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During the last twenty years our understanding of the development of complex systems has changed significantly. Two major advancements are catastrophe theory and non-equilibrium thermodynamics with its associated theory of self-organization. These theories indicate that complex system development is non-linear, discontinuous (catastrophes), not predictable (bifurcations), and multi-valued (multiple developmental pathways). Ecosystem development should be expected to exhibit these characteristics.
Traditional ecological theory has attempted to describe ecosystem stress response using some simple notions such as stability and resiliency. In fact, stress-response must be characterized by a richer set of concepts. The ability of the system to maintain its current operating point in the face of the stress, must be ascertained. If the system changes operating points, there are several questions to be considered: Is the change along the original developmental pathway or a new one? Is the change organizing or disorganizing? Will the system return to its original state? Will the system flip to some new state in a catastrophic way? Is the change acceptable to humans?
The integrity of an ecosystem does not reflect a single characteristic of an ecosystem. The concept of integrity must be seen as multi-dimensional and encompassing a rich set of ecosystem behaviours. A framework of concepts for discussing integrity is presented in this paper.
Integrity of an system refers to our sense of it as a whole. If a system is able to maintain its organization in the face of changing environmental conditions then it is said to have integrity. If a system is unable to maintain its organization than it has lost its integrity. (Change in Organization refers to changes in the function of a system and its internal connections (structure) so as to better carry out some organizational imperative. Environment refers to the biotic and abiotic components external to an ecosystem which impact upon it, including humans.)
The discussion in the literature of the notion of stability has led to quite a number of conceptual terms and definitions. (Resiliency, elasticity, vulnerability, catastrophe, etc. See the Appendix, part II for a brief review). All of these ideas describe some aspect of an ecosystem's ability to cope with environmental change. Integrity should be seen as an umbrella concept which integrates these many different characteristics of an ecosystem which, when taken together, describe an ecosystem's ability to maintain its organization. What is presented below is a description of ecosystem development and organization which will serve as a framework connecting these concepts together.
The development of such self-organizing systems is characterized by phases of rapid organization to a steady-state level followed by a period during which the system maintains itself at the new steady state. The organization of the system is not a smooth process but rather proceeds in spurts. These spurts are a sudden acceleration in the change in the state of the system. The state change may be continuous or catastrophic. (The Appendix, part 1 discusses a set of system notions such as state, stability, catastrophe, equilibrium.) The change in the state is accomplished by the addition of new dissipative structures to the system. These new structures can consist of new pathways for energy flow which connect old components or of new components and their associated new pathways. Each spurt results in the system moving further from equilibrium, dissipating more energy, and becoming more organized. Each spurt occurs when random environmental conditions exceed a catastrophe threshold for the system. The path through state space which the system follows as it develops in a stable environment is called the thermodynamic branch. Ecosystem succession is an example of this kind of process. Each of the seral stages corresponds to one steady-state plateau. The displacement of a previous seral stage by the next is an example of a spurt, the re-organization of the system to a new level of structure which dissipates more energy.
The gradient which drives ecosystem development is the solar energy impinging on the ecosystem. (Kay, 1984, 1989) As ecosystems are driven away from equilibrium they become more organized and effective at dissipating solar energy. At the same time as this self-organizing process is occurring in ecosystems, external environmental fluctuations are tending to disorganize the system. The point in state space where the disorganizing forces of external environmental change and the organizing thermodynamic forces are balanced is referred to as the optimum operating point. (See Figure 1)
Development is characterized by phases of rapid organization to a
steady-state level followed by a period during which the system maintains
itself at the new steady state. The organization of the system is not a smooth process but rather proceeds in spurts. These spurts are a sudden acceleration in the change in the state of the system. The overall direction of development is one which satisfies the necessities of increasing energy degradation while enhancing survivability. An ecosystem develops along a Thermodynamic Branch (a path in state space) until it reaches an Optimum Operating Point. This is a point in state space where the self-organizing forces are balanced by the disorganizing forces of external environmental change. (This is a simplification of the more complex process described by Holling's figure
eight.)
