This paper discussed the FLEX-REFLEX approach to modeling developed by Overton. A rationale for the approach is developed, the approach is described, and application of the approach is considered. The rationale involves the necessity of applying systems analysis to the study of ecosystems. Elements of the hierarchical theory of organizations are established. A general description of FLEX-REFLEX principles, as well as the manner in which they support the modeling phase in ecology is presented. Some implicit applications of the approach are described both at a theoretical and a practical level. Finally, the way in which the FLEX-REFLEX approach has been used for teaching systems analysis in ecology at the Universidad Aut6noma Metropolitana-Xochimilco is presented.
INTRODUCTION
During recent decades technological advance and population growth have caused fast changes in the structure and functioning, and therefore stability, of many ecosystems. The most perceptible effects are desertification, accel- erated erosion, contamination, and the extinction of species. I believe that little is said to the common citizen concerning what can be done about these problems and little is known about what is actually being done.
The investigation of ecosystems for the elaboration of ecological theory represents the best alternative to find and propose adequate methods for natural resource management. Therefore, systems analysis in ecology is an indispensable tool for the resolution of problems (Caswell et al., 1972; Dale, 1972), particularly in relation to decision making for the optimization of goods and services that come from the ecosystem. Since this is a relatively new field of research, it faces a series of conceptual and operative problems towards which the effort of a great number of scientists has been directed.
Among these problems is that of identifying the significant decomposi- tions of a system under study. This problem is addressed by Overton (1975)
through his FLEX-REFLEX approach and it pertains, on one hand, to the modeling phase of systems analysis (Caswell et al., 1972) and, on the other, to the hierarchical theory of organizations and its application to the elabora- tion of ecological models. The present paper focuses on the formulation of this approach as an important proposal for the study of ecosystems and the elaboration of an ecological theory that allows us to solve ecosystem problems.
RATIONALE FOR THE APPROACH
Systems analysis in ecology
The application of systems analysis in ecology is due, in part, to the similar definitions of system and ecosystem. A system is any structural or functional phenomenon with at least two separable components and some interaction among them (Hall and Day, 1977). An ecosystem can be defined as the assembly of flexible organisms which interact among themselves and their environment forming an organized whole with a coherent conduct (Caswell et al., 1972; Overton, 1977). On the other hand, general systems theory is the logic-mathematical field for the formulation and derivation of those general principles applicable to systems in general; and systems analysis in ecology is the application of this theory to the study of ecosys- tems. Caswell et al. (1972) propose a scheme for applying systems analysis in ecology in which four basic phases are defined: modeling, control, design, and synthesis. Modeling is defined in general terms by Jaffe (1978) as the identification of elements of the system and the specification of their attributes; and by Patten and Finn (1979) as an iterative representation from a physical to a logical domain, with reference to objectives and which,
generally, requires a reduction of size and complexity. Caswell et al. (1972) outline the following steps for the modeling phase:
(a) definition of the objects of the system, (b) selection of the behavioral characteristics of these objects, (c) modeling of the restrictions of the interactions among the objects and (d) description of the system as one object by submerging the internal behavioral characteristics. This sequence differs on its last point from the one proposed by Dale (1972), although the description of the global system implies also a validation of the system model through an analysis as did the one indicated by Dale. The sequence proposed by Caswell et al. (1972) represents the central problem considered by Overton (1975) in his FLEX-REFLEX approach; that is, the problem of characterizing the system's interactions.
The phases of control, design, and synthesis have been scarcely developed due to the lack of knowledge about the structure and dynamics of natural
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systems. As a consequence, there are very few investigations concerning the design and synthesis of ecosystems. This implies that the modeling phase is, at the moment, the essential aspect for the development of ecological theory. As Overton (1975) pointed out, an effort to develop a general model for an ecosystem is an effort to develop a conceptual structure for ecosystem study.
