Human Social Dynamics - Dougintersci.ss.uci.edu/wiki/drw/ISC_PIF_Summer_SchoolPart3.pdf · Human Social Dynamics: ... terms of correlations but need to look at human dynamics in

Part 3 Realistic dynamical modeling

( these slides incomplete )

Human Social Dynamics:Realistic modeling of complex interactive systems

http://InterSci.ss.uci.edu/wiki carries these lectures athttp://intersci.ss.uci.edu/wiki/index.php/Complexity_summer_school

with interactive links and background readings

What was learned in part 1 of the lectures, reviewing modeling of social systems from archaeological through historical to the current period

…is that we cannot look at contemporary (or past) data in terms of correlations but need to look at human dynamics in terms of time-lagged causality that makes immediate everyday comprehension difficult.

Here in part 3 we look at dynamics

Keynes (1920:11-12)

“The great events in history are often due to secular changes in the growth of population and other fundamental economic causes, which, escaping by their graduate character the notice of contemporary observers, are attributed to the follies of statesmen or the fanaticism of [nonbelievers]…. [T]he disruptive powers of excessive national fecundity may have played a greater part in bursting the bonds of convention than either the power of ideas or the errors of autocracy”

cited in Korotayev and Khaltourina (2006:113-114)

With the tightening of the world economy, the poorer sectors become poorer, destabilized, and ever more vulnerable to raw material exploitation.

More failed states.Failure to go through a demographic transition.More children in the failed states to compensate for insecurity.More child warriors exploited in the rush for raw materials in failed

states.

Greater world population growth and pressure on resources, pressure for migration.

More internal war.More external war.

These hypotheses will require testing not with correlational methods but by time-lagged multi-equation fitting for dynamical modeling (Lectures, Part 1).

Part 3 now resumes the topic of multi-equation dynamical modeling, starting with the dynamic coupling of sociopolitical conflict (e.g., internal war) and population fluctuations.

e.g. recall from lecture 1

phase diagram

Log Population

War lag R

ate of change

Log Internal warPop lag R

ate of change

http://eclectic.ss.uci.edu/~drwhite/Civ/Spuf/Tur/ChinaPopWarPhaseSpace.jpg

http://eclectic.ss.uci.edu/~drwhite/Civ/Spuf/Tur/ChinaPopWarPhaseSpace.jpg

This is Turchin's phase diagram for England, 1480-1800, for population size and sociopolitical violence as a pair of variables that drive one another interactively. Temporal movement here is clockwise. The dynamic is that the population reaches carrying capacity setting sociopolitical violence into play, which only recedes as population crisis leads to a collapse, initiating a new cycle.

Turchin tests statistically the interactive prediction versus the inertial prediction for England and China

Turchin (2005), in Structure and Dynamics eJournal

http://eclectic.ss.uci.edu/~drwhite/Civ/Spuf/Tur/ChinaEnglandPopWarPredictions.jpg

To resume the topic of multi-equation dynamical modeling, starting with the dynamic coupling of sociopolitical conflict (e.g., internal war) and population fluctuations, longitudinal hypotheses require testing not with correlational methods but by time-lagged multi-equation fitting for dynamical modeling (Lectures, Part 1).

Greater world population growth and pressure on resources, pressure for migration.

More internal war.More external war.

BUT what the Turchin theory does not explain is why does the population curve, when sociopolitical conflict abates, not simply grow following a logistic or S-shaped curve, that is, more rapid growth when more resources are available, then slowing as more resources are used per capita.

Why does world population growth follow power-law or hyper-exponential growth?

We begin there and then go back to questions of time-law causality with respect to: What is it in human dynamics that generates power-law growth?

And the answer to that question is simply this: cities, based on exchange networks, are what generate power-law growth.

The hypothesis (nature article) is that in a network model of exchange it is the presence of the strategic use of hubs, modeled by the γ (gamma) parameter in the feedback cycles model, that is different from other kinds of networks.

1. hyper-exponential growth in population: Actual world level runaway population growth spurts, producing crises of resource scarcity, and subsequent flattening of growth rates.

World population power-law or hyper-exponential growth spurts and flattening as shown in a semilog plot with successive power-law fits, 10,000 BCE to

1962 (which begins another flattening: we are in the crisis phase)

What is it in human dynamics that generates power-law or hyper-exponential growth?

