The pace of life in the city: urban population size dependence of the dynamics of disease, crime, wealth and innovation Luís M. A. Bettencourt Theoretical Division Los Alamos National Laboratory ASU - February 4, 2006 Collaboration & Support:
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Luís M. A. Bettencourt
Los Alamos National Laboratory
ASU - February 4, 2006
José Lobo : Global Institute of Sustainability, ASU
Geoffrey West: Santa Fe Institute
Dirk Helbing & Christian Kuhnert, T.U. Dresden
Support from ISCOM: European Network of Excellence
Special thanks to Sander van der Leeuw:
School of Human Evolution and Social Change, ASU
R=R0 Mb b=3/4 Power law solves: R(a N)=ab R(N)
Total metabolic rate metabolic rate/mass
Larger organisms are slower!!
The city as a ‘natural organism’ distribution networks:
Until philosophers rule as kings or those who are now called kings
and leading men genuinely and adequately philosophize, that is,
until political power and philosophy entirely coincide, […]
cities will have no rest from evils,...
nor, I think, will the human race.
Plato: [Republic 473c-d]
Raphael's School of Athens (1509-1511)
[…] it is evident that the state [polis] is a creation of nature,
and that man is by nature a political animal.
The proof that the state is a creation of nature and prior to
the individual is that the individual, when isolated, is not
self-sufficing; and therefore he is like a part in relation to the whole.
Aristotle: Politics [Book I]
Germany: year 2002
Note that although there are economies of scale in cables the network is still delivering energy at a superlinear rate:
Social rates drive energy consumption rates, not the opposite
Also true for the scaling of number of housing units
* France/1999 data courtesy Denise Pumain, Fabien Paulus
U.S. patent office
Includes all patents between 1980-2001
From “Innovation in the city: Increasing returns to scale in urban patenting”
Bettencourt, Lobo and StrumskyData courtesy of Lee Fleming, Deborah Strumsky
b=1.15 ( 95% C.I.=[1.11,1.18] )
adjusted R2= 0.89
Data courtesy of Richard Florida and Kevin Stolarick.
Plot by Jose Lobo
Supercreative professionals [Florida 2002, pag. 327-329] are “Computer and Mathematical, Architecture and Engineering, Life Physical and Social Sciences Occupations, Education training and Library, Arts, Design, Entertainment, Sports and Media Occupations”.
Derived from Standard Occupation Classification System of the U.S. Bureau of Labor Statistics
Disease transmission is a social contact process:
Borstein & Bornstein
Bornstein, IJP 1979
But cities to exist at all must also satisfy: distribution networks:
Basic individual needs (house, job, basic necessities)
Require city-wide infrastructure:
- larger population Optimization of system level
- higher density distribution networks
Result: 3 categories:
Social - interpersonal interactions - grow with # effective relations
Individual - no interactions - proportional to population
Structural - global urban optimization - economies of scale
Consider the energy balance equation:
b>1 distribution networks: : Finite time Boom and Collapse
tcrit shortens with N
over quasi-static background
Disease free fixed point:
Endemic fixed point:
m is a small parameter
b>1 distribution networks:
Ndynamics at disease free fixed point
Even if initially stable b>1 eventually
leads to endemic state.
b=1 distribution networks:
NDynamics at endemic steady state
Infected as a fraction of the population:
Human social organization is a compromise over many social activities
Epidemiological dynamics is affected by large-scale
human organization and behavior
It is expected that a social process scales with the number of contacts.
Naively for a homogeneous population N:
Or per capita ncpc=(N-1)/2
Clearly in a large population, N>1000, not all contacts can be realized.
This naïve estimate is the wrong result, an unattainable upper bound.
Now, still assume that the number of effective contacts increases with N but is constrained (time, cognition, energy) to be much smaller:
and smallest city
Now equate the change in productivity per capita R= R1Nb-1 with this increase in effective contacts:
Note that ncpc(N) may itself scale, but with a very small exponent