Egon Becker & Broder Breckling

III.5.3 Border zone between ecology and systems theory

In any field of knowledge, the study of interactions leads logically to the concept ofsystem organization.K.M. Khailov (1964)

1. Introduction

For many years now, proponents of systems theory and advocates of ecology havebeen engaged in an intense exchange of ideas, principles, concepts, theories, models,and methods.1 The dynamics of this exchange have given a boost to both fields.Individual pioneers (such as Eugene and Howard Odum) and innovativeorganisations (such as the Santa Fé Institute) have spurred on this reciprocal concepttransfer. Ecology and systems theory thus form two research fields which are onlypartially separated and which display powerful internal dynamics and borders thatare permeable from several sides. Both research areas are, however, riddled withcontroversy. Heterogeneous discourses have developed in both fields, each of thesediscourses possessing its own specific cognitive and social order, along with thecorresponding theoretical concepts and scientific practices to match. While eachdiscourse has its own history, the history of the relationship between the tworemains unwritten.

Since the 1930s, the exchange between systems theory discourse and ecologicaldiscourse has been shaped by the paradoxical idea of a “living system”. The idea is aparadox because – at least prima facie – “systems” are not living entities and “livingbeings” are not systems. Bertalanffy’s (1932) proposition generalises theunderstanding of organisms as open systems. As a general conceptual referencepoint, the idea of a “living system” enables the distinctive ideas and conceptualframeworks of each discourse to be represented without requiring any explicitconsensus.

The transfer process is closely linked with the critical question of whether thetransformation of ecology based on the adoption of systemic concepts and methodsis beneficial or harmful. The converse question, concerning the influence ofecological approaches on systems theory, is rarely asked. The rise of systems theoryin ecology (Odum 1971, 1983) is the subject of considerable controversy. Somescientists welcomed the opportunity to change ecology from a traditional,descriptive discipline into a modern, explanatory science (Fränzle 1998). For others,however, the shift in ecology towards a systemic paradigm represents a movetowards the mechanisation of living beings, linked to a technocratic turn inecological research (Trepl 1987). Despite such criticism, recent decades havewitnessed an expansion of systems thinking and formal, mathematical modelling –

1 This process will henceforth be referred to as “concept transfer”.

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along with the development of computer applications – in science as well as innumerous other fields.

2. Criticisms and Controversies

In much of the current criticism, it remains unclear what exactly is being criticised.This is because, as previously mentioned, neither systems theory nor ecologycomprise a coherent monolithic entity. In both areas, quite different theoreticalperspectives and practical orientations coexist. Both fields continue to developindependently, responding constructively to criticism and exchanging concepts withone another. Through this process, many different kinds of connections havedeveloped between the branches of the two fields. Despite this fact, all participantsin the debate tend to operate with assumptions of homogeneity, and Ludwig vonBertalanffy’s particular version of systems theory is widely considered to be systemstheory as such.

Accordingly, there are many stories in circulation about the relationship betweensystems theory and ecology. These accounts are embellished with detail and vividdescriptions of controversy, enlivened by anecdotes, and interwoven with otherstories. This enables developments in the discourse to be interpreted retrospectivelyas plausible. By and large, proponents of systems theory in ecology provideaccounts of progress - of how the transition from a metaphysical holism to a modernsystems ecology occurred, how it has succeeded in overcoming the ideologicalcontroversy of the 1920s and 1930s, and how ecology developed from a descriptivediscipline of natural history into a mathematical, model-based theoretical science.Critics of this viewpoint regard the situation from the opposite perspective and tellstories of loss: of how our understanding of life has become mechanized, howquantification has erased our understanding of the qualitative nature of livingrelationships, how organisms’ individuality and idiosyncrasies have vanished fromthe heart of ecology, how systems thinking has led to methodological constraints,and how a mechanical model of the world and technocratic approaches havegenerally taken over.

Such accounts generally serve to reinforce one’s own position in discursivestruggles for power and conceptual delimitation, especially if they are put forwardby pioneers. Detailed studies in the history of science have been able to clarify therole of such stories and to point out the myopic perspective both of the storiesthemselves and of criticisms of the same. The following is a list of some of the moststriking prejudices surrounding the critical discourse, particularly with regard to theimplied suggestion of homogeneity in systems thinking:

1. There is no homogenous systems theory, only a heterogeneous systemsdiscourse with a plethora of concepts and methods, backgroundphilosophies and practical applications. There is an enormousconceptual and methodological gulf between the systemic conceptsused in cybernetics and communications engineering on the one handand the sociological systems theory of Talcott Parsons or NiklasLuhmann on the other; as well as between the methods applied in

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operations research or mathematical game theory and those applied inecosystem research.

2. The transfer of concepts did not occur unidirectionally from systemsdiscourse to ecology; rather, ecological notions and concepts wereimported into systems discourse early on.2 The importance ofpopulation dynamics in Lotka’s (1925) and Volterra’s (1926)mathematical formulations for systems theory is often downplayed bythe theory’s founding fathers.3

3. Cybernetics is not merely a special case of General Systems Theory,nor has cybernetics ever developed fully within systems theory. Theidea of circularity as a fundamental principle turned into the notion of“circular causality” in the broad theoretical outline of cybernetics.Cybernetics thus acquired its own discursive order, shaped byquestions concerning regulation and information transfer. However,cybernetics is not identical with its technical applications inautomation and regulation technology and in computer science, as isoften implied by critics. Cybernetic concepts are also found inmedicine, psychology, political science and cultural anthropology.