And the answer to that question is simply this: cities, based on exchange networks, are what generate power-law growth.

My hypothesis is that in a network model of exchange it is the presence of the strategic use of hubs, modeled by the γ (gamma) parameter in the feedback cycles model, that is different from other kinds of networks.

The relevant literature here is Adamic, Lukose and Huberman (2003) on local search in networks in relation to power-law tails (hubs) of networks, and White and Houseman (2002) and White and Johansen (2006) on “Navigability.” Bottom line is that log-log slopes 2.0-2.3 in degree distribution tail enable hub search.

2002 Navigability of Strong Ties: Small Worlds, Tie Strength andNetwork Topology. (drw & M. Houseman). Complexity 8(1):72-81 http://eclectic.ss.uci.edu/~drwhite/Complexity/SpecialIssue.htm

2005 Chapter1 Network Analysis and Ethnographic Problems: Process Models of a Turkish Nomad Clan. drw & Ulla Johansen. Boston: Lexington Press. 2006 in paperhttp://eclectic.ss.uci.edu/~drwhite/pub/PMContFwd01.pdf

In part 2 we looked at three complex-network models with different processes in their main dynamic:

•Scale-free, leading nodes (α)•Small-world, diffusion (β)•Social-circles with feedback, with both features (α, β) plus the strategic use of hubs (γ)

But what is the connection between strategic use of hubs, cities, and population growth? Simply this: to support a city a network of exchange is needed and this network requires agents who search out and mediate optimal exchanges. This evokes the strategic use of hubs (γ) where the city is part of a signaling system involving these agents, as in the generative feedback model, in which production has also to be managed by agents who can deliver exports to be exchanged (or weapons to use for extraction) that will deliver imports that the city utilizes either for sustenance and supply of its activities (including production) and for reproduction. We have seen in part 1 how this operates in the world economy, and Algaze (2005) shows how it operates in the first cities.

We can then begin to model the causes of power-law growth in cities with results from the study of urban growth: 2007 Growth, innovation, scaling, and the pace of life in cities. Luís M. A.

Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West PNAS 104(17):7301-7306.

The growth of cities is constrained by availability of resources and rates of their consumption. The general growth equation [1] assumes a quantity R of resources used per individual, on average, per unit time, while a resource quantity E is required to add one person to the population. An allocation of resources is expressed as that is, sustenance and replacement, where dN/dt is the growth rate. Then

).()()( 0 tN

ERtN

EY

dttdN

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛= β

The solution of this equation is given by

[1]

[2].)1(exp)0()(1

1

010β

β β−

−⎥⎦

⎤⎢⎣

⎡⎥⎦⎤

⎢⎣⎡ −−⎟

⎠⎞

⎜⎝⎛ −+= t

ER

RYN

RYtN

City populations, as shown by parameter fitting for urban network input/output & import/export, exhibit β>1 in the sustenance component that includes support for the city’s production. This implies hyper-exponential growth.

All other species exhibit β<1 in their sustenance component !!!!

For scale-free networks a generating parameter α=1 for preferential attachment p(k)=k-α will often generate log-log slopes 2.0-2.3 in a (k=) degree distribution tail that enables hub search. The slope will be lower if the network has too few nodes and higher if too many nodes.

In a city network its not the spokes (roads) around each city that constitute attraction as if only by “degree.” Rather it is something like the attraction coefficient for production and marketing agents in the Bettencourt model.

We can check if the gravity model for intercity migration satisfies the function we are looking for: here, attraction ~ sizeλ/distance2.

Similarly, what values of γ, α, and β in the feedback model give the network searchability?

What we want to find for known city sizes in a geographic space is what value of λ makes the network “hub searchable” in the same sense that Adamic et al. demonstrated for scale-free networks. I suppose it would be nice if the range of λ that yields “searchability” contains the value of β from the Bettencourt et al. fitting experiment.