In the context of these ideas, our sense of the system as a whole, that is its integrity, has to do with its ability to maintain its organization and to continue its process of self-organization. In essence integrity has to do with the ability of the system to attain and maintain its optimum operating point. There is an important implicit aspect of the definition of integrity which the reader must be aware of. Ecosystems are not static. Their organization is often changing, both in the short term and in an evolutionary sense. Furthermore any loss of organization is often gradual. Thus it is not possible to identify a single organizational state of the system which corresponds to integrity. Instead there would be a range of organizational states for which the ecosystem is considered to have integrity. For the sake of discussion in what follows, the optimum operating point is treated as a single stationary point in state space. In reality it is a set of points in state space whose membership changes over time. The definition of this set would necessarily have a human component.
Also the reader should be aware that the theory of dissipative structures suggests that a number of different organizational and developmental pathways are available to ecosystems. These pathways are non-linear and may be discontinuous and multi-valued. Thus the (set of) optimum operating point or set point for the system is not unique. There will be several different possible (sets of) optimum operating point states for the system. As Holling (1986) has shown, the normal course of ecosystem development can consist of flips in state, that is catastrophic changes. Detailed discussion of these notions can be found in Appendix 1.
Will the system be moved away from its optimum operating point?
If the response is no, then organization and integrity are not immediately affected.
If the response is yes, then the question becomes:
Does the system return to its original optimum operating point?
If the answer is yes, then there are three issues:
1) How far is the system moved from its optimum operating point before returning?
2) How long will it take to return to its optimum operating point?
3) What is the stability of the system upon its return?
In any case the system is able to re-organize itself to cope with the environmental change and its integrity for the moment is preserved.
If the answer is no, the system does not return to its original optimum operating point, then there are two possibilities; a new optimum operating point exists or it does not. In the latter case the organization breaks down and the system loses its integrity. (Case 0) In the former case there are three possibilities:
Case 1: The new optimum operating point is on the original thermodynamic branch.
Case 2: The new optimum operating point is on a bifurcation from the original branch.
Case 3: The new optimum operating point is on a different thermodynamic branch and the system undergoes a catastrophic re-organization to reach it.
a) The ecosystem does not move from its original optimum operating point:
For example, consider exposure of a terrestrial ecosystem to a temporary flood or drought to which the system is adapted. If the disturbance is not particularly intense the system will not be affected. Another example is the ongoing spraying of fenitrothion on Canadian forests to control spruce budworm. This appears to have no immediate effect on the forests but it does interfere with the ability of the forest to regenerate itself. (Weinberger and others, 1981) Thus the ability of the system to deal with some future stress which requires regeneration may be impaired. Consequently this human activity may be unacceptable as it could ultimately impact the ecosystem's integrity.
b) The ecosystem moves from its original optimum operating point but returns to it:
Fire in a temperate forested ecosystem is a short term event that moves the system well away from its optimum operating point. However the forest regenerates back to the original system. Oil spills along the shores of Great Britain have had similar effect with a regeneration time of about 10 years (Nelson-Smith, 1975). Rutledge (1974) showed that a shortgrass prairie ecosystem subjected to continuous ongoing drought will reorganize itself so that, after about 20 years, it will return to its pre-drought state.
c) The system moves permanently from its original optimum operating point:
Case 0: The system collapses.
The environment changes in such a way as to be uninhabitable. An example is the process of desertification. Another is severe prolonged drought in mangrove systems which leads to the total collapse of the system (Lugo and others, 1981). A third example is the result of substances deposited by precipitation which, in the extreme case of the Sudbury area in Canada, has led to the rocky equivalent of a desert, and in the Laurentian Shield has led to "dead" lakes. In each of these cases some life forms may continue to persist, but a complex ecosystem does not.
Case 1: System remains on original thermodynamic branch. (See Figure 2)
The ecosystem maintains it original set of dissipative structures (e.g. species), or moves back to some set which represent an earlier stage in development. The level of operation of the individual structures has changed, perhaps even catastrophically. Overall the dissipative system is recognizable as the original, but its operation has been modified.
In this case, there are four issues:
1) How far is the new optimum operating point from the old?
2) How long does it take to reach the new optimum operating point?
3) What is the stability of the system about the new optimum operating point?
4) If the environmental conditions return to their original state, will the system return to the original optimum operating point?
While the system's organization has changed in this case, it will probably return to the original optimum operating point if the environmental conditions return to their previous state. This is because all the original structures (e.g. species) exist to some extent. The system's integrity has been affected in the sense that its organization has had to change. This is only noteworthy if the new optimum operating point (level of operation) is considered undesirable.
