Nonlinearity, Feedback and Stability

Linear relationship (eg. y = ax + b)

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Non-linear relationship (eg. y = ax2 + b)

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Nonlinearity suggest all relations that are not linear. Of course this is a rather awkward way of defining a relationship.


Stability

This aspect refers the the system's ability to return to a stable state after a disturbance.

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Feedback

Feedback is the mechanism whereby which some input to a system directly affects the output of the system. This can be one of two kinds of feedback:

  • Positive feedback; is where the input of the system A is directly proportional to the output of the system B
  • Negative feedback; is where the input of the system A is inversely proportional to the output of the system B

Linearity and stability

Linear systems are inherently unstable .

  • Industrial systems; lead to the depletion of resources and congested energy sink.
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Systems employing feedback mechanisms are non-linear. Their stability changes depending on the system dynamics. For example, consider the Isle Royale. For the sake of argument;

  • Consider it as a small island with rather simple ecosystem (contains deer, grass & decay-organisms)
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Of course this will not continue indefinitely. Negative feedback systems such as eventual-famine will level it out (possibly catastrophically).
If we consider the system both with positive and negative feedback, stability is possible. Consider a pack of timber-wolves migrates to the island.
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Dynamic ecosystems

Throughout modern history scientists have attempted to simplify the models of ecosystems; however, such simplification can ignore significant variables, rendering the models inaccurate.
During the past three decades researchers have begun to construct new models based on dynamics observed in the ecosystem. Non-linear systems have been found to be useful in the modelling of ecosystem dynamics.

Ecosystem dynamic characteristics

  1. Episodic changes
  2. Patchy spatio-temporal attribute
  3. Multiple Equilibria

Episodic changes

Changes in ecosystems are episodic, with periods of slow accumulation punctuated by sudden releases and reorganisation as the result of internal or external natural disturbances or human-imposed catastrophes.

The Holling model

Is a cyclical model provided by C. S. Holling of the University of Florida that describes the dynamic and organisational changes of an ecosystem.
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  • Exploitation: a gradual increase in connectedness/stability and accumulation of nutrients and biomass.
  • Conservation: a few dominant energy-material flow pathway networks are established with more and more resources channelled to them. During this phase the system typically becomes simpler and biodiversity decreases.
  • Release: energy and material locked in the accumulated biomass is released leaving abundant resources.
  • Reorganisation: the transient appearance or explosion of organisms that begin to capture opportunity.

Is useful in describing non-ecosystem processes as well, like scientific development:

  • Conservative science → conservation
  • Scientific revolution → release
  • Pre-paradigm → reorganisation, exploitation

It cannot, however, explain some ecosystem environments.

  • Aquatic systems: these are organised by external physical variability of turbulence and a number of other oceanic features. Such systems do not have gradual growth & accumulation processes.
  • Semiarid savannah: these are constrained by water. After a down-pour there is a pulse of growth; when it dries up most species return to a dormant-state. They don't enter the exploitation / conservation phases.
  • Large organisations: these deliberately break up to reduce susceptibility to dangers afforded to large organisations.

Patchy spatio-temporal attribute

Ecosystems at different locations are governed by different dynamic process and have different organisational properties.
Tropical ecology:

  • Constant high energy throughput (high temperature w/ narrow fluctuation, high biomass production)
  • Large number of species
  • Species are highly specialised
  • The species have a narrow niche width (ie: each species can only survive under certain conditions)

These are vulnerable to external disturbance which can then lead to internal catastrophic consequences (ie: eradication of one species may have a trickle-on affect)

Polar ecology:

  • Highly volatile low energy throughput (low temperature w/ wide fluctuation, uncertain food/water supply)
  • Low number of species
  • Species tend to be generalists
  • Species will have a wide niche width

These are vulnerable to internal disturbance. Each species will play a critical role in the system dynamics so extinction of any species is likely to have a massive impact on the system.

Multiple-equilibria

An ecosystem often has more than one stable state where it could return to after an internal or external perturbation.

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