SCOPE 35 - Scales and Global Change

ABSTRACT

Ecological systems are organized across a range of space and time scales. This scaling must be explicitly considered in any attempt to link ecological and atmospheric models. This chapter outlines the elements of Hierarchy Theory which are particularly relevant to this scaling problem. Results are presented as a set of nine criteria. These criteria must be considered before processes, operating on independent scales, can be accurately interfaced to make predictions at the global scale. Hierarchy Theory is proposed as a critical element in developing an understanding of global change.

INTRODUCTION

Environmental systems are complex and multiscaled. Ecologists deal with systems that range from a single organism and its environment all the way up to the biosphere. It is not surprising, therefore, to find that ecologists are beginning to look closely at hierarchy theory to help them deal with this range of systems. 

Hierarchy theory was developed by General Systems theorists, notably Koestler (1967, 1969) and Simon (1962, 1969), to deal with complex, multi- scaled systems. Overton (1972, 1974) must be given major credit for introducing ecologists to the theory. The potential utility of the theory has also been pointed out by MacMahon et al., (1978, 1981) and Webster (1979).

Recently, two books have been produced (Allen and Starr, 1982, O'Neill et al., 1986) that provide extensive analysis of the theory and its application to ecological systems. As a result, there is little need to develop a detailed tutorial for purposes of this workshop. Instead, I will focus on applying the theory directly to the problem of global change.

It has long been apparent to ecologists (e.g. Egler, 1942, and Schultz, 1967) that ecological systems are hierarchically structured. As a result, ecologists generally have a positive reaction to hierarchy theory. But while the theory is intuitively appealing as a way of looking at the natural world, ecologists have been frustrated by the lack of application of the concepts. Theoreticians, familiar with the concepts and terminology, seem able to develop the theory but progress has been slow in directing applications to research.

In this paper, therefore, I will avoid expanding the already extensive literature on the basic concepts. Instead I will consider the question at issue: understanding, measuring, and predicting global change. More precisely, I will derive a set of criteria that we can use to address workshop objectives.

Because of my background, I will rely on ecology for examples and illustrations. As I present the criteria, the basic concepts of the theory will emerge and it will become clear that the principles are general and not limited to ecological systems.

FUNDAMENTALS OF THE THEORY

To apply the theory we only need grasp some simple, underlying concepts. The theory asserts that a useful way in which to deal with complex, multi scaled systems is to focus on a single phenomenon and a single time-space scale. By so limiting the problem, it is possible to define it clearly and choose the proper 'system' to emphasize.

The system of interest (Figure 3.1, Level 0) will itself be a component of some higher level (Level + 1). Dynamics of the upper level usually appear as constants or driving variables in a model of Level 0. The behaviour of Level 0 appears to be constrained, bounded, and controlled by the higher level.

The higher level also gives the significance of the phenomena of interest. Let us consider, for example, that the object of study is an individual organism. In studying the organism, we discover reproductive structures and behaviours that are difficult to explain if our attention remains limited to the single organism. It is only by reference to a higher level, the population, that the significance of reproduction can be explained.

The next step in studying the system is to divide Level 0 into components forming the next lower level (Level -1). The Level -1 components are then studied to explain the mechanisms operating at Level 0. A mechanistic explanation ordinarily means that a phenomenon is the logical consequence of the behaviours and interactions of the lower level entities. Another characteristic of the lower level entities is that they appear as state variables in a model of Level 0.

Figure 3.1 Relationships between levels in a hierarchical system. The level of interest is in the centre of the diagram (Level 0). The dynamics of Level 0 will be constrained, bounded, and controlled by the higher level (Level +1). The higher level also gives the significance of phenomena at Level 0. Level 0 can be divided into components (Level -1). interactions among the components provide mechanistic explanations for phenomena at Level 0. 

Thus, hierarchy theory dissects a phenomenon out of its complex spatiotem-poral context. Our understanding of the phenomenon depends on referencing the next higher and lower scales of resolution. Levels higher than + 1 are too large and slow to be seen at the  level and can typically be ignored. Levels lower than -1 are too small and fast to appear as anything but background noise in observations of Level 0. In this way, the theory focuses attention on a particular subset of behaviour and permits systematic scientific study of very complex systems.

 Starting from this introduction, and without drawing out the mathematical and theoretical details, let. us see what this theory has to say about studying global change. I will develop the material as a set of criteria that must be satisfied before geophysical and ecological models can be linked.

