urban and ecosystem dynamics: past, present, future

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Urban and ecosystem dynamics: past, present, future

Douglas White1-23-07

Workshop on aspects of Social and Socio-Environmental Dynamics

School of Human Evolution and Social Change and

Center for Social Dynamics and Complexity

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Thanks to• Laurent Tambayong, UC Irvine• Nataša Kejžar, U Ljubljana • Constantino Tsallis, Ernesto Borges, Centro Brasileiro de Pesquisas Fısicas, Rio de

Janeiro• Peter Turchin, U Conn• Céline Rozenblat, U Zurich• Numerous ISCOM project and members, including Denise Pumain, Sander v.d.

Leeuw, Luis Bettencourt• Commentators Michael Batty, William Thompson, George Modelski

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Outline

• Measure for city size deviations from Zipfian constructed and fitted to three Eurasian world regions.

• Does the shape parameter q of these distributions oscillate historically in longer periods than expected at random?

• Does fall in q away from Zipfian correlate with other measures of instability, e.g., internecine warfare or sociopolitical violence?

• Do variations in shape parameter q represent alternating periods of stability and instability? Are city distributions historically unstable, as argued by Michael Batty, Nature 2006, (citing White et al. 2005)

• Does shape parameter q for China affect Europe q with a time lag (diffusion of innovation, Silk Route trade)? Do city size instabilities affect world-system centers?

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Michael Batty (Nature, Dec 2006:592), using some of the same data as do we for historical cities (Chandler 1987), states the case made here:

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.”

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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

Cumulative city-population distribution

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This typical form of the city-size distribution tends toward a power-law in the tail, with a crossover C where smaller city sizes tend more toward an exponential distribution.

Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


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This typical form of the city-size distribution tends toward a power-law in the tail, with a crossover C where smaller city sizes tend more toward an exponential distribution. This closely fits the q-exponential, Yq(S ≥ x) = Y0 (1-(1-q)x/κ)1/(1-q)

Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


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The q-exponential, Yq(S ≥ x) = Y0 (1-(1-q)x/κ)1/(1-q) asymptotes toward a power law in the tail when q>1, and levels at smaller city sizes toward a finite urban population Y0 as governed by a crossover parameter κ (kappa).

Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


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Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


Lower q steeper α in the tail

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Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


Higher q flatter α in the tail

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Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


Straight-line in semilog for Zipfian

9999812764005080403232252540201616001280100880063550840031725220215912610080635040

bins

12

10

8

6

4

2

binc1950c1925c1914c1900c1875c1850c1825c1800c1750c1700c1550c1500c1450c1400c900

Transforms: natural log

In shifting to a semilog rather than a log-log plot of Tr in which the Zipfian is expressed as a straight line, we see that many of the empirical distributions in semilog are relatively Zipfian but some bow concavely from a straight line when α>1.

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Tr=

r

iiS

1

RTr =

r

i

Mi1

Rank size power law


In shifting to a semilog rather than a log-log plot of Tr in which the Zipfian is expressed as a straight line, we see that many other empirical distributions in semilog bow concavely from a straight line either when α>1 for a rank-size power-law, or when the q-exponential has a higher crossover.

9999812764005080403232252540201616001280100880063550840031725220215912610080635040

bins

12

10

8

6

4

2

binc1970c1650c1600c1575c1350c1300c1250c1200c1150c1100c1000

Bowed-line in semilog non- Zipfian

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q is usually < 3, and >0 and China q leads Europe q by 50 years (diffusion time)

Either way. Log-log or semilog, we carry out curve fitting to the q-exponential, Yq(S ≥ x) = Y0 (1-(1-q)x/κ)1/(1-q) and do so with Chandler’s largest historical cities, 900-1970, for China, Europe, Middle Asia in between, and the Mideast.

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

Lag Number

0.9

0.6

0.3

0.0

-0.3

-0.6

-0.9

CCF

China with Europe4

Lower Confidence Limit

Upper Confidence Limit

Coefficient

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

China

Europe

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q is usually < 3, and >0 and both China q and Europe q depress the Middle Asia q within 50 years (competition?)

Middle Asia, caught between China and Europe as connected by the Silk Roads, has a different profile and interaction.

Mideast India Afghanistan

0.00.5

1.0

1.5

2.0

2.5

3.0

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

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

Lag Number

0.9

0.6

0.3

0.0

-0.3

-0.6

-0.9

CCF

China with MidEastIndiaAfghan



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

CCF

Europe4 with MidEastIndiaAfghan



Coefficient

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China boosted by Middle Asia q

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Europe not boosted by Middle Asia q

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City Size Distributions as Measured by q Departures from Zipf are

historically unstable: Middle Asia

q is usually < 3, and >0 and both China q and Europe q depress the Middle Asia q within 50 years (competition?)

