Synchrony and networks how the growth and decline of cities and the rise and fall of city-size hierarchies is related to the network structure of intercity

synchrony and networks how the growth and decline of cities and the rise and fall

of city-size hierarchies is related to the network structure of intercity connections

Doug White UC Irvine

Social Science History Association November 12-15 2009

Parts of the story in a nutshell

Pax Mongolica: The routes of the silk road leading west from Central Asia (detail of map at Tashkent University).

http://www.silk-road.com/artl/paxmongolica.shtml

Temporally: Opening and closure of the silk roads affect globalized Eurasian synchrony from China to Europe

Economic structure: The bicomponent multiple independent routes between cities as the trading nodes promote competitive pricing.

City rise and city-fall: Population scaling distributions change with temporal changes in economic links.

Cycles vs. cutpoints are key to the dynamics as polities compete for dominance of trading routes and cities.

Parts of the story in a nutshell

Pax Mongolica: The routes are subject to policies of polities and empires, falling into epochs of domination (Modelski et al. p.78,217)___Regional

N. Sung 930-

S. Sung 1060-

Genoa 1190-_________to Global____

Mongols 1250-90-1360 trans Eurasian

Portugal 1430- Global system mapping

Holland 1540- Global capital

England 1640- Global industrial exports

Britain 1740- Global organization

United States 1850-Global information- Global market

United States 1950- Decolonization

-1990 Depolarization - Global hyperspace

Euro-Hegemon examples

(Arrighi 1994)

Commercial

Financial

Constantinople

Venice

Genoa

Amsterdam

London

New York

Transaction costs, hegemony and inflation as q-correlated temporal variables

Conflict on Land Sea trade routes safer than land, 1318-1453/4+ (Spufford:407)

Inflation Lo/hi

Landed Armies safe land routes 1500-1650 Maritime Conflicts (Jan Glete)

Landed Trade Secure

Dominant Routes

Sea routes safe French Sov.

Peace of Westphalia

Baltic conflicts: connection to Novgorod and Russia (lost)

Swedish hegemony

European access

Struggle for Empire: Sea Battles to 1815

Global Maritime

Economy Industrial Rev. from 1760

Political Revolutions to 1814

Trade net

(low cost)

versus

(high cost)

Maritime (low cost)

versus

Land routes trade

(pop. growth)

Financial capital

CommercialC C C C C C C C C C I ? ? ? ? I I I I I I I I I I I ? ? I I I I I I q H i ? ? ? ? L ? ? ? h h h h L L L L L L L L h h h h h h L L L L h h L L L L L h h h L P P ? ? p P ? ? ? E E E E E E E ? ? E E E E E E E ? E E E q L o F F F F F F F F F F F F F F F 1 1 1 1 1 1 1 1 1 1 2 0 1 2 3 4 5 6 7 8 9 0 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 2 5 7 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 L/h lo/hi inflation figures (L=depression) are for that year forward

• Conclusions: city systems in the last millennium

• City systems unstable; have historical periods of rise and fall over hundreds of years; exhibit collapse.

• 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.• • SO WHY DOES THE MEDIEVAL EUROPEAN RENAISSANCE ECONOMY

COLLAPSE CIRCA 1300?• Trade dominance shifts from betweenness centrality (Genoa) to global Flow

Centrality (Bruges)• China invaded, change in Silk routes• Credit crisis between North and Southern Europe• Major problem in Population Growth/Resource base• Internecine struggles• Major collapse, long recovery "Long 13th century” reaches to today

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



etc.

Cities in the region of “MiddleEast&Afghan&India” are initially inversely related to but then affect Chinese Cities with 100-150 year lags

Whole period 900 - 1950


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

Moving to closer inter-Asian regions excluding India but on the Silk RoadTime-lagged cross-correlation effects of Mid-Asian q on China

(1=50 year lagged effect)

MiddleEast&Afghan Robust Cities affect Robust Chinese Cities with 50 year lag


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_China with mle_Europe



Coefficient

Moving between endpoints further away on the Silk RoadsTime-lagged cross-correlation effects of China q on Europe

76543210-1-2-3-4-5-6-7

Lag Number

0.9

0.6

0.3

0.0

-0.3

-0.6

-0.9C

CF

China with Europe4



Coefficient

(100 year lagged effect)

(non-MLE result for q)

Robust Chinese Cities affect Robust European Cities with 100 and 300 year lag


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



Coefficient

Time-lagged cross-correlation effects of the Silk Road trade on Europe

(50 year lagged effect)

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_Europe



Coefficient

Chinese Silk road trade affects Elite tails of European Cities with 50 year lag

Robust Mideast Cities small effect on Robust European Cities with 150 year lag

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

Fmle_Europe with ParisPercent



Coefficient

Elite tails of European Cities maintain Paris as Euro Elite Capital with 100 year decay

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

q measures the shape of the body of the curve, while beta10 measure fits the log-log slope of the tails, which vary independently of q.