HIERARCHICAL CRITERIA

The first three criteria deal with scale-dependent biases. These biases are common in applications of hierarchy but they are based on a naive concept of hierarchy that does not stand up to careful analysis.

(1) Searching for the fundamental hierarchy

It is seldom fruitful to go in search of the one and only hierarchy that characterizes the natural world. There is no single, a priori criterion for developing a hierarchy. Instead, a number of different hierarchies may be used to address different problem areas. There is no dogmatic way to determine the superiority of one way of cutting the pie.

To illustrate this point, let us consider the ways one might divide a forest ecosystem (Level 0) into state variables (Level -1). For a physiological problem, one might divide the system into leaves, boles and roots. This division permits one to emphasize the differences in function among the state variables. For another problem, one might choose a more structural subdivision into canopy, understory, herbaceous, and below ground. This division, emphasizes different species strategies within the system. For a problem dealing with species composition, one might choose a taxonomic subdivision that retains the identity of species or groups of species. Any of these subdivisions would be useful for a particular class of problems and no single division stands out as a fundamental. There certainly seems no good reason to force all problems into a single framework.

A similar situation arises in choosing higher levels (Level + 1). Allen et al. , (1984) illustrate this point for observations on insect feeding. If one is interested in how this behaviour results in the pollination of plants, the next higher level might be a guild of insects. If one is concerned with the calories of plant being eaten, the next higher level might be a trophic level with the insects aggregated with other consumers.

To summarize, the theory recommends that we set up some hierarchy for studying global change. However, requiring that the hierarchy fit a priori biases is an unnecessary constraint. The bias might force our thinking into a framework that was designed for, and is probably more appropriate for , another problem area.

It may be argued that other natural sciences, such as physics, eventually converged on hierarchical levels that are fundamental in some sense. Nevertheless, physics required several centuries to arrive at this point. During that period, the commonalities between light, magnetism, electricity, and gravity were not evident and each set of phenomena required its own explanatory structure. It suffices to state that at the present stage of development, no absolute, a priori designation of scales is imposed on us by nature in such a way that no other way of looking at the natural world is feasible or useful.

(2) Searching for the fundamental level

It follows from the preceding discussion that it is not fruitful to designate the one and only level to which all other phenomena must be reduced. While most ecologists agree that environmental systems are multi-scaled, some still attempt to reduce all of ecology to a fundamental level such as the population or ecosystem. 

In fact, the phenomenon of interest is likely to determine the time and space scales that will be emphasized. There may be as many 'fundamental' scales as there are problems. Once again, it might be argued that progress in physics depended on focusing on the atom as a fundamental level. Similarly, ecology should focus on the organism, the population or the ecosystem. However, we must realize that physics made considerable progress in optics dealing with waves rather than particles and that it eventually dismissed the atom as a fundamental particle.

To illustrate how the scale of observation determines the level of interest, we can consider the study of Sollins et al. (1983) on soil organic matter formation at Mt. Shasta. At a time scale of thousands of years, the data show a gradual and continuous accumulation of organic matter. The dynamics causing variation around this curve involve long-term processes such as fire, flood, vulcanism, and earth flow. If one focuses on a shorter time scale, perhaps a hundred years, the long-term accumulation is not evident and the observed dynamics are due to seasonal production and plant succession.

As indicated by the theory, Sollins et al. (1983) found it useful to focus on a single level of resolution for each phenomenon and explain dynamics by reference to lower and higher scales of organization. At the same time, adequate explanations of the larger scales were possible without explicit reference to some fundamental level, such as individual organisms or species. In fact, at the largest scales, it was quite irrelevant which plants were involved. It was sufficient to know that a viable plant community existed on the site.

Thus, the theory recommends focusing on a single level but the appropriate level should be based on the problem at hand. It is not useful to force a new problem area into the mold that was appropriate for other problems at other levels.

(3) Translating principles between levels

This brings us to the relationship between levels in a hierarchy. Given that the system is scaled, what can we say about interactions between adjacent levels?

In general, it is not possible to transpose principles developed at one hierarchical level to higher and lower levels. Most concepts and models in ecology have been developed for a single scale. Yet this hidden assumption of scale is often ignored. As a result, some strange errors crop up when a scale-dependent concept is applied at other levels.