As an example consider the practice of spraying the end product of the secondary treatment of municipal waste water on terrestrial ecosystems. Pine forests subjected to such spraying are shifted back to an old field community (i.e the developmental stage prior to a forest) (Shure and Hunt, 1981). The ecosystem is still on the original thermodynamic branch, but at an earlier stage of development. As another example consider Maple forests subjected to acid rain. They are shifted to a state of less productivity and lower biomass. (Unfortunately the level of acidity in the rain is increasing with attendant further changes in the ecosystems. The question is whether the response of the maple forests will remain as in Case 1 or become one of the other cases discussed here. The latter case would imply the loss of some of the characteristics of these forests which we value.) A final example is that of a cold snap in 1962-63 during which the shoreline systems in Southern England where driven back to an earlier stage of development. Recovery to the original state seems unlikely. (Nelson-Smith, 1975)
Case 2: System bifurcation to a new thermodynamic path (See Figure 3)
In this case some new dissipative structures are added to the system and/or some of the original ones disappear. The new structures can be new pathways for energy flow connecting old components or the emergence of new components and their attendant pathways. Also the level of operation of the system is changed. The system is seen as slightly different than the original.
The same four questions apply here as apply to Case 1. (See Table 1.) However the answer to the fourth question is probably different. The system is not likely to return to its original optimum operating point, unless the bifurcation point is the original optimum operating point. (It should be noted that it is theoretically possible by manipulating the environmental conditions to return to the original optimum operating point.) If it is not, then the organization of the system has probably been permanently altered by the addition of new dissipative structures. However bifurcations represent variations on the original theme. Thus the new ecosystem's organization will not be extraordinarily different from the original. The integrity of the system has been affected in the sense that the organization has been permanently altered, although not dramatically. Again, this is only noteworthy if the bifurcation branch and the new optimum operating point are considered undesirable.
An example of this case is the change in a marsh gut ecosystem, Crystal River Florida. (See Kay, 1984, Ulanowicz, 1986) The system is stressed by warm water effluent from a nuclear power station (6 degree C increase in water temperature). The result is the loss of two top predators, two lower predators, the addition of a three lower predators and a herbivore species, and a dramatic change in the foodweb in terms of cycling and trophic positions. These are examples of changes in the dissipative structures in an ecosystem. Odum's state variables (such as net productivity) decrease, thus the overall functioning of the system has changed. However, overall the ecosystem is clearly a variation on the original. It is not clear that a cessation of the effluent would result in a return to the original system. Similar results have been found for Par Pond on the Savannah River in South Carolina (Sharitz and Gibbons, 1981).
Another example of this case is the switch from a white spruce community to a black spruce community when the former is subjected to a sharp reduction in nutrient availability. In these forested taiga ecosystems, black spruce are better suited to low nutrient situations and once established tend to exclude white spruce by maintaining the low nutrient situation. The white spruce is not able to reassert itself once displaced. (DeAngelis and others, 1989)
A final example is the introduction of exotics into the Great Lakes. New species associations (dissipative structures) occur. (The sea lamprey is a case in point.) It appears that the system has been permanently altered, but it still resembles the original.
Case 3: The system moves to a new thermodynamic branch. (See Figure 4)
In this case, the system undergoes a catastrophic change which leaves the system so re-organized that it is clearly recognized as being different from the original system. There is no possibility of the system returning to its original optimum operating point, even if the environmental conditions return to their original state. (This is an hypothesis. In this case the system is made up of very different dissipative structures than existed in the original. The author has been unable to find a single example of an ecosystem flipping back after undergoing such a dramatic re-organization.) In one sense the integrity of the system has been seriously undermined, as the system will be quite different from the original. However the fact remains that an ecosystem still exists, so in some sense, it has been able to maintain its integrity.
Clearwater Lake is an excellent example of this phenomena (Stokes (1984), pp 246-249 in particular). This lake is subjected to acid rain and has a pH of 4.3. Consequently there are no fish in the lake. The phytoplankton zooplankton balance has been shifted significantly. "The system has flipped from one domain of stability to another." The ecosystem has reached a new optimum operating point on a new thermodynamic branch and further change is unlikely. Even if the acid rain stopped the ecosystem would be unlikely to return to its former state without human intervention.