Goodness of fit for q and beta10 are found by bootstrap probability simulation, where with added iterations around each of four periods

Variations in q and the power-law slope β for 900-1970 in 50 year intervals


1970

1950

1925

1900

1875

1850

1825

1800

1750

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

1000

900

1970

1950

1925

1900

1875

1850

1825

1800

1750

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

1000

900

1970

1950

1925

1900

1875

1850

1825

1800

1750

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

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

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

1000

900

1970

1950

1925

1900

1875

1850

1825

1800

1750

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

1000

900

1970

1950

1925

1900

1875

1850

1825

1800

1750

1700

1650

1600

1575

1550

1500

1450

1400

1350

1300

1250

1200

1150

1100

1000

900

3.0

2.5

2.0

1.5

1.0

0.5

0.0

MinQ_BetaBeta10MLEqExtrap

Are these random walks or historical Periods? Runs Test Results


Runs Tests at medians across all three regions

MLE-q Beta10 Min(q/1.5,

Beta/2) Test Value(a) 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_Europe mle_MidAsia mle_China Test Value(a) 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

a Median

(figures courtesy of Andrew Sherratt, ArchAtlas)

Cohesive extension of trade routes leads to a host of other developments…

Multiconnected regions => structural cohesion variables



Some changes in the medieval network from 1000 CE


to 1500 CE

(note changes in biconnected zones of structural cohesion)

Project mapping is proceeding for cities and trade networks for all of AfroEurasia and urban industries for Europe in 25-year intervals, 1150-1500

(our technology for cities / zones / trade networks / distributions of multiple industries across cities for each time period includes dynamic GIS overlays, flyover and zoomable web images)


0900 AD

low q with thin power law tails of global hubs CORRELATES with global network links

From first stirrings of globalization to the 21st Century

Europe

Central Asia

Medit. China

Near East

India

In these slides I will connect the city network & city size distributions and power-law tails connected to q-exponential scaling of city sizesQ

(sc

alin

g si

zes)

ChanganChanganChangan

Bagdad & Changan (Xi’an)

Silk routes

1000 AD

960: Song capital at Kaifeng, invention of national markets, credit mechanisms diffuse

Global network links characterize low q (power law tail for city sizes)

Silk routes

N~3

1100 AD

Global network links characterize low q (more exponential body with power law tail for city sizes)

Silk Routes

1150 AD

Global network links characterize low q (more exponential body with power law tail for city sizes)

1127: No. Song capital of Kaifeng conquered, Song move to south, capital at Hangchow

Silk Routes diminish

1200 AD

Song capital at Hangchow

Golden Horde silk routes

Global network links characterize low q

Silk Routes diminish

1250 AD

Broken network links lead change to high q – led by China, 50 years

cutnodes edgecut

1300 AD

Broken network links characterize high q (here: tenuous interregional connectors)

1279: Mongols conquer Song

Kublai Khan Mongol trade

1350 AD

Broken network links characterize high q (here: tenuous interregional connectors)

Mongols refocus on Yuan administration of China

Silk routes unimportant

1400 AD

Renewed network links characterize low q (power law tail)

1368 Ming retake China


1450 AD

Renewed network links characterize low q (power law) – high q led by China, 100 years

1421 Ming move capital to Peking


World population growth turns super-exponential

1500 AD

Renewed network links characterize low q (power law tail) – but China high q leads change

1550 AD

Broken network links characterize high q

1600 AD

Renewed network links will lead change to low q (here: tenuous interregional connectors)

1650 AD

Renewed network links characterize low q (power law tail) – China synchronized

1700 AD

Broken network links return to high q – esp. for China leading

1750 AD

Broken network links typify high q – China leading – bifurcated world

1800 AD

Broken network links typify high q – bifurcated world

Circum-European cities start to overtake China in number

1825 AD

Broken network links typify high q – trifurcated world – best example of high local navigability

European cities overtake China in number and size

Industrial revolution

British opium trade from India

1850 AD

Broken network links typify high q – trifurcated world – but China developing power-law tail

(here: tenuous interregional connectors)

1875 AD

Broken network links typify high q – bifurcated - China power-law tail thinning toward low-q

(here: tenuous interregional connectors)

1900 AD

Broken network links typify high q – trifurcated Eurodominant - China leads shift to low-q 50 yrs

1925 AD

Broken network links typify high q – trifurcated - rise of Japan - China returns to high q

Start of a low q Zipfian tail for world city distribution – trifurcated – but linked by airlines

1950 AD

N-cohesion (2=competitive 1=monopoly land trade) leads Q (city rise/fall) :

fragments

Is there Eurasia synchrony?

Yes: but it is not simultaneous.

Rather, it is time-lagged synchrony

and not always in the direction.

It goes from leading to trailing economies following the dynamics of trade.

And the dynamics of trade is influenced by whether the trading network is monopolized by chokepoints or is competitive.

Competition is defined by biconnectivity.

(A special case of structural cohesion)

Documents

Synchrony and networks how the growth and decline of cities and the rise and fall of city-size hierarchies is related to the network structure of intercity