatial and information hierarchies.
The project is open to collaboration. One element we need is someone to write a PERL script or robot search to systematically collect, formatted and dated information about the world’s active trade links, commodities and volumes at different historical periods.
45
0900 AD
Zipfian q with global hubs CORRELATES with global network links
From first stirrings of globalization to the 21st Century
Europe Central Asia China
Medit. Near East
India
Bagdad & Changan (Xi’an)
Silk routes
Europe MidAsia China
These slides connect the city network & city size distributions to changes in power-law tails and q-scaling of city sizes
46
1000 AD
960: Song capital at Kaifeng, invention of national markets, credit mechanisms diffuse
Silk routes
N~3
Europe MidAsia ChinaZipfian q with global hubs CORRELATES with global network links
47
1100 AD
Silk Routes
Europe MidAsia ChinaIndic cities fall with Ghorid/Seljuk invasions; China q remains Zipfian, European Zipf with silk routes
48
1150 AD
Song China loses Kaifeng; Seljuks move into Turkey to consolidate silk route links
1127: No. Song capital of Kaifeng conquered, Song move to south, capital at Hangchow
Silk Routes diminish
Europe MidAsia China
49
1200 AD
Song capital at Hangchow
Golden Horde silk routes
Silk Routes diminish
Europe MidAsia ChinaZipfian q with global hubs CORRELATES with global network links, silk route integration
50
1250 AD
Ghengis Khan breaks network links with conquests, severs Europeans trade (q falls)
cutnodes edgecut
Europe MidAsia China
51
1300 AD
Mongol administrative takeover of China pushes q higher (Imperial capitals),
1279: Mongols conquer Song
Kublai Khan Mongol trade
Europe MidAsia China
Administered trade flourishes but punishes merchant cities
52
1350 AD
Regionalization with Zipfian q (interregional connections tenuous as Yuan focus on China)
Mongols refocus on Yuan administration of China
Silk routes unimportant
Europe MidAsia China
53
1400 AD
Regional markets, Zipfian q
1368 Ming retake China
Silk routes unimportant
Europe MidAsia China
54
1450 AD
1421 Ming move capital to Peking
Silk routes unimportant
World population growth turns super-exponential
Europe MidAsia ChinaEast-West competition; mercantile cities in Europe flatten the urban hierarchy (lower q)
55
1500 AD
Europe MidAsia ChinaIndic, Near East, China resurgent as European cities vie for dominance; 1453 fall of Constantinople
56
1550 AD
Regional markets, Zipfian q, Western trade dominance of Muslim Constantinople
Europe MidAsia China
57
Conclusions: Forager societies, counter intuitively and contrary to mistaken “closed world” models of 20th century ethnography, utilize network linkages to construct continental scale “small-worlds” that solved problems of reproductive survival, buffering reproductive crashes and extinctions.
Similarly, urban civilizations utilize network linkages to construct continental scale “small-worlds” that expand productive and population growth. These created problems of survival however, that have not yet been solved: population growth surpassing the capacity for distribution of resources, operating within Lotka-Volterra oscillatory dynamics with periodic city system crashes resulting from inter-regional competition and war.
58
Thanks to those who contributed to these projects
• Woodrow Denham, Anthropology Department, Alice Lloyd College• 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
59
END – Supplementary materials continue, e.g., Eurasia from 1550
60
1550 AD
Regional markets, Zipfian q, Western trade dominated by Muslim Constantinople
Europe MidAsia China
Portuguese Asian trade expansion
61
1600 AD
Regional markets, Zipfian q, Western inland trade blocked by Muslim Constantinople
Europe MidAsia China
Portuguese Asian trade expansion
62
1650 AD
Europe MidAsia ChinaRegional markets, Zipfian q, Western inland trade blocked by Muslim Constantinople
Dutch Indonesian trade expansion
63
1700 AD
Europe MidAsia ChinaRegional markets, Zipfian q, Western trade routes to the orient
Dutch Indonesian trade expansion
64
low lowhigh[Q3- high
For the next series q-periods fit with
2:1 Secular Population cycles (not shown) 3-4:1 Modelski world leadership cycles, circa 8:1 Kondratiev cycles (doublings)
65
1750 AD
Bifurcated world
Europe MidAsia China
British Indic trade expansion
66
1800 AD
Bifurcated world, Indic subdominant
Circum-European cities start to overtake China in number
Europe MidAsia China
British Chinese trade expansion
67
1825 AD
European cities overtake China in number and size
Industrial revolution
Europe MidAsia China
British Chinese trade expansion and Industrial Revolution
Bifurcated world, Indic subdominant
68
1850 AD
Europe MidAsia China
British Chinese trade expansion and European Industrial Revolution
Euro-dominant
69
1875 AD
Europe MidAsia China
British Chinese trade expansion and European Industrial Revolution
Euro-dominant
70
1900 AD
Europe MidAsia ChinaEuro-dominant, Japan, Russia, Calcutta rising
71
1925 AD
Trifurcated - rise of Japan, Soviet Union
Europe MidAsia China
72
1950 AD
linked by airlines
Europe MidAsia China
73city systems in the last millennium
Color key: Red to Blue:
Early to late city entries
The world system & Eurasia are the most volatile. Big shifts in the classical era until around 1000 CE. Gradual reduction in shifts until the Industrial Revolution. US shift lower, largest 1830-90. UK similar, with a 1950-60 suburbanization shift
UK
World
Slides from Michael Batty, Nature 2006
74city systems in the last millennium
Color key: Red to Blue:
Early to late city entries
The world system & Eurasia are the most volatile. Big shifts in the classical era until around 1000 CE. Gradual reduction in shifts until the Industrial Revolution. US shift lower, largest 1830-90. UK similar, with a 1950-60 suburbanization shift
UK
World
Back to Batty:“Gibrat’s model provides universal scaling behavior for city size distributions” but the rank clocks reveal very different micro-dynamics. Historical dynamics of proportionate random growth generating scale-free effects (in tails) can be informed from rank clocks, as for networks.