Another example of this case is the clear cutting of a terrestrial system such that soil erosion is so severe as to effectively change the soil type and preclude the original system from reappearing. (The loss of tropical rainforest is a case in point.) Another example is of a burn in a spruce hardwood forest which is on thin soils. This has resulted in a new bare rock-shrub ecosystem appearing as the climax (Bormann and Likens, 1979). A final example is the irreversible change of savanna ecosystems to woody vegetation brought on by cattle grazing (Walker and others, 1981).
The above discussion systematically lists the issues which need to be examined when considering the possible direct responses of an ecosystem to environmental change, and the implications of these responses for ecosystem integrity. This framework encompasses all of the stability related concepts discussed in the appendix and identifies other issues which need to be examined.
The environmental change causes the ecosystem to move from its original optimum operating point (1) to a new optimum operating point (2). An example of this would be a stress which causes an ecosystem to return to an earlier successional stage. The practice of spraying the end product of the secondary treatment of municipal waste water on terrestrial ecosystems is such a stress. Pine forests subjected to such spraying are shifted back to an old field community (i.e. the developmental stage prior to a forest)
In response to changing environmental conditions the system moves away from the original optimum operating point (1) through a bifurcation point (2) and onto a new path and then to a new optimum operating point (3). An example of this case is the switch from a white spruce community to a black spruce community when the former is subjected to a sharp reduction in nutrient availability. In these forested taiga ecosystems, black spruce are better suited to low nutrient situations and once established tend to exclude white spruce by maintaining the low nutrient situation. The white spruce is not able to reassert itself once displaced.
The environmental change drives the ecosystem from its original optimum operating point (1) through a catastrophe threshold (2) to a new thermodynamic branch at (3) and eventually to a new optimum operating point (4). An example is the elimination of fish in lakes caused by acid rain. Another example of this is the switch between pelagic and benthic ecosystems in shallow lakes as discussed earlier.
Some researchers are uncomfortable with definitions which are not "objective", that is, reflect the viewpoint of an observer. Physicists, during this century, have come to realize that there are no preferred observers. Each observer brings a unique viewpoint of, and interaction with, that which he observes. As long as the reference frame of the observer and his interactions are clearly defined, there is no problem. The observations will be reproducible, assuming that they are accurate to begin with. In the study of complex systems, the exercise known as systems identification is equivalent to the exercise of defining the observer's frame of reference in physics. What is proposed here would be part of a systems identification exercise for studying the integrity of ecosystems. It would explicitly involve defining why the observer is examining integrity and what he would consider a loss of integrity in terms of changes in the optimum operating point.
While the above framework identifies a number of types of ecosystem organizational change in response to environmental change, it tells us nothing about which type of organizational change to expect for a given environmental change. Before such theoretical predictive power will be available, a much better understanding of ecosystems as self-organizing thermodynamic system is required. In this regard, second law/exergy analysis (analysis of the irreversibilities in the system as measured by entropy production and decreases in the quality of energy (exergy)) and network theory hold much promise (Kay, 1984, 1989). However, such approaches require time-series data at a level of detail which is available for only a few systems. In the interim, we will have to depend on empirical and intuitive understanding of ecosystems for the prediction of ecosystem response to environmental change.
A third point about this framework is that it only deals with immediate changes in an ecosystem caused by an environmental change. Some environmental changes will not immediately affect an ecosystem. Rather they affect the ability of the system to cope with other future environmental changes. An example is the Fenitrothion spray of forests to control spruce budworm. This has no immediate impact, but interferes with the ability of the forest to regenerate itself in the face of other environmental changes. Similarly, forest fire suppression now appears to interfere with the ability of the forest to cope with fires at later times. The impact of environmental change on the integrity of an ecosystem is not just immediate but has implications for its ability to maintain its integrity in the face of future environmental changes.
Even if we could monitor systems continuously, developments in self-organizing systems (dissipative systems) can proceed in spurts during which changes in the system suddenly accelerate very rapidly or even occur catastrophically, independent of environmental changes. The onset of such spurts may not be predictable and this is surprising, e.g., a pest outbreak, such as spruce budworm. Also, continuous environmental changes can drive ecosystems past catastrophe thresholds, e.g., an algae bloom in response to nutrient loading beyond a threshold could be a surprise. Finally a catastrophic event in the environment (such as a lightening strike) may be the source of surprising change in the ecosystem (a forest fire).