Consider the following hypothetical example. Fisheries' managers often take information on rates of reproduction and carrying capacity and calculate an optimum sustained yield. This is the largest continuous harvest that permits the population to persist. On the basis of this calculation, they set limits on the number of fish that can be caught. For the sake of our example, let us assume that 50% of the population can be harvested in a given year. The fishermen, however, operate on a different scale. For example, the fishing fleets may go to Georges Bank in the North Atlantic and harvest almost all of the population over 50% of its total global range.

Now the conditions of the model have been satisfied: 50% of the population has been harvested. However, the recovery rate is no longer proportional to the reproductive rate but to a dispersal rate that can be much slower. The result is that the population begins to drop in numbers. The model was appropriate for a finer scale than was used to harvest the fish. The change to a large spatial scale violated the assumptions of the model because there was a  hidden dependence on scale. 

Another example of a transposition of scale is provided by our experience with pesticides. If a chemical causes significant mortality in a laboratory population, it seems logical to assume that it will eliminate populations in the field. However, at the larger scale, the additional factor of genetic variability must be considered. Often a small fraction of the total population develops resistance. Instead of decimating the population, as predicted from the fine-scaled model, the population flourishes as the resistant strain expands. 

These examples illustrate that it is perilous to transpose principles across hierarchical levels. Constraints imposed at higher levels may dominate, and the overall system behaviour may have little resemblance to the behaviour of isolated components. It is certainly well known among experimentalists that dynamics in the field may be quite different from what is measured in the laboratory.

(4) Be prepared to accept innovative approaches

There is a clear conclusion to be drawn from the first three criteria. We must be prepared to investigate innovative approaches to global measurement and study. A likely conclusion of this workshop and an almost inevitable conclusion of subsequent research is that a new scale of resolution will require new approaches.

It is unlikely that the approaches required to understand global change will reduce to simple repetitions of approaches we have taken in the past. In particular we must avoid the temptation to translate global change into a new justification for old approaches. Obviously, we will not simply dismiss the tremendous resource of manpower and methodology available to study ecological systems at small scales. We still have the obligation to mobilize the existing resources and apply them to the new problem. However, we must also accept that many things will be difficult to transfer to the global scale. We can begin with what we know, but we cannot afford to reduce the global problem to one that fits neatly within existing programmes, approaches and methodologies.

We must be prepared for new approaches because it is notoriously difficult to measure long-term changes at the scales currently emphasized in ecology. Likens (1983) has concluded that 20 years were needed to describe trends in the water chemistry data at Hubbard Brook. Goldman (1981) indicates that 15 years were required to establish a statistically significant trend in the turbidity of Lake Tahoe. Limiting ourselves to familiar scales of measurement may mean that we cannot even detect a significant trend until it is too late to prevent permanent changes. It is very likely, therefore, that significant measures of global change may require larger scale approaches than we have traditionally dealt with in ecology.

In the short period of this workshop, it is unlikely that we can come up with a definitive list of new approaches. The approaches will emerge as we begin serious research on the global problem. But it may be possible to point to some of the general properties of these new approaches.

It seems likely that the study of global change must take advantage of the technology of remote sensing. Satellite imagery has already proven its capabilities of measuring and predicting agricultural productivity and trends in land use changes. It also seems clear that the new measure of global change will deal with larger landscape units than we have traditionally considered. Thus, the question of landscape indices that can be remotely sensed may be a relevant topic of discussion for the workshop.

A good example of a landscape index has recently been proposed by Krummel et al. (1987). They calculated the fractal dimension of land use types on disturbed landscapes. The fractal dimension indicated the complexity of the shape of patches on the landscape. Natural forested areas tended to be small and simple in shape. Disturbed, agricultural areas tended to be large and complex. Based on their results it appears possible to sense remotely a single index that indicates the degree of disturbance to the landscape.

The message of the first four criteria may prove difficult to deal with. The problem of researching global change is unlikely to reduce to aggregating known scales and known ecological principles. This is not to say that we will not take advantage of what we already know, but it does mean that the new problem on the new scale is unlikely to reduce to the familiar and comfortable.

But if it is not possible simply to move concepts and laws across levels, and it is not possible to simply translate this new problem into finer and familiar scales, then how are we to deal with the insights and data that we have available on other scales of resolution? This question brings us to the next two criteria that deal with interlevel relationships.

