Collapse of Civilizations: A Mathematical Model

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Collapse of Civilizations A Mathematical Model

• M. Bologna and J. C. Flores, EPL, 81 (2008) 48006

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Reasons for a Collapse

• Global or regional catastrophe
• Overexploitation of the resources

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Anasazi

• Located in Colorado, Utah, Arizona and New Mexico
  (700-1200 AD)
• Global or regional climate change (prolonged
  periods of drought)
• Environmental degradation (de-forestation)

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What and How to Model?

• The ideal candidate
• Closed System
• Isolated system
• Limited kinds of resources

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Rapa Nui (Easter Island), Area of 64 square
milesIt lies in the Pacific Ocean approximately
2,000 miles from Chile
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The Beginning

• Few dozens of individuals, first landed around
  400 A.D.
• Palm trees Bahn P. and Flenley J., Easter
  Island, Earth Island (Thames Hudson, London)
  1992

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Difficult fishing activity (cold water,
impervious shape of the coast)
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Development of the Society

• Potato cultivation
• Fishing activity (far from the coast)
• Moai construction
• Its peak 7000 inhabitants around 1300-1400

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The Demise

• 1600 - 1700 A.D. Easter Island society declined
  from 7000-8000 to 2000-3000 inhabitants (First
  report The Dutch Admiral Roggeveen visits the
  island on Easter Sunday 1722 ).
• The islanders were trapped as without trees there
  were no canoes.
• Deforestations impact was equally important to
  society and cultural.
• Slavery became common.
• Cannibalism resulted due to lack of available
  protein.
• By 1877 only 111 inhabitants were left on the
  island due to deportation to Peru and Chile and
  diseases brought by Westerners.

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Logistic EquationPierre Verhulst (1845, 1847).
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• Nonlinear Birth-Death Processes (Population
  dynamics).
• Chemical reaction kinetics.

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Easter Island Model

• r and r grow rates
• Rc Carrying Capacity
• Alpha technological parameter

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Exploitation of Resources -gt Effective Area
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Evaluation of Parameters

• r0.01 1/year Fort J. and Mendez V., Phys.
  Rev. Lett., 82 (1999) 867

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Copan Maya

• Ninth century.
• Population declined in 100 years from 20000 to
  5000 individuals.

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Conclusion

• A mathematical model, considering the interaction
  between carrying capacity and population, has
  been considered and applied to the Easter Island
  society. An estimation of the technological
  parameter a is obtained and applied to another
  ancient civilization, the Maya of Copan, with a
  reasonably precise estimation about their
  collapse time. This confirms the consistency of
  the adopted model.