4. The classical cybernetics of Wiener and Ashby has not stagnated;rather, it has evolved into a “second-order cybernetics”. The newcybernetics attempts to include the “observer” into the system; itexplores the importance of “positive feedback” and concentrates onnonlinear aspects. This makes it possible to comprehend self-organization and emergence through the lens of cybernetics as well.Second-order cybernetics has had a strong influence on the more recentsystems discourse and has helped to prevent its decline. In addition,numerous modelling approaches have emerged more recently.Examples of these are to be found in neuroinformatics, artificial lifeand biorobotics.

5. A systems ecology centered on the analysis of energy flows is not theonly systems theoretical approach in ecology. Gregory Bateson, forexample, taking his lead from early cybernetics, drafted a systemicconcept of ecology in which he particularly emphasized the importanceof information flows and communication networks in ecosystems(Harries-Jones 1995). However, this concept was not taken up inbiological ecology; instead, it was the analysis of bioenergetic transfers(Odum 1971, 1983) that largely became dominant here. Something

2 It would be highly instructive from an historical point of view to examine exactly whatrole the ecologist Evelyn Hutchinson played in the development of early cybernetics (Heims1991, Taylor 1988, Pias 2003, Schwarz & Schwoerbel 2001). At any rate, cybernetics’ centralconcept of “circular causality” was certainly influenced strongly by Hutchinson.3 “Apart from the ecological import of Lotka’s ideas, his book also anticipated Ludwig vonBertalanffy’s development of General Systems Theory in the 1950s. Bertalanffy ratherungenerously downplayed the similarities between his method and Lotka’s, but Lotka hadclearly set down the basic procedure of systems analysis first” Kingsland 1985, p. 26.

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akin to a “semiotic shift” is currently occurring in cybernetics, a shiftthat has now extended as far as biology and has adopted the ideas putforward by Bateson. A new research field – biosemiotics – isemerging, in which communication within and among organisms iscentral (Hoffmeyer 1996).

The heterogeneity of systems science discourse repeatedly gives rise to afundamental dispute over the ontological and epistemological status of ecologicalsystems. This dispute continues to be a source of controversy in the debate over thesystems concept most appropriate for ecology, and it influences the concept transferbetween ecology and systems science. The problems involved in this dispute arediscussed in more detail in the following sections. Behind the various controversieslurks the question of the relationship between the formal representation of a“system” and specific ecological conditions.

3. Real World and Abstract Systems

Neither in systems discourse nor in ecology is there agreement regarding whatexactly systems are, much less how they should be perceived and described.Accordingly, different opinions abound with regard to how the term “system”should be understood and used. In ecology, these issues continue to ignitecontroversy of the “realism versus nominalism” kind, in which concepts are hotlycontested along with differing understandings of systems and the various ontologicaland epistemological implications involved. The main arguments resemble topoifrom the famous controversy between nominalists and realists in medievalphilosophy, which was waged vehemently between the eleventh and the fourteenthcentury, and which erupted again in the twentieth century, particularly withinanalytical philosophy.4

The original conflict was conducted over the issue of whether general concepts –the universals (the “Good”, the “Divine”, “Man” or “Animal”) – exist as such(outside the mind), or whether universals are merely a property of things and thusmerely a name? In classical Greek philosophy the universals were understood as anidea or principle (Plato), or again as a form or archetype (Aristotle). In later debates,the epistemological status of the universals was discussed using ethical ormathematical examples in particular. At issue for the medieval dispute were, on theone hand, observed forms and principles of thought and, on the other, questionsabout the mode of existence of thoughts themselves. As a scientific discipline,biology was dragged into the dispute as early as the Middle Ages: are genera andspecies real, or are they just a product of classification-oriented thought processes?The realists followed Plato. For him, universal concepts existed as ideas in theirown realm, beyond the earthly world of things. According to Plato, they can bediscovered by human thought. Aristotle, by contrast, held that universals existedonly in things or individual beings because only the individual could be “real”. The

4 In the philosophy of mathematics and quantum theory, this debate was played out in thecontrast between “Platonist” and “constructivist” views (Stegmüller 1978, Khlentzos 2004).

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medieval nominalists radicalized Aristotle’s notions and ultimately considered theuniversals as merely a name for spoken generalizations or philosophicalabstractions. The universals do not represent a specific ontological status. Onlyindividual things and living beings are real.

In ecology, the issue at hand is whether ecological systems really exist, orwhether they are constructed conceptually by science. For “systems realists”ecological systems do exist as ontological entities, and therefore they cannot bedefined freely or according to human preferences; for “systems nominalists” (whoare nowadays usually called “constructivists”) ecological systems are scientificconstructions, such as logical classifications, which can be interpreted in terms ofgenus as well as of species (Trepl 1987, p. 140). It is possible to identify threedifferent positions which gradually emerged in the course of ecological researchpractice. These are (1) image naturalism, (2) analytical realism and (3) constructivistrealism.