(5) Effect of a higher level on a lower

One of the most powerful insights of hierarchy theory deals with the concept of constraint. Simply stated, higher levels set constraints or boundary conditions for lower levels. This insight has had widespread influence, for example, on the way engineers control complex systems (Mesarovic et al., 1970) .

The dynamics of upper levels are much larger in scale and much slower in time than the level of interest (Level 0). Therefore, over a normal period of observation, the upper levels appear to be constant. Upper level dynamics also appear unaffected by the level of interest, while Level 0 is constrained to follow the dynamics set by the higher level. Thus, upper level dynamics ordinarily appear in a model of Level 0 as forcing functions or driving variables. Thus, the theory has something very definite to say about the effect of the global on the local. Given sufficient difference in scale, it is possible to predict how the higher level will affect the lower.

An excellent example of how higher level constraints can determine system behaviour is provided by the aquatic production relationship worked out by Vollenweider (1975, 1976) and Schindler (1977, 1978). In nutrient-limited, fresh water systems, annual production is closely related to phosphorus loading. It is possible to predict productivity without information about the species of phytoplankton involved in the process. Dynamics can be determined simply by knowing the higher level phosphorus constraints. Detailed data on lower levels are not required.

(6) Predicting the higher level from the lower

While hierarchy theory predicts how higher levels affect lower ones, it is more difficult to move in the opposite direction. Some higher level properties are the sum or integral of lower level dynamics; for example, biomass production may be summed over forest stands. However, this is not always true and serious problems can result.

To illustrate the problem we can consider a recent example worked out by Cohen (1985) for the concept of fitness. It is possible to talk about the fitness of a genotype. If genotype A is more fit than genotype B, individuals with genotype A will produce more offspring. However, given environmental and genetic variability, it is impossible to aggregate this information upward and talk about the fitness of a species. A species with almost all genotype A may or may not be more fit than a species with almost all genotype B.

The dilemma is best illustrated by an example. Cohen (1985) considers the case in which there are small areas in the environment within which the relationship is reversed and genotype B is more fit than genotype A. Even though these areas are small, the reproductive rate of B within these areas may more than compensate for the disadvantage that B experiences elsewhere. As a result, species B does much better than expected. The situation is similar to the pesticide example discussed earlier. The fine-scaled information that almost every mosquito dies when exposed to DDT could not be moved up scale to predict the response of the species.

Stated as a general problem, the influence of lower levels on the higher is known as the 'aggregation problem.' The problem is of real importance to this workshop because the most extensive ecological information is at small scales; for example, physiological responses of organisms and processes operate at the ecosystem scale. The problem is how to make use of the available data and expertise when we deal with larger scales. How can the smaller scale phenomena be aggregated to understand global levels?

The problem is a complex one that is best approached in several stages. Under many circumstances, hierarchy theory has little difficulty with this question. Level -1, the next lower level, forms the components of a model of Level 0. The component dynamics and interactions are the dynamics of Level 0. Thus, there is no problem seeing how the dynamics of Level -1 relate to Level 0.

Under ordinary circumstances, the rapid dynamics of much lower levels can be ignored. They usually appear as averages or assumptions in the model. In fact, it is a good objective to set up the problem so that lower levels do not have to be considered.

When we are dealing with the normal, unperturbed dynamics of the system, hierarchy theory provides a clear explanation of how lower levels affect higher levels. However, there are exceptions and it is sometimes very insightful to seek explanations at much finer scales. Consider, for example, the Monod function for nutrient limitations on production and decomposition processes. Although the function is useful at macro-scales, it is derived from enzyme kinetics at biochemical scales. Thus, although the theory states that it is not necessary to look at much finer scales, it may still be advisable under some circumstances.

But it is the possibility of global catastrophe that introduces the real problem for the workshop. The theory states that finer scales can be ignored as long as the system is behaving normally and stably. But when the system is disrupted, it is the rapid dynamics of the lower levels that break up the constraint system and move the system into a new configuration. In global problems, we are most interested in these catastrophic changes and the problem of aggregation is a real one.

Thus, the problem of aggregation becomes important for three reasons:

1. we wish to take advantage of available fine-scaled information
2. it is sometimes insightful to seek explanations at much finer scales
3. we need to understand lower level behaviour to predict when unstable responses will occur. As a result, the aggregation problem may be a serious impediment to understanding and predicting global change.

