Quantifying Sustainability

There has been a recent breakthrough in Complexity Theory, as Sustainability has become measurable with a single metric as an optimal balance between "efficiency" and "resilience".

• Sustainability is the capacity to survive, to thrive and flourish in different environments and different contexts.
• Effiency - in case of natural ecosystems - is the capacity to process quantity of biomass (in other words: throughput).
• Resilience is the capacity to adapt to changes in the environment.

The interplay between presence and absence plays a crucial role in whether a system survives or disappears. It is the very absence of order (in form of a diversity of processes) that makes it possible for a system to persist (sustain itself) over the long run.

The capacity for a system to undergo evolutionary change or self-organisation consists of two aspects: It must be capable of exercising sufficient directed power to maintain its integrity over time. Simultaneously, it must possess a reserve of flexible actions that can be used to meet the requirements of novel disturbances.

The "Capacity for System Development/Evolution" (C) - also "aggregate system indeterminacy" - can be decomposed into two different components: ( C = A + R )

• The "System Ascendency (=Überlegenheit)" (A) - also "scaled average mutual constraint" - quantifies all that is regular, orderly, coherent and efficient. It encompasses all the concerns of conventional science.
• The "System Reserve" (R) - also "scaled conditional entropy" - represents the lack of those same attributes, or the irregular, disorderly, incoherent and inefficient behaviours. It quantifies and brings into scientic narrative a host of behaviours that had remained external to scientific discourse so far.

The key point is: If we want to address the issues of persistence and sustainability,  the system reserve (R) becomes the indispensible focus of the discussion, because it represents the "reserve" that allows the system to persist.

Systems with either vanishingly small ascendency or insignificant reserves are destined to perish before long. A system lacking ascendency has neither the extend of activity nor the internal organisation needed to survive. By contrast, systems that are so tightly constraint and honed into a particular environment are prone to collapse in the face of even minor novel disturbances. Systems that endure - meaning which are sustainable - lie somewhere between these extremes.

Sustainable Ecosystems all seem to exisist within a "window of vitality", which is created by four boundaries:

• An  upper and lower boundary of the "effective number of transfers a typical quantum of medium makes before it leaves the system" (or "diversity") as a transformed indicator of System Ascendency - and -
• An upper and lower boundary of the "effective connectivity" (or "interconnectivity") as a transformed indicator of System Reserve

Examples of high and low diversity and interconnectivity in an natural ecosystem are:

• Low Diversity: Monoculture Forests
• High Diversity: Rain Forests
• Low Interconnectivity: Pandas (eating only one specific type of bamboo)
• High Interconnectivity: Squirrel (eating almost everything it gets)

It has yet to be investigated whether any sub-regions of the window of vitality might be preferred over others. It can be assumed that systems plotting too close to any of the four boundaries could be approaching their limits of stability for one reason or another. Under such consideration, the most conservative assumption would be that those systems most distant from the boundaries are those most likely to remain sustainable.

Available data on existing flow networks of natural ecosystems (e.g. Amazon, Serengeti Plain) allowed an empirical calculation of this optimum (highest likelyhood for the system to remain sustainable) at a=0,4596. This means that the system is most sustainable when System Ascendency ("Efficiency") represents 45,96% and System Reserve ("Resilience") accounts for the remaining 54,04% of the total Systems Capacity for Evolution ("Sustainability").

Systems can risk unsustainability in relation to this "optimum" on two accounts:

• When a<0,4596 the system likely requires more coherence and efficiency. There may be insufficient or under-developed autocatalytic pathways that could give additional robustness to the system.
• When a>0,4596 the system might be over-developed or too tightly constrained. Some autocatalytic pathways may have taken up too many resources into their orbit, leaving the system with insufficient reserves to persist when new emergencies arise.

Reserve Capacities are necessary to sustain ecosystems. We need to be careful with maximizing efficiencies, as systems can become too efficient for their own good.

In particular the human population and its accompanying agro-ecology is rapitly displacing reserves of wild biosphere, driving the global ecosystem far beyond the optimum balance for sustainability. We need to conserve the diversity of biological processes if we want to sustain the biosphere, which is the system we as humans are living in and hence entirely depending on.

Also in economics we seem all too willing to sacrifice everything for an improved market efficiency. Establishing complementary currencies would be a systemic solution to increase the diversity and recreate a better balance toward a more sustainable economic system.

The dynamics described above are likely to also be applicable to other flow systems such as the stability of genetic control networks and the immune system.

(For further details see Robert E. Ulanowicz, University of Maryland Center for Environmental Sciences, Quantifying Sustainability)