Position 1: Image naturalism (Abbildrealismus) is an extreme variant of realism.While rarely adopted as an epistemological position, it is widespread in scientificpractice. Ecological systems are understood as given objects in the real world,comprising a diversity of individual organisms and species, complex patterns ofinteractions, and entangled processes. Such systems can be delimited, identified andnamed in both spatial and temporal terms, and empirical research can generateincreasing amounts of knowledge about them. In this sense, physicists speak of the“planetary system” while ecologists identify particular forests, frog ponds or antcolonies as “ecological systems”. Empirical data collection, carried out asextensively as possible by means of impartial observation in the field or in thelaboratory, along with inductive generalizations of such observation, are consideredto be the foundation of scientific knowledge. If this knowledge is regarded as a moreor less accurate image, or depiction, of nature as it is, then what follows from theontological option for systems realism is an epistemological option for what wecalled image naturalism. This way of thinking stems from the “naturalistic myth ofthe given” (Hesse 2002). “System” is, in this case, merely a general name for anycomposite and internally structured part of reality. In this respect, naïve imagenaturalism contains a nominalist ontology. To put the point somewhat paradoxically,it is a “nominalist realism”. Whenever the basic principles of this position aresubjected to epistemological analysis, it quickly becomes apparent that “imagenaturalism” is in urgent need of corrective adjustment.

Position 2: Such revisions tend to occur especially in those areas whereecological questions are the subject of empirical investigation and mathematicalmodelling. This leads to a content-focused analytical realism: from an ontologicalpoint of view, it is a form of realism to the extent that it is based on the hypothesisthat ecological systems exist in and of themselves, independently of any externalobservation or description. Such realism is analytical because it acknowledges that,in research, particular aspects of an ecological reality are always accentuated anddistinguished analytically from the environment. It is also recognized thatknowledge acquired as a result of the research process is then represented as a“system”. Exactly which aspects are emphasized depends on the research interests

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and questions pursued by the scientists. This type of empirical-analyticalunderstanding dominates scientific research in general and is not specific to systemsanalysis in ecology.

Position 3: The specific implications of the systems approach are given greateremphasis in cases where the understanding of the system is developedmethodologically rather than on the basis of content. In this case, “system” isrecognized as the hallmark of a particular method. In other words, an empiricalcontext is interpreted according to its internal organization and its relationship toother objects in the world. According to this view, the object of perception does notexist independently of the act of perceiving it. Rather, a systems object must first be“constructed” according to specific thought patterns, concepts and methods. Onlyafter an appropriate theoretical model for this object has been developed can theempirical context be reconstructed as a “system”. Systems methodology reveals theoperations undertaken to construct the system in a logical and transparent way. Inthis respect, the corresponding systems theory can be interpreted in constructivistterms. In this analytical-constructive view of systems the term “system”, in terms oflinguistic logic, is a so-called “abstractor” through which abstract objects can beconstructed and named. Thus, what we have here is a kind of nominalism, insofar as“system” refers to a methodologically generated abstraction. This constructivist ormodel-based nominalism represents a counter position to both systems viewsdiscussed above, image naturalism as well as analytical realism. Sukachev (1964)formulated an explicit and conceptually pointed distinction between the idea of anecosystem as a theoretical model and the notion of biogeocenosis as the empiricallyaccessible object of observation. Weideman and Koehler (2004) are currentlyworking on this distinction within the field of ecological succession.

A veritable arsenal of abstracting methods has been developed in systemsdiscourse. Image naturalism considers these methods to be instruments for depictingecological matters; analytical realism sees them as a way of isolating and connectingparticular aspects of a phenomenon. A more exact analysis reveals that all methodsenable abstractions to be formulated. “Systems” can be constructed as epistemicobjects, as things that humans can and want to know about, and as items which aredescribed using appropriate language (Rheinberger 2001). A similar phenomenon ofmultiple interpretations occurs in everyday life. A thing of nature, such as an appletree, can, in this sense, become an epistemic object. It can also be taken as aneconomic object (the apples could be sold as a commodity or be used as a rawmaterial to make cider) or as a cultural-aesthetic entity (someone could write a poemabout the apple tree). The tree’s role in perception and analysis shifts depending onthe context - epistemic, producing or contemplating – in which it appears. Similarly,in ecology, an area of grass could be classified systematically as a particularvegetation association, it could be seen as a pasture system or again it could bedesignated as a habitat type. In specific cases, an area covered with grass may evenbe of interest only as a basis for defining the parameters of spatial resistance that areused to understand the dispersal dynamics of other organisms.

This example shows that the mere classification of an object (such as “grass”) asa “system” brings into sharp relief the question of what mode of existence “systems”

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actually have. In General Systems Theory (GST), systems are generally viewed asmodels of real (material-energetic or communicative-symbolic) relations. Despitethe constructivist epistemology that dominates GST, these models continue to be re-interpreted in everyday research in a realistic manner. This is because, according toprevailing scientific understandings, the models represent knowledge generatedmethodologically about a domain of ecological reality. In order to avoid theconfusion caused by this situation, one should explicitly distinguish between theoperations related to the construction of systems and the interpretation of thoseoperations as models; this rarely happens, however. What we are left with areidealizing abstractions on the one hand and concretizing interpretations on the other.