Time-lagged cross-correlation effects of MidAsia q on Europe and the Silk Road trade on European β (ten top cities)

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

Lower Confidence Limit

Upper Confidence Limit

Coefficient

Figure 4: Cross-correlations of q for temporal effects of one region on another

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



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



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



Coefficient

1 100 10000

5e+

025e

+03

5e+

045e

+05

city size [105]

1 5 10 50 200 1000 10000

103

104

105

106

1750180018251850187519001914192519501970

1 100 10000

5e+

022e

+03

5e+

032e

+04

5e+

042e

+05

city size [105]

1 5 10 50 200 1000 10000

103

104

105

180018251850187519001914192519501970

becomes fully globalized.

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

Fitted parameters for city size distributions in Eurasian Regions (β in Pareto I tail, q in Pareto II body, and their normalized minimum)

Slides not complete, please stop here.

Slides not complete, please stop here.

Rome: Sorokin's index of internal war

Year

-500 -400 -300 -200 -100 0

y

0

50

100

150

200

250

Turchin 2007 SFI talk

Western Roman Empire (Lewit 1991)

Century

-1 0 1 2 3 4 5

Occ

upat

ion

Inde

x

0

20

40

60

80

100


Popular Immiseration, England: 1250 - 1800

Year

1200 1300 1400 1500 1600 1700 1800

Var

iabl

es, l

og-s

cale

, arb

itrar

y co

nst.

Inv. wageRel. Pop


England

1100 1200 1300 1400 1500 1600 1700 1800

Inst

abili

ty In

dex

0

5

10

Events per decadeSmoothed, h =25 y


Bohemia, Moravia, and Silesia

Year

1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850

Hoa

rds

per d

ecad

e

0

50

100

150

200Hussite Wars (1420-36)

Thirty-Year War (1618-48)


Hoards in NW Germany

1000 1100 1200 1300 1400 1500 1600 1700 1800

Hoa

rds

per h

alf-c

entu

ry

0

10

20

30

40

50

W. WestfalenE. WestfalenPfalz/SaarNordrhein

Welf/Hohen-staufencivil wars

LateMedievalCrisis

Crisis of XVIIc


Instability Index (log-transformed)

-0.2 -0.1 0.0 0.1 0.2

Com

poun

d an

nual

gro

wth

rate

0.0

0.2

0.4

0.6

0.8

CAGR: 1540-1870 (Wrigley et al. 1997)


Bohemia/Czech Republic (McEvedy & Jones 1978)

1100 1200 1300 1400 1500 1600 1700 1800

Popu

latio

n, m

illion

0

2

4

6

8Turchin 2007 SFI talk

Spain (McEvedy and Jones 1978)

1100 1200 1300 1400 1500 1600 1700 1800

Pop

ulat

ion,

mill

ion

0

2

4

6

8

10

12


Population push to cities


(a) Paris

1200 1300 1400 1500 1600 1700 1800

Pop

ulat

ion

of P

aris

(tho

usan

ds)

100

200

500

1000

1500

(b) Urbanization

1200 1300 1400 1500 1600 1700 1800

Per

cent

of p

opul

atio

n in

the

capi

tal

0

1

2

3

4


Novgorod

1000 1100 1200 1300 1400 1500

Am

ber b

eads

per

cul

tura

l lay

er

0

10

20

30

40

50

60


For scale-free networks a generating parameter α=1 for preferential attachment p(k)=k-α will often generate log-log slopes 2.0-2.3 in a (k=) degree distribution tail that enables hub search. The slope will be lower if the network has too few nodes and higher if too many nodes.

In a city network its not the spokes (roads) around each city that constitute attraction as if only by “degree.” Rather it is something like p(k) = k -αβ where β is the attraction coefficient for production and marketing agents in the Bettencourt model and α is the coefficient of the transport degree network. (E.g., what values of γ, α, and β in the feedback model let the network be searchable?)

We can check if the gravity model for intercity migration satisfies the function we are looking for: here, attraction ~ sizeλ/distance2.

What we want to find for known city sizes in a geographic space is what value of λ makes the network “hub searchable” in the same sense that Adamic et al. demonstrated for scale-free networks. I suppose it would be nice if the range of λ that yields “searchability” contains the value of β from the Bettencourt et al. fitting experiment.



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Human Social Dynamics - Dougintersci.ss.uci.edu/wiki/drw/ISC_PIF_Summer_SchoolPart3.pdf · Human Social Dynamics: ... terms of correlations but need to look at human dynamics in