Expected growth rate can be composed into overall growth and change at different spatial scales (information distance), enabling different systems (and types) to be integrated through spatial and information hierarchies (Batty p. 593; 1976; Theil 1972; Tsallis 1988).
Gibrat’ law: proportionate random growth? Pi(t) = [Г+εi(t)] Pi-1(t), log-normal, becoming power-law with Pi(t) > Pmin(t), i.e., “losers eliminated”
Slides from Michael Batty Nature 2006
75
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 S1 to the smallest of size Sn as a total population distribution Tr for all people in cities of size Sr or greater, where r=1,n is city rank
Tr=
r
iiS
1
RTr =
r
i
Mi1
Rank size power law M~S1
Empirical cumulative city-population distribution
P(X≥x)
76city systems in the last millennium
For the top 10 cities, fit the standard Pareto Distribution slope parameter, is beta (β) in
Pβ(X ≥ x) = (x/xmin)-β ≡ (Xmin/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 the curve shape q=1+1/Ө (Ө=1/(q-1).
PӨ,σ (X ≥ x) = (1 + x/σ)-Ө (2)
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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
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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.
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Cities Abstract• A 25 period historical scaling of city sizes in regions of Eurasia (900 CE-1970) shows both rises
and falls of what are unstable city systems, and the effects of urban rise in the Middle East on China and of urban rise on China on Europe. These are indicative of some of the effects of trade networks on the robustness of regional economies. Elements of a general theory of complex network dynamics connect to these oscillatory "structural demographic" instabilities.
• The measurements of instability use maximum likelihood estimates (MLE) of Pareto II curvature for city size distributions and of Pareto power-laws for the larger cities. Collapse in the q-exponential curve is observed in periods of urban system crisis. Pareto II is equivalent under reparameterization to the q-exponential distribution. Further interpretation of the meaning of changes in q-exponential shape and scale parameters has been explored in a generative network model of feedback processes that mimics, in the degree distributions of inter-city trading links, the shapes of city size distributions observed empirically.
• The MLE parameter estimates of size distributions are unbiased even for estimates from relatively few cities in a given period, They are sufficiently robust to support further research on historical urban system changes, such as on the dynamical linkage between trading networks and regional city-size distributions. The q-exponential results also allow the reconstruction of total urban population at different city sizes in successive historical periods.
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– Batty, Michael. 2006. Rank Clocks. Nature (Letters) 444:592-596. Batty 1976 Entropy in Spatial Aggregation Geographical. Analysis 8:1-21
– 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
– Theil, Henri. 1972. Statistical Decomposition Analysis. Amsterdam: North Holland.
– 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 working paper.
– White, Douglas R.,and Woodrow W. Denham. 2007. The Indigenous Australian Marriage Paradox: Small-World Dynamics on a Continental Scale
References
city systems in the last millennium
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Note on the Institutional structure of intersocietal marriage and classificatory kinship linkages in Australia
Alternate generation moieties, named or not, are universal in Australia (Dousset p71), either in the patriline or the matriline (Brendt and Brendt 1983:29), which define the generations.
The nonexogamous (alternating) generation, however, extends not only through siblings and half-siblings, but siblings-in-law.
Parents are not necessarily of the same genealogical generation altho they are of the same classificatory generation.
Once these links are made with a single person, classificatory kinship is extended to everyone in that local or regional network.
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Level of stress Low Mod High
Stress responses
Freq of polygyny Low Mod High# marriage classes Low Mod High
Marriage to close kin High Mod LowGenetic load inbreeding High Mod LowExogamy Low Mod HighStratification Flat Shallow slope Steep slope
Symmetric marriage Yes No NoClosure/Aperture Closure Transitional Aperture
H-W age difference Low Mod HighCognitive Model
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Level of stress Low
Moderate High
Closure/Aperture
Closure Transitional Aperture
H-W age difference
Low slopeMedium slope High slope
S I G N A T U R E S
OF
STRESS