If no ontological distinction is made between the real and the ideal world (forexample, by interpreting the ideal world as a mere reflection of the real one – or viceversa), then the meaning of abstractions cannot be properly comprehended. In thisrespect, the understanding of model construction held by analytical realism isontologically unsatisfactory. Within systems discourse, however, an analyticalrealism can certainly be justified epistemologically: According to this perception,systems are models of real phenomena limited by time and space. It is the differencebetween model and reality, the modelling relationship, which becomes the keyepistemological question. Is it even possible to conceive of and define “reality”without models?

In order to avoid systems terminology, one can designate the “reality” to bemodelled as a “spatio-temporal context of phenomena”, as a “specific area ofexperience”, as a “specific unit of investigation”, or as a “part of reality”. Theseformulations all contain elements of a realistic ontology, which holds that a thing-in-itself can be directly accessed as an object of empirical and theoretical insight. Thecritical question of whether the object of investigation is given naturally or whetherit is constructed as an epistemic object within systems discourse is rarely posed. Wemaintain the position that modelling constitutes a specific class of “epistemicobjects”: An ecological context is observed and described as if it was a system;whether or not it exists ontologically as such need not be decided. This situationbecomes clearer if one compares different ways of observing and describing the“same” object, such as, for example, in one case as “landscape” – in the other asecosystem. This level of reflected understanding goes beyond a constructivist“nominalism”. “System” is not merely a name for a methodologically generatedabstraction; systems are models of knowledge about ecological issues. This positioncan be called model-based constructivism. However, it can only be adoptedseriously if systems are regarded as abstract objects in an ideal world. These objectsmay be of a logical mathematical kind, and can be implemented, at least in principle,in a computer programme; graphic, metaphorical and conceptual models, as far asthey represent complex networks of interaction, can also be considered as idealobjects in this sense.

4. A Genealogy of Systems Concepts

Conceptual ambiguity and confusion are always prevalent when one not onlyfocuses on individual organisms, but also considers larger “syn-ecological units”

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(populations, animal or plant associations, communities) that are comprised ofindividual organisms. Do the complex relationships between individual organismsexhibit characteristics that the individuals themselves do not possess? And can these“syn-ecological units” themselves be understood as “living systems”? Taking theindividual organism as a starting point, it follows, by analogy, that syn-ecologicalunits would necessarily be seen as a kind of “super-organism”. Taking the system asa starting point, however, syn-ecological units would have to be conceived of asemerging systemic levels, not of a super-organism but rather taking the form of ahierarchically organized system. The problems raised here feed into a fundamentalcontroversy over whether organisms and syn-ecological entities can even beanalysed adequately at all using the concepts and methods developed within systemstheory discourse.

Numerous controversies exist over the systems concept best suited to ecology.These controversies appear to exist independently of the question of principleconcerning the ontological and epistemological status of ecological systems. Ingeneral, the dispute has focused on the definition of the concept of ecosystem per se(Breckling & Müller 2003). This dispute can be comprehended particularly well ifone examines the way in which ecological discourse and systems discourse arelinked together by the concept of “living systems”. This enables the developmentaltrajectories of different systems concepts to be traced and their genealogies mapped.What comes to light in the process are a number of notable conceptual differencesbetween the various systems ecologies. In ecology, all the entities between which arelationship exists are called an ecological system. Such a system may also comprisethe relationships between individual organisms and other entities in theirenvironment. A spatio-temporally localized biocenosis, i.e. a community oforganisms, together with its abiotic context, is called an ecosystem. This notionsometimes expresses a naïve view of systems ontology in terms of what we havecalled image naturalism; more frequently, however, it goes hand in hand withanalytical realism. It might be possible to argue for a type of systems metaphysicsusing this approach, but no systems theory in the modern scientific sense can beconstructed on this basis. It is only when the relationship between model and realityis reflected upon that an analytical understanding of the system can be achieved. Allserious systems concepts are therefore analytical by nature. In the version of model-based constructivism for which we are arguing here, the difference between modeland reality constitutes the starting point for systems theoretical reflection.

We neither wish nor are we able to present here a complete genealogy of modernsystems thinking in its entirety. Even if one were to restrict oneself to biology andecology alone, such a genealogy would be confusing enough on account of beingclosely linked with philosophical controversies and the advancement of biologicalknowledge. In natural scientific systems discourse of the late nineteenth and thetwentieth century, a variety of distinct systems concepts and understandings weredeveloped and set up against one another. Nevertheless, serious attempts to order,classify, assess and synthesize heterogeneous systems concepts were undertakenearly on within this discourse (Klir 1972). Ordering attempts using classical pairs ofopposites (such as realist/nominalist, concrete/abstract, real/ideal, material/formal)

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predominated. However, it was frequently unclear if a distinction was being madebetween different systems concepts or between different types of systems. A morefruitful approach appears to us to consist in arranging all the different variants of ageneral systems concept not in terms of pairs of opposites but rather in terms of thebasic distinction that goes with each variant. While each basic distinction impliesdifferent specific limitations, it also implies distinct ontologies and epistemologies:

• One common conceptual strategy originates from the distinction betweensystem and environment. A pattern of interaction is defined as a system andis thus separated off from the surroundings in which it is embedded. Thisdistinction can be traced more or less as far back as Plato. The moderngenealogy of this concept began in the 1930s when organisms were definedas thermodynamically open systems in a flow equilibrium. This was,notionally, a physical model, which Prigogine and others were later toelaborate in relation to nonlinear flows, introducing the systems concept ofa “dissipative structure” in the context of thermodynamically irreversibleprocesses (Glansdorff & Prigogine 1971, see also Prigogine & Stengers1981). The “system” was originally characterized as a black box with aninput, throughput and output of materials and energy. The relationshipbetween input and output can then be described in functional terms on thebasis of the system’s transformational functions. This is known, therefore,as a functional systems concept.

