On the Rise and Fall of Complex Societies

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On the Rise and Fall of Complex Societies

• Markus Brede and John Finnigan
• CSIRO Centre for Complex Systems Science

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Introduction

• Complex societies as an exception? (Human pop.
  99 of the time in a state of low organization)
• Most societies rose rapidly, flourished for some
  time and came to a rather sudden end
• Examples
• (old) Egypt 2500 BC invasions?
• Akkad 2200 BC environmental?
• Harappa 1800 BC environ./Aryans?
• Minoan Palaces 1400 BC vulcanoes?
• Hittites 1200 BC barbarians?
• Classic Maya 800 AD environmental?
• Anasazi 1300 AD environmental

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Introduction

• Strong emphasis on correlations with climatic
  events that cause environmental change
• However
• Real cause-effect relationship often unclear
• Many examples of societies that survived
  environmental challenges
• Often minor reasons cited that appear
  insufficient to cause major effects like collapse
  (SOC?)

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Tainters Economic View

• Perceived cause of collapse often only trigger,
  underlying reason is change in structure of
  society over time
• Evolution of a society steady increase of
  complexity as a result of problem solving
  attempts
• Initially Strong growth, large rewards for early
  complexity
• Saturation, marginal benefit of complexity
  decreases
• Reserves depleted, lacking buffering capacity
  makes society prone to collapse
• But why Collapse?

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Complexity

• Unevenness of wealth distributions
• Existence of class structures
• Investment in infrastructure (sunk costs)
• Here Number and type of relationships between
  subsystems

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Network Picture of Societies

• Subsystems (nodes) connected by relationships
  (links)
• Examples
• People Acquaintanceship
• Groups of people Resource exchange
• 
  Dependencies
• Administrative units Control

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Benefits and Costs of Interactions
S2
S5
S1
S3
S4

• Benefit S1 can cooperate with S2,S4 and to a
  lesser extent with S3 and S5
• Cost S1 has to maintain its links with S2 and S4

technology factor
cost of maintaining links
net network effect
nodes i can Interact with
efficiency of interactions decreases with
distance from i
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Benefits and Costs in Random Graphs
pathlength
cluster size
links
links
net effect Dr
links
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Dynamic Model

• Consider simultaneous resource
• And Network dynamics, subject to resource
  availability at node i
• Add new node with probability pnode
• Delete links from i to randomly selected
  neighbours as long as Ri(t)ltrmin
• (if afterwards still Ri(t)ltrmin remove node)
• If Ri(t )gt0 with probability padd add new link
  from i to
• randomly chosen target node

resource at node i
waste
harvest (stochastic)
cost and benefits from interactions
consump- tion
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Parameter Regimes

• Some network structures ...
• Either no network or fully connected network?
• Trees define a minimum sustainable network
• size N0 for cf a lt 1

Complete graph
2-cluster
Regular tree
D -N(N-1)cf a
D -1cf a
D -kfNb
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Parameter Regimes
cf a lt 1
cf a gt 1
Benefits always outweigh costs
No permanent interactions
Small, fluctuating clusters
Complete graph

• High waste rate, low harvest surplus
• No buildup of reserve stockpiles possible
• Tree threshold N0 never reached
• Low waste rate, large harvest surplus
• Buildup of reserve stockpiles that help reach
  threshold size N0
• Then formation of system-spanning networks
  possible

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Simulation Results
Typical Growth-Decline Cycle
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Summary

• Network interpretation of complexity of societies
• Simple network model for Tainters idea that the
  increase in complexity leads to decreased
  marginal returns
• If technology not too advanced (cf a lt 1) and
  improvements small compared to link formation
  growth-decline cycles are found