Hollings multiple stable states and resilience

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Hollings multiple stable states and resilience
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Readings

• Holling, C.S. 1973. Resilience and stability of
  ecological systems. Annual Review of Ecology and
  Systematics. 41-23.
• L. Gunderson and Holling, C.S. 2002. Panarchy
  understanding transformations in human and
  natural systems. Island press
• Carpenter, S.R., and L.H. Gunderson. 2001. Coping
  with collapse ecological and social dynamics in
  ecosystem management. BioScience 51451-457.
• Scheffer, M., S. Carpenter, J. Foley, C. Folke,
  and B. Walker, 2001. Catastropic regime shifts in
  ecosystems. Nature 413591-596.

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Types of dynamic behavior

• Stability
• Instability
• Damped oscillations
• Limit Cycles
• Un-damped oscillations

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Stability

• The tendency of the system to return to an
  equilibrium when disturbed
• A ball in a bowl

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Instability

• The failure of a system to return to an
  equilibrium once disturbed
• The Unstable Equilibrium - a pencil balanced on
  its eraser
• Rocket design

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Damped oscillations

• A stable system - but one that cycles on its way
  back to the equilibrium

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Stable limit cycles

• A system that maintains cycles, but is stable --
  that is if disturbed from the cycle it will
  return to the cycle

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Un-damped oscillations

• An unstable system that cycles more and more
  violently until some elements die out.

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An attractor region

• The behavior is stable within the attractor, but
  either unstable outside, or into the bounds of
  another attractor.

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Resilience

• The ability of a system to utilize perturbation.
  
• The size of the attractor may depend on the
  perturbation history, in the absence of
  perturbation, the size of the attractor shrinks.
• Materials resilience
• Fire example

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Ecosystem resilience is the capacity of an
ecosystem to tolerate disturbance without
collapsing into a qualitatively different state
that is controlled by a different set of
processes. A resilient ecosystem can withstand
shocks and rebuild itself when necessary.
Resilience in social systems has the added
capacity of humans to anticipate and plan for the
future. "Resilience" as applied to ecosystems, or
to integrated systems of people and the natural
environment, has three defining characteristics
The amount of change the system can undergo
and still retain the same controls on function
and structure The degree to which the system
is capable of self-organization The ability to
build and increase the capacity for learning and
adaptation
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• Budworm
• Fire

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HollingsMyths

• Balance of nature
• Stable equilibria Nature forgiving
• Randomness
• Spatial Balance - meta populations
• Multiple stable states

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Carpenter lake fisheries example

• Actors managers, resident and transient
  fishermen, lakeside property developers
• Development removes shore-side vegetation
  decreasing fisheries productivity potential

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Dynamics with fixed bag limit policy
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Key concepts

• Slow and fast variables
• The dynamics of fast variables change
  dramatically with state of the slow variables
• In particular the bounds of stable regions change
  and may disappear