Hierarchical theory of organizations
The fact that ecological systems analysis is closely related to the hierarchi- cal theory of organizations is deduced from the definition of system. Systems almost always are defined in terms of three levels: (a) the level of interest (the system), (b) the internal level (the components of the system) and (c) the external level (the environment of the system). Caswell et al. (1972) point out that an abstract object can be defined by its dynamic behaviors and an assembly of such abstract objects can then form a hierarchy by means of a relationship defined in the behaviors. Or as Webster (1979) defines it, each element (of a natural system) consists of systems of the next lower level and is characterized by behaviors that occur more slowly than the behaviors of the next lower level. Also, Von Bertalanffy (1950) indicates the property of hierarchical order of systems by mentioning that the elements (subsystems) of a system can be systems of lower order.
In a general way, hierarchical theory implies that the understanding and explanation of science involves generalization and simplification, and that is why we establish hierarchical levels in our objects of study. Therefore, as Webster (1979) pointed out, for the study of ecosystems the discussion about the hierarchical or non-hierarchical character of nature is trivial since our perception of it is hierarchical.
There are two opposite approaches to the hierarchical relation between the different organizational levels of a system. On one hand, the holistic approach propose that the behavior of a level cannot be explained in terms of the behavior of lower levels, since it is more than the sum of these parts. On the other hand, the reductionist approach states that the behavior of the superior level is only a definable combination of behaviors of lower levels. However, Overton (1975) demonstrates that the distinction between one approach and the other is only semantic since both levels, the holistic (or behavioral) and the reductionist (or mechanistic), need to be combined to completely understand the system.
The rest of this section consists of a general review of several propositions for the study of hierarchical levels. As an important precedent to Overton's (1975) work, Simon (1962) described the hierarchical structure of organiza- tional levels with a vertical separation that isolates each level from lower and superior levels; and a horizontal separation that divides the components of
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any level into groups and determines the superior level. The vertical sep- aration is based on behavioral frequencies and the horizontal depends on the isolation of the system by forming a level. For this last aspect, the degree of connectivity among the components is very important.
The quasi-decomposability concept of Wilson (1973) involves use of the topologic relationships as the inclusion of a spatial environment that coin- cides with the extension of a physical object or which may bound it within one or more closed surfaces. In this manner, Wilson suggests that the decomposition of the entities must be defined from their bonding or closing forms.
Rosen (1973) states the necessity to locate first the information that describes the system at the upper levels and afterwards to establish a procedure that handles this information (here is where the elaboration of models comes in). Koenig and Tummala (1972) suggest a procedure of multiple level analysis that moves from one level of analysis to another by using the systems models of a given level as objects in the level above.
Finally, Koestler's concept of holon represents the most important pro- position for our discussion of hierarchical schemes. According to Patten et al. (1976), the holon defines the component objects of a system. Webster (1979) states that the holon refers to the systems that at each level adjust to the laws of inferior levels, and that through natural selection have their behaviors restrained by the superior levels. From Webster's definition, the behavior at any level is explained in terms of the lower level and its significance is found at the level above. Translating this definition to the ecological system, the behavior of an ecosystem is explained in terms of the behavior of the organisms that compose it; and the significance of the behavior of the organisms is found in the global behavior of the ecosystem. However, the simplest definition of holon is the one by Overton (1975) who states that it is a subsystem of a major system and, at the same time, a collection of inferior subsystems joined together. In this manner, Overton refers to the objects that are part of a bigger whole and that also have properties giving them their own individuality. The holon thus becomes the basis for the construction of hierarchically organized systems.
DESCRIPTION OF THE APPROACH
At a general level, the FLEX-REFLEX approach is part of what Klir (1979) defines as structure modeling. This term originates from the concep- tual frame for the resolution of problems presented by Cavallo and Klir (1978, in Klir, 1979) and pertains to the hierarchy of epistemological levels. This hierarchy is formed by three system levels: the data system, the generative system, and the structure system. For structural identification of
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the system, Klir (1979) indicates two alternatives, the first of which is used in the F L E X - R E F L E X approach.
The hierarchical connotation of the holon concept allows formulation of the approach for two modeling forms (FLEX and REFLEX) suitable to ecosystems, since they can be considered as hierarchically organized systems. However, the F L E X - R E F L E X approach does not consist only of the application of Koestler's concept. Overton (1975) starts from a hierarchical view of the system by proposing that its conceptualization, characterization, and modeling must be done at a holistic level with regard to the behavior of the system as an object, and at a mechanistic level with regard to the interrelationships of the subsystems.