As this discussion illustrates we should expect the rate of change in ecosystems to accelerate or decrease very dramatically with little or no warning. Hence we should expect to be surprised. Better historical information about an ecosystem can help us to better design our monitoring techniques so as to reduce some surprises. However, the only way to deal with surprise is to have human systems which are adaptive and prepared to respond appropriately to surprises.
First, dissipative systems can respond to environmental change in qualitatively different ways. One response is for the system to continue to operate as before, even though its operations may be initially and temporally unsettled. A second response is for the system to operate at a different level using the same dissipative structures it originally had (for example, a reduction or increase in species numbers). A third response is for some new structures to emerge in the system to replace or augment existing structures (for example, new species or paths in the food web). A fourth response is for a new dissipative system, made up of quite different structures, to emerge. We must be aware of these different possible response to environmental change if we are to anticipate the stress-response of ecosystems.
The second point of note is that if the concept of integrity is to be useful, it must have an anthropocentric component which reflects which changes in the ecosystem are considered acceptable by the human observers. Otherwise we are restricted to defining integrity as the ability of an ecosystem to absorb environmental change without any ecosystem change. This would rule out the acceptability of the other three ecosystem responses to environmental change discussed above. This does not seem reasonable to this author.
The third point is that an environmental change has implications for the future ability of an ecosystem to respond to other later occurring environmental changes. Put another way, the response of an ecosystem to environmental change is a function of both the immediate environmental change and changes that the ecosystem has been subjected to in the past. Historical environmental change can have both positive and negative implications for the ability of the system to cope with current changes.
Finally it is to be noted that by their nature, dissipative structures exhibit surprising behaviour, behaviour which cannot be a priori predicted and which may be catastrophic. No matter how much knowledge we have, we will always be subject to surprise when we observe ecosystems. Therefore any human systems which are meant to deal with ecosystems (or any dissipative systems) must be adaptive in their response, that is able to cope with surprise.
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A state space is a space whose axes are the state variables. In a predator-prey system, the state variables would be the population numbers for each species and the two dimensional space with the number of predator on one axis and the number of prey on the other would be the state space. There would be a curve (a path in state space) which describes the relationships between the predator and the prey. (Figure A-1a & A-1b are examples.)
For a given set of forces acting on a system, there will be at least one point in state space where the forces are balanced. This is known as the equilibrium point. (For example, the equilibrium point for a population is the point where the mortality and birth rates balance.) The issue of importance is the stability of the equilibrium point. That is, is the system able to stay in equilibrium? Consider a cone that has a very narrow blunt top. If it is placed upside down on its top, then a small disturbance will cause it to fall over. On the other hand if it is placed with its top up and its broad base down only a very large disturbance will cause the cone to topple over. In the former case, the equilibrium is said to be unstable and in the latter it is stable. In a strict mathematical sense an equilibrium point is stable if after a disturbance the state of the system returns to the equilibrium point.
Another possibility is that the state of the system does not return to the equilibrium point after a disturbance but oscillates about it with a maximum amplitude. Consider a perfect pendulum. The equilibrium point is at the bottom of the swing. The system oscillates about this point with a maximum amplitude after it has been disturbed. In the case of real pendulum, it eventually comes to rest at the equilibrium point. Both the ideal and real pendulum are considered stable.
These two types of stability are mathematically defined by the Lyapunov stability criteria. (See Lewontin (1969) and Harte and Levy (1974) for a review of this theory as applied to ecology.) The key question is whether the state of the system will return to the equilibrium point or oscillate about it when the system is disturbed, or if the state of the system is permanently moved to another point in state space (the cone falls over). It was through a Lyapunov stability analysis of thermodynamic systems, with entropy production as the state variable, that Prigogine discovered the self-organizing phenomena for which he was awarded the Nobel prize.
The optimum operating point for an ecosystem is an equilibrium point in state space which represents a balance between the forces acting on the ecosystem. In the real world, the environment is not static. The forces acting on an ecosystem are constantly changing. Therefore, the equilibrium point is constantly changing. For the purpose of discussion in this paper, the optimum operating point has been treated as being stationary. In reality it is constantly changing and would be more realistically represented by a distribution in time. This distribution would reflect the distribution of environmental parameters.
Notwithstanding this variability, it is possible that the ecosystem has cyclic stability much like a pendulum. Holling (1986) has shown this to be the case for some pest outbreaks in forested ecosystem which happen with a fixed frequency. The forested ecosystem swings between maximum foliage just before an outbreak and minimum foliage just before the outbreak ceases. Another example is ecosystems driven by phytoplankton blooms.