(7) Interactive state variables

To this point in the discussion, I have focused on the criteria needed to set up the levels to be studied within a single discipline. But the objectives of the workshop require that we interface hierarchical levels in several disciplines. So now we must turn our attention to additional criteria for interfacing different hierarchies.

The seventh criterion is both simple and powerful. You have found a useful scale for interfacing different disciplines (e.g. atmospheric and ecological processes), if and only if the state variables of a model from one discipline appear as state variables in the model of the other discipline.

The simplest way to explain this criterion is to consider an example involving the interfacing of atmospheric and ecological processes. At the scale of a single, isolated tree, moisture content of the air appears as a higher level constraint. The scale of water dynamics in the air is much larger than a single tree. Precipitation constrains the dynamics of the tree which is unable to exert any control back on this driving variable.

Let us now increase the scale and consider a larger forest area. Eventually the water content of the air is significantly affected by moisture released from the vegetation through transpiration. Given sufficient lifting of the air mass due to topographic relief, local precipitation results. At this scale it is possible to interface the two hierarchies. The critical element is that precipitation is a function of transpiration and vegetation dynamics is a function of precipitation. At this scale, the vegetation appears as a state variable of the precipitation model and precipitation appears as a state variable of the vegetation model. The loose criterion of 'equivalent' scales can, through the hierarchy theory, be given much more precise definition in terms of interacting state variables.

Of course, the problem of interfacing atmospheric and ecological hierarchies is still not solved. There are any number of levels at which the criterion is satisfied. At a microscopic scale, a single leaf affects, and is affected by, the immediate envelope of air. At continental scales, vegetation cover determines whether desertification processes will take over. So exactly which of these scales is most appropriate for studying global change remains an open question for the workshop. Once we choose a problem area, the theory provides a means for determining a specific scale at which atmospheric and ecological processes can be interfaced.

(8) Seek coherent levels

The discussion under the previous criterion might lead one to believe that any level of resolution can be chosen arbitrarily. This is not the case, and an additional criterion is needed based on the concept of 'coherent levels' (Sugihara, personal communication).

Once again, it is easiest to explain this concept by way of example. It is difficult to predict the behaviour of a single animal. The information required to predict whether it will walk to the right or to the left makes the problem almost unsolvable. However, the problem becomes simpler as we move up scale. It may be possible to predict the movement of a herd of individuals, for example, as they move along a migration route. Thus, there are scales at which one's predictive capability is improved over slightly larger or slightly smaller scales. The scale at which the predictive power is maximized is the coherent level. A coherent level is one that 'makes sense' as an isolated object of study and it is quite likely to correspond to a traditional level of study within a discipline.

While it would be possible to interface disciplines at arbitrary levels of resolution, arbitrary scales do not take advantage of the innate organization in hierarchial systems. It is only when we focus on coherent levels that we are able to take advantage of the information and insights that have developed in each discipline about their own systems.

Together, Criteria 7 and 8 form a guideline for interfacing disciplines. The scales of interest in both disciplines must be coherent levels as well as appearing as state variables in the model from the other hierarchy.

To illustrate the power of Criteria 7 and 8, let us consider a difficult situation which arises in the context of global change. Ecological systems are scaled in a particular way in space and time. Small systems change rapidly and large systems change slowly. But atmospheric phenomena may be arrayed in quite a different manner and large spatial areas may change rapidly. Thus, sub-continental areas show similar seasonal changes in temperature. How can one interface large space, small time changes in temperature with either small space, small time or large space, large time ecological systems?

The answer to the dilemma can be deduced from Criteria 7 and 8. The state variables describing large ecological systems do not change on a seasonal basis and there are no common state variables at the large spatial scale. We must go to the smaller common scale, the rapid time response, to find interactive state variables. However, ecological systems are not organized in large space, small time scales. Therefore we must apply Criterion 8 and find the coherent ecological system which reacts at the common time scale. That is, the relevant point of intersection is the coherent ecological system that responds seasonally, e.g. a forest stand or a grassland patch. Ecological models at the stand/patch scale can handle changes in gaseous exchange in response to seasonal changes and we have found interactive state variables.

