Stable Equilibrium & Feedback Mechanisms (DP IB Environmental Systems & Societies (ESS))

Stable Equilibrium

• An equilibrium refers to a state of balance occurring between the separate components of a system

• Open systems (such as ecosystems) usually exist in a stable equilibrium

  • This means they generally stay in the same state over time

  • A stable equilibrium allows a system to return to its original state following a disturbance

  • This state of balance is maintained by stabilising negative feedback loops

Stable equilibria

• The main type of stable equilibrium is known as steady-state equilibrium

  • A steady-state equilibrium occurs when the system shows no major changes over a longer time period, even though there are often small, oscillating changes occurring within the system over shorter time periods

  • These slight fluctuations usually occur within closely defined limits and the system always returns to its average state

  • Most open systems in nature are in steady-state equilibrium

    • For example, a forest has constant inputs and outputs of energy and matter, which change over time

    • As a result, there are short-term changes in the population dynamics of communities of organisms living within the forest, with different species increasing and decreasing in abundance

    • Overall, however, the forest remains stable in the long-term

• Another type of stable equilibrium is static equilibrium

  • There are no inputs or outputs (of energy or matter) to the system and therefore the system shows no change over time

  • No natural systems are in static equilibrium—all natural systems (e.g. ecosystems) have inputs and outputs of energy and matter

  • Inanimate objects such as a chair or a desk could be said to be in static equilibrium

Stable vs unstable equilibria

• A system can also be in an unstable equilibrium

  • Even a small disturbance to a system in unstable equilibrium can cause the system to suddenly shift to a new system state or average state (i.e. a new equilibrium is reached)

Negative & Positive Feedback

• Most systems involve feedback loops

• These feedback mechanisms are what cause systems to react in response to disturbances

• Feedback loops allow systems to self-regulate

• There are two types of feedback loops:

  • Negative feedback

  • Positive feedback

Negative feedback 

• Negative feedback is any mechanism in a system that counteracts a change away from equilibrium

• Negative feedback loops occur when the output of a process within a system inhibits or reverses that same process in a way that brings the system back to its average state

• In this way, negative feedback is stabilising—it counteracts deviation from equilibrium

• Negative feedback loops stabilise systems

The Daisyworld model

• James Lovelock and Andrew Watson created the Daisyworld model as a computer simulation in the 1980s

  • The model was based on a theoretical planet with only two types of organisms: black daisies and white daisies

  • These daisies interacted with the environment by affecting the planet's albedo (the amount of solar radiation it can reflect away)

• Global temperature regulation due to life:

  • In the Daisyworld simulation, as the amount of sunlight (solar luminosity) is increased, black daisies thrive more due to their ability to absorb more sunlight

  • This causes the planet's albedo to decrease, trapping more heat and leading to an increase in global temperatures

  • This makes the planet more habitable for white daisies

  • The growth of white daisies causes the planet's albedo to increase, leading to a decrease in global temperatures

  • As both daisy populations compete, they eventually reach a stable equilibrium

  • This steady-state equilibrium stabilises Daisyworld's surface temperature, ensuring both populations can survive in the long-term

  • This cycle of temperature regulation serves as an example of an important negative feedback loop, in which processes that work to stabilise the system in one direction counteract changes in the opposite direction

• Contrast with a dead planet:

  • In contrast, on a dead planet without daisies, there are no negative feedback mechanisms for regulating temperature

  • Without organisms to adjust albedo and therefore trigger temperature changes, the dead planet's climate becomes more extreme over time, either excessively hot or cold, depending on the initial conditions, resulting in a planet that cannot sustain life

Positive feedback

• Positive feedback is any mechanism in a system that leads to additional and increased change away from equilibrium

  • Positive feedback loops occur when the output of a process within a system feeds back into the system in a way that moves the system increasingly away from its average state

  • In this way, positive feedback is destabilising—it amplifies deviation from equilibrium and drives systems towards a tipping point where the state of the system suddenly shifts to a new equilibrium

  • Positive feedback loops destabilise systems

Other examples of positive feedback

• Positive feedback loops amplify changes within a system

  • They can lead to either an increase or a decrease in a system component.

• Example: population decline

  • Population decline reduces reproductive potential

  • Reduced reproductive potential further decreases the population

  • This amplifying loop accelerates the decline

• Example: population growth

  • Population growth increases reproductive potential

  • Increased reproductive potential triggers further population growth

  • This positive feedback loop accelerates population expansion