Another aspect of the F L E X - R E F L E X approach refers to two of the five definitions of system made by Klir (1979; Overton, 1975). The first one considers the system according to its permanent behavior and the second defines it in terms of its universe-coupling structure. These elements are integrated in a paradigm in which the holistic-behavioral level is called FLEX and the mechanistic-structural level is called REFLEX. The relation established between FLEX and REFLEX levels permits that each subsystem REFLEX can be passed to a FLEX level and thus be modeled in its behavior; at the same time, each FLEX system can be decomposed in its REFLEX level to be modeled structurally. In this way, the recursive character of the approach is defined. Returning to Klir's (1979) definitions, we see that the first corresponds to the FLEX level since it defines the terminal subsystems which represent the system's behavior. The second definition corresponds to the hierarchical structure of the REFLEX level which represents the universe-coupling structure of the system.
Finally, the F L E X - R E F L E X approach also considers the elaboration of aims and objectives as an essential aspect. The structure created by an investigator in the initial stages of a system study will be reflected in its results. Thus any discussion and analysis of a system must be preceeded by explicit statements of the observer's interests and aims and of the way in which the structure imposed on the system is related to those aims. This is important because of the hierarchical character of the aims (Akhmetzianov, 1973; Mesarovic and Macko, 1973; Hall, 1978; Mesarovic et al., 1978).
APPLICATION OF THE APPROACH
The F L E X - R E F L E X approach has been considered by Patten as a valuable contribution to the development of ecosystem theory and by Webster as one of the few specific applications of hierarchical structures to the study of ecosystems. Nevertheless, there are no examples o f explicit use of the FLEX-REFLEX approach, other than the work of Overton (1975). However, the approach has been used implicitly with regard to ecological
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studies such as the Hubbard Brook Ecosystem Study (Bormann and Likens, 1981). The approach taken at Hubbard Brook is both holistic and mechanis- tic. On one hand, there is the 'black box' point of view in considering meteorological, geological, and biological inputs and outputs. On the other hand, the internal fluxes among components as well as the processes of nutrient uptake, decomposition, weathering, and mineral formation are analyzed. With the information obtained at the mechanistic level, Botkin (1977) elaborated the JABOWA model which predicts on an annual basis the following ecosystem parameters: density, frequency, basal area, biomass and nutrient standing crop (Bormann and Likens, 1981).
The majority of works that consider the effect of environmental variables on productivity and matter and energy balances belong to the FLEX level. On the REFLEX level are those analyses that consider the interactions among components of the ecosystem, as well as the manner in which their interactions influence the system's global response (J.M. Chfivez, personal communication, 1984).
At the Universidad Aut6noma Metropolitana-Xochimilco, systems analy- sis in ecology is introduced to biology undergraduates to achieve an integra- tion of the knowledge acquired previously and to direct this knowledge towards natural resource management. This involves the development of student projects that consider: (a) the statement of a resource management problem, (b) the formulation of an aim and a purpose from which an objective function is defined, (c) the formulation of objective questions and working hypotheses, (d) the elaboration of diagrammatic models, and (e) the formulation of a mathematical model following Shoemaker's tactic (Shoe- maker, 1977). In the first four steps, the application of the FLEX-REFLEX approach allows the student to decompose the elements of the system object of study in agreement with the aims and objectives formulated.
CONCLUSION
The FLEX-REFLEX approach developed by Overton is not only a result of the general systems theory developed up to the time of its formulation (1975), but also an important advance in the elaboration of a sound ecological theory. Therefore, it is hard to understand why the approach has scarcely been reconsidered by systems ecologists. It is my belief that applica- tion of this approach will prove useful to anyone involved in a complex multilevel ecosystem study.
ACKNOWLEDGMENTS
The presentation of this paper at the 1985 Annual Meeting of the International Society for Ecological Modeling was supported by the CON- ACyT contract PCECCNA-730567.
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