We have found the relevant model. How do we extrapolate the results of the stand model to the large spatial scale of the atmospheric model? The problem reduces to finding the expected value of the small scaled process distributed across space. The expected value is, by definition, the integral of the stand model across the frequency distributions representing the spatial variability of the relevant independent variables. In our example, the independent variables would include seasonal temperature and the biotic parameters of the model. There may be additional sources of variability but these seem to be the most important. Given that this information is available and given that there are no spatial correlations in the response of stands, Monte Carlo simulation of the . small scaled model yields an unbiased estimate of the expected value of the process across the region.

Thus, Criteria 7 and 8 provide the necessary background for interfacing phenomena on very different spatiotemporal scales. The positive part of the result is that it is possible to devise a specific approach to answering the question. The negative part of the result is that the information requirement (frequency distributions characterizing the spatial variability of seasonal temperatures and biotic parameters) is rigorous and such data may not be available.

(9) Critical points in parameter space

Once we have picked a scale, we must decide what to measure. Large scale changes occur very slowly and are difficult to detect, as was pointed out earlier. We are once again caught in a dilemma. The need to detect change on the global scale is apparent. Yet long-term changes are very difficult to detect and it may take 20 years before the first significant results can be stated. Monitoring at this scale may be too little too late. Without a way of interpreting changes, we may be able to detect the change only after the catastrophe has begun. So how can hierarchy theory help us determine what it is we want to measure?

A potential solution can be offered if we are not overly concerned with the normal functioning of the system. It is this normal, stable behaviour of the system which is most difficult to monitor. In fact, we are most concerned with the unusual circumstances in which the system will respond unstably to a new perturbation. That is, we are interested in monitoring for the critical points in the behaviour space of the biosphere, the points of bifurcation.

The concept of critical points in parameter space should be familiar to ecologists. For example, we are familiar with the Holdridge classification system. In this system, temperature and moisture parameters are used to array the world's vegetation types. When climate parameters pass certain critical  points, the state of the system can change drastically. An example of a critical point would be the annual temperature below which permafrost becomes a feature of the environment. Below this value, the vegetation can change radically. Other examples would be moisture changes that alter forest into grassland or grassland into desert. The ecologist is also familiar with the fact that, over geologic time, it is quite possible for the climate to move across these critical points and change the vegetation.

Movement across these critical points need not be caused by climate or catastrophic perturbations. The radical changes seen in the fossil record can occur through the normal dynamics of a complex nonlinear system.

As an example of how this can happen, let us consider the following hypothetical scenario. At some  point in geologic history, diatoms evolved a new enzyme that permitted a silicon shell. The change could have been as simple as a single point locus change. Because none of the predators had silicacious jaws, the diatoms were freed from a constraint and expanded rapidly both in numbers and in taxonomic varieties. Eventually, the diatoms became the dominant organisms on the continental shelves. As a result of breaking a constraint, the well-behaved system became unstable and the diatoms expanded until they hit a new constraint, probably lowered concentrations of silica in sea water. In this scenario, the radical change in the system did not require any radical change in the environment.

Of course, similar hypothetical scenarios could be developed for many of the major changes in the fossil record. Such changes are normal in nonlinear systems. Thus, global monitoring should be designed to indicate whether or not the system is approaching such a point.

Examples of rapid changes illustrate that the aggregation problem is important. The critical change that altered the taxonomic composition of the continental shelves of the world could have been a single mutation, explainable at the subcellular level. The changes we are most interested in monitoring at the global level may be caused by alterations at much lower levels in the hierarchy. This fact significantly complicates what we are trying to do. But the fact remains that the scenario is feasible.

Is the effort to monitor and predict global change a quixotic task, a search for the Holy Grail? Fortunately, we need not draw this conclusion. It may still be possible to monitor for the approach to critical changes such as desertification, glaciation, or the initiation of an erosion or peneplanation cycle. It may be possible to detect the approach of such changes, even though we do not have at our disposal all of the lower level information required to provide a mechanistic explanation for the change.

To see how this prediction is possible, we need to consider some technical details of the theory. The points of critical change are called bifurcation points in the underlying mathematical theory. There is a necessary and sufficient condition for determining when the radical change will occur. The change occurs when the rapid components cease to be stable, that is, the lower level components do not return to normal behaviour following a minor perturbation.

What causes the system to behave normally is that the rapid portions of the system are constrained by higher levels. If the system is perturbed, the rapid components simply return to the slowly changing trajectory. The rate of recovery can be taken as an indicator of the relative stability of the system. It seems reasonable to assume that as the system approaches a bifurcation point, the recovery becomes slower (i.e. the system becomes less stable).