A very important system's notion is that of a catastrophe. Catastrophe theory was brought to prominence by Rene Thom (1969) and an analytical basis for it was discovered by Huseyin (1977, 1980). The importance of catastrophe theory is that it shows how systems can exhibit behaviour which is discontinuous and occurs without warning. Usually the phenomena is very dramatic.
The herbivore-vegetation system follows the equilibrium path through its state space as indicated by the arrows. At point X the equilibrium path becomes unstable and the system drops from the upper solid curve to the lower solid curve. At point Y the system is again unstable and moves from the lower to the upper solid curve.
A similar situation for spruce budworm
There is an equilibrium path through state space. The solid curves represent the stable part of the path. The dotted curve represents the unstable part of the path. (The system can not stay on the unstable part, only on the stable part.) For points P1 and P3 there are single values of X possible. The value of X at P2 depends on which curve the system is currently following. The catastrophe is the system jumping from the upper to the lower curve, or vice versa. This occurs at the thresholds (X & Y in Figure A-1b above)
The set of equilibrium points for the system is a surface in state space. The path followed by the system may pass through a catastrophe threshold (from A to B above, the red dotted part of the curve corresponds to the jump) or it might not (from C to D). The system may hit a cusp (see above), which is a bifurcation point. (The system may follow either bifurcation line after the cusp, which one it follows is not predictable.) Two points in state space (A and C, figure below left) may be very close, but the system may diverge quite dramatically later on in its development (From A to B as versus C to D). Also there may be different paths that the system can follow from A to B (See figure below right) One path may involve a catastrophic system change (the dotted line) while another does not.
A more complicated form of catastrophe is shown in Figure A-2. This is the Riemann-Hugoniot catastrophe. This behaviour is more complicated than the fold because the system may move along an equilibrium path with a catastrophe threshold (A to B) or one without (C to D). It may also exhibit bifurcations or divergences or multiple paths. The Riemann-Hugoniot catastrophe is still quite simple, being of order 3. There are examples up to order 7. (Thom's swallow tail and butterfly being order 4 and 5 respectively) The point is that systems can exhibit very complicated and dramatic behaviour, even when they are deterministic. The lesson is, be prepared for surprise. To explore these notions is more detail see Holling (1986) or Jones (1975) for excellent discussions.
An observant reader will note that the notion of equilibrium used throughout this appendix is different than the one used in the main body. Equilibrium in a stability sense is different from equilibrium in a thermodynamic sense. The former refers to a balance of the forces acting on a system and has its origin in Classical Mechanics. Thermodynamic equilibrium refers to a system state which is uniform throughout and undistinguishable from its surroundings. For a biological system this represents death. Non-equilibrium thermodynamics is about the organization of systems such that they are not in thermodynamic equilibrium. Needless to say this difference causes great confusion. Non-equilibrium systems can be stable, that is the forces acting on them are in equilibrium!
Organization refers to changes in the function of a system and its internal connections (structure) so as to better carry out some organizational imperative. The end point in the process of organization represents an optimal tradeoff between the different objectives of the system. It is in this sense that the term optimum operating point is used. For more detailed discussion of the organizational imperatives of ecosystems and the tradeoffs involved see Kay (1984,1989).
Thermodynamic Branch is used to indicate the path through state space followed by an ecosystem as it develops from (thermodynamic) equilibrium to its optimum operating point (i.e steady state stable equilibrium point in state space which is far from thermodynamic equilibrium) under normal conditions. An example would be the path normally followed by an ecosystem as its develops from a bulldozed field (thermodynamic equilibrium) to a climax forested ecosystem (optimum operating point). This is not precisely the definition used for this term by Prigogine (see Nicolis and Prigogine, (1977) pp.57-58). He uses this term to refer to the initial path followed by a system from equilibrium to its first instability point. His usage is appropriate for simple physical systems, but is not useful for complex systems. What is of interest in this discussion of complex systems is their deviation from their normal development path as they move away from equilibrium.
When an ecosystem is described as being stable it usually means that it is, in some sense, well behaved. Many attempts have been made to formalize this definition using mathematics. The most natural approach is to use a definition of stability commonly used in the physical sciences, that is Lyapunov stability. This requires that some function be found which describes the system and which satisfies Lyapunov's stability criteria (see Lewontin (1969) and Harte and Levy (1975) for a review of stability theory as applied to ecology).