Mideast India Afghanistan

0.0

0.5

1.0

1.5

2.0

2.5

3.0

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

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City Size Distributions as Measured by q Departures from Zipf are historically unstable: Europe

0.0

0.5

1.0

1.5

2.0

2.5

3.0

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Europe

q is usually < 3, and >½ and China q leads Europe q by 50 years (diffusion time)

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City Size Distributions as Measured by q Departures from Zipf are historically unstable: China

q is usually < 3, and >0 and China q leads Europe q by 50 years (diffusion time)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

China

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

Lag Number

0.9

0.6

0.3

0.0

-0.3

-0.6

-0.9

CCF

SPIm with q



Coefficient

City Size Distributions as Measured by q Departures from Zipf are

correlated with instability: China

Chinese SPIm=Sociopolitical Instability (moving average) as measured by Internecine wars (Lee 1931), 25 year periods interpolated for q

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Conclusion• Measure for deviations from Zipfian (q, kappa) constructed and fitted to

three Eurasian world regions.

• Shape parameter q of these distributions oscillates historically in longer periods than expected at random (detrended kappa also).

• Fall in q away from Zipfian explored for China, found to be strongly correlated with internecine warfare, more generally SP Instability.

• Variations in shape parameter q represent periods of stability, instability city distributions are historically unstable.

• Shape parameter q for China affects Europe q with 50 year lag (diffusion of innovation, Silk Route trade). China and Europe q affect Middle Asia q negatively (competition) city size instabilities affect world-system centers.

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Implications• Connect these results with those of Geoff West, Luis Bettencourt and Jose

Lobo (Chapter 1, ISCOM book), showing the energetic inefficiency of larger cities.

• That, along with city system instabilities, has implications for more severe consequences as urban population systems grow in size.

• Energy inefficiencies that are cumulative, growing since the industrial revolution severe global warming with no end in sight.

• This includes a 240-300 foot rise in oceans by 22nd C., and flooding of huge number of coastal cities, displacing 10% or more of world population.

• Need to consider new design principles for redesigning cities that are energetically efficient in self sustaining local and global systems.

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Policy Research on Urban Redesign, Energy, and Ecosystem• With a 240-300 foot rise in oceans by 22nd C., and flooding of

huge number of coastal cities, displacing 10% or more of world population and greater infrastructural efficiency energy inefficiencye of larger cities (and conversely for smaller cities), need to study redesign of

• new cities inland in the smaller range that are energetically efficient in self-sustaining local and global systems.

• Existing cities inland in the larger range that are energetically efficient and sustainable in global systems.

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Cohesive Info.Redesign, Minimum Energy, and Ecocoupling

• If the network hubs found in cities attract population, then membership in cohesive netgroups per capita might be lower in cities because of centralization, road design, and now, developer design of suburbs.

• In the era prior to developer design of segmentary suburbs (tree-like intaburb streets, aparteid in sociopolitical effects), ecological psychology found greater productive role density and satisfaction in smaller settlements. This could become a renewed design principle.

• Similarly, in large cities, cohesive designs could be tested against segmentary aparteid principles and used in design principles for energetic and ecological efficiencies and sustainabilities.

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Scaling Issues• Good deal of time devoted to finding reliable and unbiased estimates of the q-exponential

parameters.

• Excel solver can be used, solving a whole series of distributions at once.

• Spss /Analyze/Regression/Nonlinear can be used, one distribution at a time.

• We are testing a candidate model for unbiased MLE of the q-exponential.

• Current findings replicated by different fitting methods.

• Crucial problems:– Accuracy when there are relatively few cases– Accuracy and unbiased estimation when the lower-sized cities are missing– Consistency of results when there are fewer or greater top ranked cities.

• Examination of possible biases in historical distributions.

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Replication and Consistency• Data for other continents beside China will be run against indices of sociopolitical

instability. Some such data are available from Peter Turchin.

• Regional variability in q studied for China in relation to Turchin’s historical dynamic models. Questions of accuracy of total population data for China, possibly other regions.

• Tests of population peaks for China show predicted dynamic lags to changes in SPI indices.

• Consistency tests work for Y0 estimates < Total population, and give estimates of percentage urbanization that for China appear to improve on Chinese census estimates.

• The kappa crossover parameter plays a role in the dynamics.

• The Yq distribution is differentiable. Use of the derivative allows direct mapping into size-specific processes of urban demographic change.

urban and ecosystem dynamics: past, present, future

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