Thus, it should be possible to monitor globally for the approach to a catastrophic change by monitoring the recovery rate of lower levels in the hierarchy. If the response times are increased the system is being moved toward a point of radical self-amplifying change. Thus, even though the actual point of change could be precipitated by fine-scaled changes, the proximity to any point of radical change should be indicated by a change in recovery times.

Perhaps an example of such approaching change would help clarify the concept. Unfortunately, such examples are hard to come by and once again we are limited to a hypothetical experiment. Suppose we were using remote sensing to monitor for land use change in the tropics. In addition to monitoring the square miles that are converted from forest to agriculture, we also measure the shorter term successional recovery rate of a number of sites. As the cleared areas increase, we might find erosion cycles beginning or changes in air moisture and precipitation. In either case, we might be able to measure decreases in the succession rate. At this point, we know not only that a gradual change in a large-scale phenomenon is occurring but also that the change is occurring in the direction of an instability. In this way, a shorter term measurement of stability might permit interpretation of the large-scale change, but would be considerably easier to measure.

The difficulty of aggregating lower level behaviours to higher levels remains and there is a real problem with maximizing the fine-scale understanding we possess. Nevertheless, the theory provides us with an intriguing new approach. In so far as we want to prevent catastrophic changes, measurement of natural rates of recovery could be a key ingredient in any study of global change.

CONCLUSION

To be most useful, the conclusions we draw from this analysis of hierarchy theory must be directly related to the objectives of the workshop. Therefore, I will summarize the criteria by emphasizing the major points and their application to the objectives.

(1) What are the scales in each discipline?

Hierarchy theory cannot tell us which scales of resolution would be most useful to study at the global scale. It can, however, guide us away from a naive concept of hierarchy which would force this new wine into old bottles. The theory recommends that we look at global change as a new and challenging problem area and not try to force it into hierarchies (Criterion 1) or levels (Criterion 2) that are more appropriate for other problems. The theory also warns us not to feel that once the appropriate hierarchy is selected it will be a simple matter of transposing principles developed at finer scales up to the new scale of interest (Criterion 3).

(2) How to integrate scales across disciplines

The theory provides concrete advice for choosing scales that will permit fruitful interfacing between disciplines. We should seek coherent levels (Criterion 8) at which state variables from one discipline appear as state variables in a model for the other discipline (Criterion 7). These criteria are straightforward and it would be well to adhere closely to them during the workshop.

(3) How does the global affect the local?

The theory is particularly helpful in describing how larger scales affect the smaller. Under normal operating conditions, the higher levels appear as constraints or boundary conditions (Criterion 5). When the normal operation of the system is disturbed, many of these constraints disappear as the system changes to a new configuration.

(4) How local determines global

Under normal circumstances, the dynamics of a system are determined by the dynamics of Level -1, the next lower level. Smaller scales operate much too rapidly to be of interest (Criterion 6) and can be ignored. As a result it is ordinarily of little interest to aggregate very fine scales in an attempt to describe large-scale phenomena.

The situation changes dramatically when the system becomes unstable. Now, the fine-scale dynamics are unconstrained and tend to change the system drastically. However, there is no theory available to predict exactly which fine-scaled processes will be most important. The theory is of little help then in deciding what fine-scaled research would be most useful to explain global change. The only guidance comes from the scientific method: once a potential disruption or change is identified, we can formulate and test hypotheses about the significant fine-scale mechanisms.

(5) Research needs

The major challenge of the workshop is to begin to develop a sensible research plan to attack the problems of global change. Hierarchy theory makes it clear that this new research must develop innovative approaches (Criterion 4) even while we attempt to synthesize and apply what we know about ecological systems at smaller scales. It is likely that these new approaches will take advantage of remote sensing and large-scale landscape measures.

It is also clear that the most critical problems of global change will deal with catastrophes (Criterion 9). The theory is particularly valuable here since it suggests measuring recovery rates as an indicator of whether or not gradual changes are leading toward bifurcation points.

As one could anticipate, hierarchy theory is useful in leading us away from naive errors and suggesting new directions to take. However, it is beyond the purview of this or any theory to constrain our deliberations and the theory does not dictate which scales of resolution or which research will be most fruitful. Hopefully the theory does provide a framework which can guide workshop deliberations in the most fruitful directions.

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