• Classical cybernetics pursues a different conceptual strategy. In this case, adistinction is made between regulation and disturbance. According to thecybernetic view, systems are units of regulation which, on account ofpositive and negative feedback loops (“circular causality”) as well ascommunication networks, are operationally closed. This enables them toreact to external and internal disturbances. The distinction implied here isone between system components and system states. Classical cyberneticsexamines changes of states in systems with structurally stabilizedcomponents. This can be called an operative systems concept.

• Another conceptual strategy was elaborated within nascent systems theoryafter World War II. This strategy is based on the distinction betweenelement and relation. Systems are defined abstractly as sets of elements,above which sets of relations exist (Hall & Fagen 1956). Such anunderstanding involving the theory of sets is based on a structural conceptof the system and introduces, in true Platonist style, the greatestconceivable abstraction: systems are defined as genuine mathematicalobjects, that is, as sets of related objects that can therefore, in principle, beisolated.

The different conceptual strategies give rise to genealogical lineages thatsometimes run in parallel but repeatedly intersect. New concepts may originate fromthese points of intersection. One such concept is “autopoiesis” (Maturana & Varela1987), in which “living systems” are defined as being materially and energeticallyopen, but operationally closed. All the system’s elements and the relations betweenthese elements are generated by internal operations. In ecology one finds variations

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of all the various distinctions and conceptual strategies and therefore also a range ofsystems ecologies based on very different conceptual foundations. In the researchcontext, these different systems ecologies can be drawn upon constitutively tovarious degrees by different sub-disciplines – providing another starting point forcriticism. Just two examples will be mentioned here. In their standard textbook,Begon et al. (1986) generally avoid the concept of ecosystem, preferring the notionof relationships between individuals, populations and communities that can beinterpreted both qualitatively and formally. In contrast to this, Odum (1983) placesthe concept of ecosystems at the center of ecology and focuses on energy flows asthe key unifying measure.

With the exception of naïve image naturalism, one can detect a certain proximitybetween the different conceptual strategies identified here and analytical realism onthe one hand and constructivist nominalism on the other. The functional systemsconcept is largely interpreted realistically in ecology. In contrast to this, sociologicalsystems theory advocates a programme of de-ontologization using a radicallyconstructivist epistemology by generalizing the system/environment distinction.5

The operative systems concept developed in cybernetics balks at a realistinterpretation because it abstracts from the material realization of the system.Second-order cybernetics attempts to establish a radical epistemologicalconstructivism. The structural systems concept can be interpreted in either realist orconstructivist terms. In a realist interpretation, however, “set” is not understood inthe strict mathematical sense but rather as a diverse array of concrete objects. In aPlatonically inspired constructivist interpretation, which we prefer here, systems areabstract objects in an ideal world.

5. Concept Transfers

The dispute between realist and constructivist positions was understood for a longtime as a debate over the empirical content of General Systems Theory (GST).6 Thelatter was viewed first as a general theory of very different systemic contexts - as ageneral theory of physical, organic, psychological and social “systems”. This is stillclaimed to be the case in systems philosophy, although it has been disproved inpractice. Methodologically speaking, GST provides numerous ways of formalisingnetworks of interaction; however, GST methods are simply not capable of capturingthe structurally variable networks appropriate to describing the complexity and 5 This approach attempts to define all existing concepts in terms of operations and to relatethem strictly to “communication” as a point of both departure and of reference (Luhmann1997). Whether or not this has led to a renewal of sociology’s explanatory foundations, asclaimed by its adherents, has been the subject of heated debate for a number of years (cf.Merz-Benz & Wagner 2000, Clam 2002).6 In 1950 Carl G. Hempel had already rejected the empirical relevance of GST andlabelled it as “a branch of pure mathematics” (Hempel 1951, p. 314-15). In later works hethen argued against simulation methods, against the functional explanation, againstsuggestions of isomorphism, and against the emergence thesis (Hempel 1965). Müller 1996(p. 245ff.) provides a summary of the dispute over the empirical content and explanatorypower of GST.

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variety of “living systems”. Structurally variable networks are used in the context ofobject-oriented modelling, for example, as a way of representing networks ofinteraction between individuals that are temporally, spatially and structurallyvariable (individual-based modelling) (deAngelis & Gross 1992, Breckling 2004).

Bertalanffy had originally conceived of General Systems Theory as a system ofordinary differential equations. However, although GST was applied in this form toorganic, psychological and social systems, it achieved only modest success. Only byextending the theory to include systems based on non-linear, partial differentialequations is it possible to formalize the emergence of organizational patterns and ofemerging, self-organizing structures and differentiation processes. Turing raised thispossibility in 1952 in the context of chemical morphogenesis, and the approach wastaken further by Gierer (1972) and Meinhard (1982).