Many workers have attempted to use the stability of the species population to define ecological stability. Usher and Williamson (1976) state "Roughly speaking ecological stability is the strength of the tendency for a population or set of populations to come to an equilibrium point or to limit cycle, and also, related to that, the ability of a population system to counteract disturbances". Many articles and books have been written using this definition of ecological stability, (for the ultimate see Granero-Porati and others (1982)) but an equal number of papers and books have been written challenging this approach.
Hirata and Fukao (1977) and others have used the biomass of species as the important function which must be stable. This is a slightly more flexible approach because it allows for fluctuations in populations as long as the total biomass is stable. Others have talked about the stability of the functioning of a species, that is their niche remains stable. More recently, Bormann and Likens (1979) have discussed stability in terms of the functioning of the entire ecosystem, as measured by stream water input. Another suggestion is that the stability of the structure (i.e foodweb) of the ecosystem characterizes ecosystem stability. Presumably this would be measured using the measures developed by Rutledge (1976) and Ulanowicz (1979, 1980, 1986). Still others have suggested that the stability of the macro (i.e. external) or micro environment are the important characteristics. (This would be measured by such things as temperature fluctuations, rainfall fluctuation, humidity fluctuations, etc.) Unfortunately, no one of these system measures is sufficient to characterize ecological stability. Any one of them may not be stable, in a Lyapunov sense, while the system as a whole may be "well behaved".
In the last few years, the term ecological stability has been used to mean the stability of so many different characteristics of ecosystems, that one must be very careful to understand what an author means when he used the term ecological stability. Clearly such a situation is undesirable. Several authors have suggested that a broadening of the definition of stability is necessary if it is to be usable in an ecological context. What follows is a sampling of the ideas of a few authors.
Preston (1969) states "Stability lies in the ability to bounce back ... An ecological system may be said to be stable, from my point of view, during that period of time when no species becomes extinct (thereby creating a vacant "niche") and none reaches plague proportions, except momentarily, thereby destroying the niches of other species and causing them to become extinct". This is an interesting definition because it does not require that the populations be stable in the Lyapunov sense, only that they be non-zero.
Rutledge (1974) identifies three different properties of ecosystems, all of which should be encompassed under "ecological stability". The first is the sensitivity of the components of the ecosystem to perturbation. The larger the sensitivity, the less the stability. The second is the persistence of the ecosystem over time. The longer it has survived the more stable it is. The final property is the ability of the ecosystem to return to its equilibrium state after being perturbed from it.
May (1974) identified three tributaries to the stream of ecological stability theory. "One draws inspiration and analogies from thermodynamics, and is concerned with broad patterns of energy flow through food webs. A second theme, ... deals with the physical environment, and the way it limits species' distributions and affects community organization. A third tributary concentrates on the way biotic interactions between and within populations acts as forces moulding community structure".
Margalef (1975) is a little more pessimistic and suggests that "it is perhaps questionable whether the term stability should be retained, as it has been used too much in different and divergent speculation". Wu (1974) suggests that perhaps it is more relevant to talk about ecosystem health, where an ecosystem is considered healthy if its state variables are within a certain range.
My own opinion is that the idea of stability should be kept, but only in the narrow confines of the Lyapunov definition. In order to define what is meant by a "well behaved" ecosystem, other ecosystem properties, besides stability, must be defined and quantified. A number of authors have attempted to do just this. Many of them work with the idea of an N-dimensional state space. Usually each of the N axes correspond to the population of one of the N species. However other state variables can be used as well. There are a number of points in this hyperspace which are stable equilibrium of the ecosystem. About each of these stable points is a cloud. If the system is displaced from equilibrium, but remains within the cloud, it will return to the initial equilibrium points. If it is displaced outside of this cloud it will move to some new stable equilibrium state.
