1 urban and ecosystem dynamics: past, present, future douglas white 2-21-07 workshop on aspects of...
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1
Urban and ecosystem dynamics: past, present, future
Douglas White2-21-07
Workshop on aspects of Social and Socio-Environmental Dynamics
School of Human Evolution and Social Change and
Center for Social Dynamics and Complexity
2
Three slides of background in the literature and modeling on structural demographic theory in
historical dynamics and innovation
3Chinese phase diagram
Turchin 2005:
Dynamical Feedbacks in
Structural Demography
Innovation
4
– Arrighi, Giovanni. 1994. The Long Twentieth Century. London: Verso.
– Fischer, David Hackett. 1996. The Great Wave: Price Revolutions and the Rhythm of History. Oxford University Press.
– Goldstone, Jack. Structural Demography. Book chapter, and discussed in Turchin 2003.
– Sherratt, Andrew. 2005. ArchAtlas. http://www.arch.ox.ac.uk/ArchAtlas/
– Spufford, Peter. 2002. Power and Profit: The Merchant in Medieval Europe. Cambridge U Press.
– 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/
– West, Geoff, Luis Bettencourt, José Lobo. 2005 ms. The Pace of City Life: Growth, Innovation and Scale.
– White, Douglas R. Natasa Kejzar, Constantino Tsallis, Doyne Farmer, and Scott White. 2005. A generative model for feedback networks. Physica A forthcoming. 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.
– White, Douglas R., and Peter Spufford. (Book Ms.) 2005. Medieval to Modern: Civilizations as Dynamic Networks.
References
5
Turchin 2005 validates statistically the interactive prediction versus the inertial prediction for England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000)
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Outline: Main body of talk
• 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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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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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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City Size Distributions for Measuring Departures from Zipf
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
Cumulative city-population distribution
11
City Size Distributions for Measuring Departures from Zipf
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
Cumulative city-population distribution
12
City Size Distributions for Measuring Departures from Zipf
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
Cumulative city-population distribution
13
City Size Distributions for Measuring Departures from Zipf
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
Cumulative city-population distribution
Lower q steeper α in the tail
14
City Size Distributions for Measuring Departures from Zipf
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
Cumulative city-population distribution
Higher q flatter α in the tail
15
City Size Distributions for Measuring Departures from Zipf
Tr=
r
iiS
1
RTr =
r
i
Mi1
Rank size power law
Cumulative city-population distribution
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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City Size Distributions for Measuring Departures from Zipf
Tr=
r
iiS
1
RTr =
r
i
Mi1
Rank size power law
Cumulative city-population distribution
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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City Size Distributions for Measuring Departures from Zipf
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
CC
F
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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City Size Distributions for Measuring Departures from Zipf
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
0.0
0.5
1.0
1.5
2.0
2.5
3.0
900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
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 MidEastIndiaAfghan
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
Europe4 with MidEastIndiaAfghan
Lower Confidence Limit
Upper Confidence Limit
Coefficient
19
China boosted by Middle Asia q
20
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
22
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)
23
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
CC
F
SPIm with q
Lower Confidence Limit
Upper Confidence Limit
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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Summary of these results • 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 SocioPol.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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Digression: Effect of Credit/Liquidity collapse on China q
76543210-1-2-3-4-5-6-7
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
CC
F
Money3 with Abs_q_1.5
Lower Confidence Limit
Upper Confidence Limit
Coefficient
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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.
32
33
Three slides of background in the literature and modeling on structural demographic theory in
historical dynamics and innovation
34Chinese phase diagram
Turchin 2005:
Dynamical Feedbacks in
Structural Demography
Innovation
35
– Arrighi, Giovanni. 1994. The Long Twentieth Century. London: Verso.
– 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.
– Fischer, David Hackett. 1996. The Great Wave: Price Revolutions and the Rhythm of History. Oxford University 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.
– Sherratt, Andrew. 2005. ArchAtlas. http://www.arch.ox.ac.uk/ArchAtlas/
– Spufford, Peter. 2002. Power and Profit: The Merchant in Medieval Europe. Cambridge U Press.
– 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/
– West, Geoff, Luis Bettencourt, José Lobo. 2005 ms. The Pace of City Life: Growth, Innovation and Scale.
– 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.
– White, Douglas R., and Peter Spufford. (Book Ms.) 2005. Medieval to Modern: Civilizations as Dynamic Networks.
References
36
Turchin 2005 tests statistically the interactive prediction versus the inertial prediction for England, Han China (200 BCE -300 CE), Tang China (600 CE - 1000)