However, all of this does not necessarily lead to the oft-cited conclusion thatGST has failed as a theory and that it can only be employed as a meta-theory or as asystems philosophy. What has failed, however, is GST’s claim to universality and,along with this, its ambition to unify science. Thus far, no mathematical model hasbeen found that is applicable to all empirical sciences – nor, presumably, will oneever be found. The endeavour to develop a general empirical theory for vastlydifferent areas of reality has also failed. Systems science gave up on both of theseattempts at generalisation long ago. In this respect, criticism has yielded success.Where these claims to generality continue to be attacked, criticism is directed eithertowards certain visionary philosophical exaggerations or towards an object inhistory; it has no relation to contemporary scientific practice. Nevertheless, oneendeavor that remains is the pursuit of empirically oriented systems research in verydifferent spheres of reality, as well as the search for adequate integrative conceptsand mathematical models. During the course of its ongoing development, GeneralSystems Theory has dissolved into a multiplicity of specialised systems sciences,and it continues to exist in the form of a heterogeneous discourse with pronouncedontological and epistemological contradictions.

By contrast, however, another aspect of early systemic self-understandingproved to be highly successful in methodological terms: General Systems Theory isa field of concept transfers and possesses an arsenal of ideal systems models. Thefounding fathers – especially Ludwig von Bertalanffy and Anatol Rapaport –justified the possibility of such transfers by pointing to the existence ofisomorphisms in the empirical sciences. They also recognized the methodologicalimportance of systems theory in stimulating concept transfers and monitoring themmethodologically. Metaphors and analogies play an important heuristic role in thisprocess. Thus far, little research has been carried out with regard to exactly what istransferred from one field to another in a concept transfer – and whatepistemological consequences can be expected to follow. Early General SystemsTheory emphasized the formal structural similarity of laws and thus concluded thatprinciples and models could be transferred.

Nevertheless, this sort of transfer is in no way innocuous because, along with theprinciples and models, theories and concepts are also transferred, and this is exactlyhow new epistemic objects are constituted. The phenomena of one field come to be

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regarded as if they structurally resembled those of another field. Moreover, atransfer of principles always denotes a similar transmission of categories from onerealm of a being to another, for example from organisms to machines, or fromecosystems to cities – or vice versa. The transfer of models may involve atransmission of model structures as well as a transmission of modelling techniques.If concept transfer is differentiated in this way, different premises, problems andmistakes come to light – as, indeed, do interesting solutions. Similarly, though,criticism of concept transfers should also be differentiated – something that rarelyhappens. It makes a difference whether concept transfer is viewed from a realistic ora constructivist perspective. In the one case, the existence of strong isomorphismsmust be assumed, and in the other, concept transfer adds to the arsenal of logical-mathematical objects that can be used as models.

6. Systems as Objects in an Ideal World

It is sometimes questioned whether mathematics can be applied to the highlycomplex phenomena of biology, the psyche, society or history. Despite significantrefinements, say the doubters, current mathematical tools are not yet up to the taskof addressing the demands posed, say, by hydrodynamics, subatomic particlephysics and cosmology (Castoriadis 1981, pp. 178f.). The special feature of biologyand sociology is not only the complexity of their objects but, above all, thepeculiarity and structural variability of the various relationships involved, as well asthe specific character of their processes. Even very high levels of complexity can behandled mathematically, though. Moreover, mathematics is not simply an“instrument” of empirical science but rather, a theory of abstract objects andrelationships. Despite the skepticism that exists regarding the performance ofmathematics in its current stage of development, scarcely anyone concludes thathydrodynamics, subatomic particle physics or cosmology cannot be represented inmathematical terms. However, such conclusions are put forward time and time againin relation to biology and ecology. To us, it seems more productive to make use ofadvances in mathematics and of the many mathematical - i.e. formal - approachesthat are already well-known for the benefit of ecology. This could help in theprocess of identifying and filtering out coherent elements and patterns from amongthe mass of details and data.7

Formalizations founded on set theory set in motion a powerful trend towardsabstraction. It becomes possible to abstract logical-mathematical systems objects,

7 In research practice, and especially in the analysis of ecological data, this is happeningmore and more. In landscape ecology, the methods of fractal geometry have maintained theirhold (Turner & Gardner 1994), while population ecology uses object-oriented modellingmethods (Breckling 2004). In ecological research, techniques such as Petri-Nets (Gnauck2001) are available. Techniques from the fields of machine learning and data mining areapplicable in structure identification and analysis of large data sets (Dzeroski et al. 1994,Dzeroski 1995). Admittedly, these techniques did not originate in pure mathematics; they do,however, utilize formal descriptions.

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such as partial differential equations, sets, graphs and topological structures, fromdescriptions of ecological circumstances. More recent computer-based modellingtechniques (cellular automata, genetic algorithms, etc.) are used to model thefeatures of systems with a large number of elements and relations (and thereforehigh numerical complexity). Attempts are regularly made, especially in popularrepresentations, to describe the properties of such logical-mathematical systemsobjects in words, using general principles. Hence, one reads: “Ecological Systemsare complex, hierarchical, dynamic and adapted to an environment.” This is how, bymeans of multiple concept transfer, new verbal languages emerge for describingecological circumstances: mathematical objects are interpreted using concepts froma biological context (cells, genetics, hierarchy, adaptation, self-organization, etc.)while descriptions of the dynamic behavior of these mathematical objects can thenbe used to describe ecological patterns. Mathematics becomes a system ofmetaphors.