Holling (1973) introduced the idea of resilience. He defines resilience as the minimum distance from the equilibrium point to the edge of the cloud. Thus resilience is measured by the minimum disturbance necessary to disrupt the system and cause it to move to a new equilibrium state. Stability is the degree of oscillation, the system exhibits, about its stable equilibrium point. Holling points out that forests which undergo pest outbreaks, such as the spruce budworm, are unstable. They experience extreme oscillations in populations. Yet the system almost always bounces back to its original state. It is resilient. Holling notes that resilient systems normally aren't stable and vice versa. Hill (1975) expands on Holling's idea and observes that there are two kinds of stability involved. One is "no-oscillation" stability and refers to the stability of the state variables in the absence of stress. The other, he calls stability-resilience. This refers to the stability of the state variables while the system is under stress and after the stress is removed. This latter stability refers to the degree of oscillation (flutter) the system experiences while under stress and how quickly this is dampened out when the stress is removed.
Cairns and Dickson (1977) have examined the stability-resilience of stream ecosystems. They have identified four properties of ecosystems which determine the stress recovery characteristics of ecosystems: ecosystem vulnerability, elasticity, inertia and resiliency.
VULNERABILITY is defined as the lack of ability to resist irreversible damage (which is defined as damage which requires a recovery time greater than a human life span). Presumably it is measured by the size of disturbance necessary to cause irreversible damage.
ELASTICITY is defined as the ability to recover after displacement of structure and/or function to a steady state closely approximating the original. Presumably this is measured by the rate of recovery after disturbance.
INERTIA is the ability of an ecosystem to resist displacement or disequilibrium in regards to either structure or function. Presumably it is measured by the size of the disturbance needed to displace the system.
RESILIENCY is the number of times a system can undergo the same disturbance and still snap back.
Cairns and Dickson are not clear about how to measure these properties or in the difference between them. But, they do point out that the size of the disturbance necessary to displace the system, how far the system can be displaced before it will not bounce back, how long it takes to bounce back from the disturbance, and how many disturbances the system can tolerate are all properties which influence the reactions of an ecosystem to stress and need to be understood in detail.
Orians (1975) has identified seven properties of ecosystems which are related to their stability:
CONSTANCY: the lack of change in some parameter of the system.
PERSISTENCE: the survival time of the system.
INERTIA: the ability to resist external perturbations.
ELASTICITY: the rate at which the system returns to its former state following a perturbation.
AMPLITUDE: the area over which the system is stable (the same as Holling's resilience).
CYCLICAL STABILITY: the property of a system to cycle about some central point or zone.
TRAJECTORY STABILITY: the property of a system to move towards some final end point or zone despite differences in the starting points.
The factors which increase each of these properties are listed in Table A-1.
Orians believes that an understanding of these properties can only be obtained from an understanding of the interactions of species and an appreciation of the past disturbances and selection pressures which have acted on the species. We must examine stability from this perspective using a precise definition of the property of an ecosystem we are trying to understand, and in the context of a specific type of disturbance.
Robinson and Valentine (1979) review the idea of stability and introduce their version of the concepts of Elasticity, Invulnerability and Invadability. Van Voris, O'Neill, Emanuel and Shugart (1980) introduce the notion of functional stability.
More recently DeAngelis and others (1989), in the context of nutrient dynamics and foodweb stability, identify five types of stability. These are:
LOCAL STABILITY: the tendency of all system components to return to their steady-state equilibrium values following small perturbations.
STABILITY TO LARGE PERTURBATIONS: This deals with the possibility that the system flips to a new steady-state equilibrium point when subjected to large perturbations.
RESILIENCE: The rate of return of the system to its steady-state equilibrium point after a disturbance.
STRUCTURAL STABILITY: Can small gradual changes result in a catastrophe?
PERSISTENCE: The tendency for the components of a system to stay within specific positive bounds through time.
Their paper ends by noting: "In fact, even the existence of steady-state equilibria in natural ecosystems, on which four of the five types of stability considered here depend, is open to some question. Nevertheless, it is doubtful that ecologists will abandon stability as a concept in the near future, so critical assessments will continue to be of value."
Holling and his colleagues have introduced the use of catastrophe theory in ecological systems (Ludwig and others, 1978, Jones, 1975, May, 1977, Holling 1986). The last of these references is an excellent, readable overview of Holling's ideas about dynamic stability and surprise. It is left to the reader to pursue.
Clearly, before any real understanding of ecosystem response to environmental change can be obtained, the confusion about concepts which fall under the umbrella of "stability" or "well-being" must be dealt with. Hopefully the discussion of the concept of Integrity in this paper will aid in the resolution of this confusion.
Table A-1: Environmental factors and phenotypic characteristics of species that increase different kinds of stability. After Orians (1975)
A. Persistence
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