Urban%20and%20ecosystem%20dynamics:%20past,%20present,%20future

1
Urban and ecosystem dynamics past, present,
future

• Douglas White
• 1-23-07
• Workshop on aspects of Social and
  Socio-Environmental Dynamics
• School of Human Evolution and Social Change
• and
• Center for Social Dynamics and Complexity

2
Thanks to

• Laurent Tambayong, UC Irvine
• Nataša Kejžar, U Ljubljana
• Constantino Tsallis, Ernesto Borges, Centro
  Brasileiro de Pesquisas Fisicas, 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

3
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?

4
Michael Batty (Nature, Dec 2006592), using some
of the same data as do we for historical cities
(Chandler 1987), states the case made here
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.
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.
5
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 r1,n is city rank

Cumulative city-population distribution
Rank size power law MS1
6
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.

Cumulative city-population distribution
Rank size power law
7
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/?)1/(1-q)

Cumulative city-population distribution
Rank size power law
8
City Size Distributions for Measuring Departures
from Zipf

• The q-exponential, Yq(S x) Y0
  (1-(1-q)x/?)1/(1-q) asymptotes toward a power law
  in the tail when qgt1, and levels at smaller city
  sizes toward a finite urban population Y0 as
  governed by a crossover parameter ? (kappa).

Cumulative city-population distribution
Rank size power law
9
City Size Distributions for Measuring Departures
from Zipf

• The q-exponential, Yq(S x) Y0
  (1-(1-q)x/?)1/(1-q) asymptotes toward a power law
  in the tail when qgt1, and levels at smaller city
  sizes toward a finite urban population Y0 as
  governed by a crossover parameter ? (kappa).

Cumulative city-population distribution
Lower q steeper a in the tail
Rank size power law
10
City Size Distributions for Measuring Departures
from Zipf

• The q-exponential, Yq(S x) Y0
  (1-(1-q)x/?)1/(1-q) asymptotes toward a power law
  in the tail when qgt1, and levels at smaller city
  sizes toward a finite urban population Y0 as
  governed by a crossover parameter ? (kappa).

Cumulative city-population distribution
Higher q flatter a in the tail
Rank size power law
11
City Size Distributions for Measuring Departures
from Zipf
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
agt1.
Cumulative city-population distribution
Straight-line in semilog for Zipfian
Rank size power law
12
City Size Distributions for Measuring Departures
from Zipf
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 agt1 for a rank-size
power-law, or when the q-exponential has a higher
crossover.
Cumulative city-population distribution
Bowed-line in semilog non- Zipfian
Rank size power law
13
City Size Distributions for Measuring Departures
from Zipf
Either way. Log-log or semilog, we carry out
curve fitting to the q-exponential, Yq(S x)
Y0 (1-(1-q)x/?)1/(1-q) and do so with Chandlers
largest historical cities, 900-1970, for China,
Europe, Middle Asia in between, and the Mideast.
q is usually lt 3, and gt0 and China q leads Europe
q by 50 years (diffusion time)
14
City Size Distributions for Measuring Departures
from Zipf
Middle Asia, caught between China and Europe as
connected by the Silk Roads, has a different
profile and interaction.
q is usually lt 3, and gt0 and both China q and
Europe q depress the Middle Asia q within 50
years (competition?)
15
China boosted by Middle Asia q
16
Europe not boosted by Middle Asia q
17
City Size Distributions as Measured by q
Departures from Zipf are historically unstable
Middle Asia
q is usually lt 3, and gt0 and both China q and
Europe q depress the Middle Asia q within 50
years (competition?)
18
City Size Distributions as Measured by q
Departures from Zipf are historically unstable
Europe
q is usually lt 3, and gt½ and China q leads Europe
q by 50 years (diffusion time)
19
City Size Distributions as Measured by q
Departures from Zipf are historically unstable
China
q is usually lt 3, and gt0 and China q leads Europe
q by 50 years (diffusion time)
20
City Size Distributions as Measured by q
Departures from Zipf are correlated with
instability China
Chinese SPImSociopolitical Instability (moving
average) as measured by Internecine wars (Lee
1931), 25 year periods interpolated for q
21
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.

22
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.

23
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.

24
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.

25
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.

26
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 Turchins 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 lt 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.

27
(No Transcript)