Systems and Stability

Garry Peterson
The discussion of stability of resource systems last week revealed the problems of system and stability definition that occur when discussing the 'systems' properties of nature. There are no easy answers on what definitions are 'correct' even when addressing a specific issue, however misunderstandings over definitions can impair understanding what is actually occurring in a system.

What is a System?

The major problem when using the language of systems to talk about some real entity is defining what actually is the system. The definition process is a purely subjective one. Defining a system requires a definition of its boundary and its components. These two decisions serve to define three scales of analysis - the context of the system, the system itself, and its components. A good system definition define useful boundaries and a minimal useful number of system components. A useful system boundary is usually one at which many different types of system properties of interest change simultaneously, or a boundary that has more of the relevant interactions within it than outside it. An example of such robust boundaries, are the skin of a person or the edge of lake. However, these boundaries are not always appropriate if a key question one is trying to understand is nutrient dynamics of disease spread other system boundaries are likely more appropriate. This difficulty of bounding a system can be seen in a discussion of the Everglades. Does the Everglades include the Everglades Agricultural Area, Miami, or Big Cypress.

Static and Dynamic Systems

The previously mentioned definitions of systems are static, however ecological systems are dynamic. Not only do the relationships between components of the system change, for example nutrient levels and algal populations, but also the components of the system can change, birds can migrate or species can invade. When the components of a system change is it still the same system? This is a definitional choice that determines whether one can consider a system to have multiple stable states or not. For example as the Everglades is invaded by exotics will they produce a new stable state of the Everglades or an entirely novel neo-Everglades. One can examine changes in the system from either viewpoint, one just has to chose which is most useful. If the Everglades with exotics is considered along with the Everglades without exotics, then exotics can be thought of as a perturbation. If exotics remain once introduced they are stable state, if they eventually are replaced by native vegetation then the Everglades is only in a temporary state. If exotics can be eliminated and the system returned to its previous state, then the Everglades has multiple stable states.

Forcing Functions

Any system exists within a broader system, that influences and constrains its behaviour. For example the Everglades is influenced by regional climate variation, and the decisions of migrating wading birds. If these 'forcing function' change, for example climate becomes wetter or birds move somewhere else and the system changes, is it useful to say the system is in another stable state? It can be but one has to be clear about what they mean. Change can be due to either endogenous or exogenous causes. For example if we consider a system to be an area of savanna composed of trees amid grassland. That system could change from endogenous process of tree spread or tree elimination, or it could change from an exogenous processes such as tree cutting, climate change, or fire introduction. The definition of a change as exogenous or endogenous depends upon your definition of the system, particularly upon how you conceptualize its cross scale relationships. A system that has multiple stability points is one that endogenously maintains a stable state, but exogenous disturbance can switch it to another endogenously maintained stable state. Therefore, whether a system is considered to exhibit multi-stable states depends upon how endogenous and exogenous events, and processes are classified.

What is Stability?

Now I've already been discussing stability, but people use the term differently to describe different viewpoints of the system. There are three common approaches to defining the stability of a system. 1) System Dynamics A system is stable is it remains in the same state, and returns to that state after perturbations. This is stability from the point of view of the system. From this point of view the spruce budworm system has only one stable state (a cycle) and that is the spruce budworm cycle. 2) Component Dynamics. A system is stable if it is in a self-maintaining state, from the point of view of one of its components. From the point of view of the budworm, outbreak and non-outbreak stages are multiple stable states, triggered by external processes such as weather fluctuations and changes in forest canopy volume. The shift to an outbreak state or the outbreaks decline are times of system instability. 3) Anthropogenic. This point of view ignores the systems intrinsic dynamics and defines stability from a human system point of view, that is from outside the system. Usually stability requires that the system be constant or predictable over a specific human time frame. From this point of view the budworm system has been at times stable and at other times unstable .
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Copyright Last modified: Feb 21 1996