Nevertheless, it is misleading to view mathematics as an exact “language” inwhich “the characters of the book of nature are written,” as Galileo Galileiconjectured almost 400 years ago. Pure mathematics is a system of signs andsymbols with which formal implications in abstract networks of relations can bediscovered and represented. It turns into a language only when it is interpretedsemantically as a model of an area of reality. The newly described circumstances canthen also be represented mathematically. Hence, metaphor can turn again intomathematics. The characteristics of a particular mathematical object which fulfilsthe criteria for self-organisation can be approximated in everyday language, andfrom these words a new, verbal language for describing ecological features can bederived. Such a language facilitates the emergence of new and unusual distinctionsand descriptions. It then becomes possible to clarify something that was previouslyshrouded in mystery (in this case, processes of self-organization).

7. Systems Theory as a Theory of Logical-Mathematical Objects

Between World War I and World War II, the ancient metaphysical scheme of partand whole was displaced in many fields of science as a result of the influence ofmathematical Set Theory (Cantor 1884), the theory of Logical Classes ofAbstraction (Frege 1893), the theory of Logical Types (Russell & Whitehead 1910),as well as quantum physics. The formal scheme of element/relation/system took itsplace. Thus, a development that had begun with Newton’s mathematical formulationof classical mechanics and the corresponding claim to universality reached itsclimax: the substitution of traditional substance metaphysics by an ontology ofrelations.

Although ecology was well prepared for this type of categorial change, it was notready for the processes of logical-mathematical abstraction. It was certainly ripe formodern systems thinking beyond atomism and metaphysical holism: since thesecond half of the nineteenth century, ecology has been concerned with concrete“relations” as causal patterns (connections, interactions, exchanges) betweenorganisms and their biotic as well as abiotic environment. In doing so, ecology hasfocused either on the related elements (for example, plants and animals) or on

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“patterns of relations” (for example, food chains, relationships of competition, formsof co-existence). Yet ecology’s systems concept remained realistic and biological:“populations” and communities (biocoenoses) describe actually existing ecologicalcircumstances; they represent the systemic character of the latter as supra-individualentities.

Only slowly and only through a process of concept transfer from GeneralSystems Theory did ecology adopt the presumptions of logical and mathematicalabstractions. In the 1950s (nearly fifty years after the foundational mathematicalworks of Cantor, Frege, Hilbert, Russell and Whitehead), the systems concept wasstrictly formalized. Using methods taken from set theory, Mesarovic (1972)attempted to summarize the different understandings of systems that werecirculating in his day (open and closed systems, multilevel systems, control anddecision-making systems, etc.) and to turn them into an axiomatic presentation.These understandings were strongly oriented toward cybernetic notions of systems.The most influential explanation of an abstract systems concept based on set theorywas that put forward by Hall & Fagen (1956). Their definition was short andconcise: “A system is a set of objects together with relationships between the objectsand between their attributes.” Pages?

In our view, this definition is the most significant conceptual innovation in thegenealogy of systems discourse: even today, it is still capable of unravelling thetangle of errors found there. Once the systems concept had been explicated using settheory, this opened the way for a construction of logical-mathematical systemsobjects. It linked systems discourse to the developments and insights of modernlogic, mathematics and meta-mathematics – including the fundamental questionsthese entail. The fact that such links can be fruitful has been acknowledged more incybernetics than in organism-based systems theory.

Hall and Fagen defined systems in a completely abstract way as a set ofdistinguishable elements between which a set of distinguishable relations exists.Systems defined in this way do not constitute anything real; instead, they are classesof abstraction. The “elements” of an abstract system are not identical to the actual“individuals” in a real sphere of reality. A “system”, as defined by set theory,contains no hares or foxes, no beeches or oaks – nor does it contain any people. Atbest, certain characteristics selected by the defining criterion might appear in thesystem – and even then only in abstract form. This is because in modern set theory“elements” of a system are no longer defined by real objects, but rather by thequalities of similar classes. Two classes qualify as “similar” if an unambiguousrelation exists between them. In the set theory definition of a system, the “elements”that are defined by abstraction classes are only of interest insofar as they constitute a“system-like” context.8 The circularity of the definition is avoided when theelements are determined by the classes of relations that exist between them. In otherwords, systems are related sets. 8 The Lotka-Volterra equations from the late 1920s applied this principle – and Verhulst’s1838 growth equation from the mid-1800s anticipated such a formalization. Set Theoryprovides a consistent basis for the possibility of mathematically representing specificconnections between related entities.

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If one follows the path laid out by the abstract systems concept expounded by settheory, one leaves behind the actual reality of ecological circumstances and entersan ideal world of abstract objects. Systems exist in this world alone. The set theoryexplication and associated processes of abstraction make it possible to conceive ofsystems through the formal means of logic and mathematics (for example, throughthe logic of relations, through systems of interconnected differential or differenceequations, through topological patterns, through graphs or networks). As a result,systems discourse gives rise to an ideal world of logical-mathematical systemobjects. This ideal world is undoubtedly a human creation and no divine revelation.However, once it has been created through the work of abstraction, the objectswithin it exist – just like Platonic forms – eternally. The only condition for theexistence of these timeless objects is that they be free of inner contradiction and thatthere be a logical or quantitative link between the different objects. The ordering ofsystems objects in an organized network of logical connections is continuouslythreatened, however, by the fact that the absence of contradiction cannot easily beproven. Gödel (1931) used a study of number theory to provide formal proof of thefact that no sufficiently complex logical or mathematical system can simultaneouslybe complete and free of contradiction. This is because systems always containstatements, whose degree of truthfulness cannot be decided using the resources ofthe system itself. A system can either be complete or free of contradiction, but notboth. Thus, in the ideal world of abstract objects, ideas exist whose truth or falsenessremains unknown.9 Human activity creates eternal objects in the ideal world, andlogical contradiction accounts for their mortality.

For ecology it is perfectly natural to be able to call concrete entities such as frogponds or forests “systems” and to be able to describe their systemic characteristicsverbally or graphically. Such descriptions may then be used to generate systems inthe strict, abstract sense. This is because it is always possible in principle to find aset of objects and a set of relationships that, in the sense of intuitive set theory, forma “whole”. However, applying the term “system” to the description of anybiocoenotic context always brings with it the danger of reification: systemsgenerated through abstractions are then confused with real frog ponds and forests,and statements about the qualities and dynamics of mathematical systems objects aremisunderstood as statements about real circumstances; this then provokes thecomplaint that abstract systems are not concrete.

In order to reduce the confusion caused by reification and conceptual ambiguity,we propose that use of the term “system” should be restricted to logical-

9 One can illustrate a related scenario in hydrobiology: Fish can be organized in twocategories: those that are cannibalistic and eat their own kind if they happen to becomeaccessible, and those that do not do this. And then there are species-specific trophicpreferences. There may be a category of predatory fish that feeds only on those other fish thatdo not consume their own fry. What would a fish of that category do if one of its ownoffspring appeared in front of it? Would it snap at it? This setting is an ecological disguise ofRussell’s famous barber paradox. The poor fish cannot take up either option withoutbecoming entangled in a net of contradictions – consuming its fry would violate the conditionof not consuming it, and not consuming it would qualify the fry for consumption...

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mathematical objects and strictly distinguished from real circumstances. A similarargument is made whenever a clear distinction is made in ecology between a modeland the reality represented. If these objects conform to the systems definition givenby set theory, they can be called mathematical systems objects. Systems theorywould thus become a theory of abstract logical-mathematical systems objects. Wedoubt that it will ever be possible to develop a general theory for all potentialsystems objects. What would be the substance of a theory which encompasses notonly systems of partial differential equations but also neural networks, cellularautomata, fractals, chaos theory and all manner of other phenomena? Such a theorywould presumably be just as broad and general as Hall & Fagen’s (1956) set theoryexplanation of systems concepts – and correspondingly lacking in substance as well.

8. Modelling as an Interpretation of Logical-Mathematical Objects

As far as systems research and ecology are concerned, a theory of mathematicalsystems objects is relevant to practical research only if it can be connected withecological issues of practical relevance. Thus, it is wise to treat the relationshipbetween system and reality in the same way as that between mathematics andphysics: mathematical objects can be used to generate a descriptive language forphysical objects because their components (terms, operators, functions, etc.) can begiven semantic substance, in other words, they can be made into referents for thecharacteristics of physical objects. The same procedure is largely followed inecological modelling.

An elegant procedure was developed for this situation in Einstein’s theory ofrelativity and in quantum theory: reference to reality is secured through amathematical description of observables and thus through mathematical expressionsfor measurable variables. Modern physics is thus a science of the measurable world.Similarly, it is possible to relate abstract systems objects to ecologicalcircumstances. For example, the abstract variables in the Lotka-Volterra differentialequation can be interpreted in the context of population ecology. Nevertheless, thequestion remains as to how the particular population-ecological variables canactually be observed. It is common to use counting methods to determine populationsizes empirically, although this says nothing about the interrelations that existbetween different organisms. In predator-prey models, for example, theseinterrelations appear in the form of rates, which are derived from changes inpopulation sizes over time.

For the purposes of ecology, models emerge in this way that represent complexstructural hypotheses, and these can, in turn, be tested empirically. The abstractmathematical systems object is therefore interpretively connected with a concretephysical or ecological object. This object may be a technical artifact (a thermostat, aservo mechanism…) or a natural context (populations of hares and foxes in alandscape). In the same manner, cybernetics attempts to construct technicalrealizations of mathematical systems objects (for example, electrical circuits forBoolean algebra and for logical operations, analogue computers for mathematicalfunctions, etc.). However, this does not mean that logical-mathematical systems

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objects are merely abstractions of technical objects. Certain systems objects can betechnically implemented; others are substantiated biologically.

In systems research there is frequently no strict distinction between a logical-mathematical systems object and its practical representation by a physical ortechnical object. Thus, it often happens that physical objects (for example, acompound pendulum or a diffusion process) or technical objects (such as athermostat) are used directly as a model for other types of objects, without thesystems object having first been represented mathematically in an abstract form.This implicitly sets up a structural similarity between the physical object and theecological context under examination, a supposition that can lead to familiarphysicalistic errors. Certain epistemological interests may be subtly reinforced inthis way and may shape the process of model construction. One example of thiswould be to plan and design landscapes or conservation areas in terms of matter andenergy flow models in order to fulfill politically motivated environmentalobjectives. Such technocratic notions are subject to criticism in ecology, and rightlyso.

Acknowledgement

We would like to thank Joseph Wilde-Ramsing and Birka Wicke, who provided abasic translation of the German manuscript to English.

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