A SUMMARY OF THE PRINCIPLES OF HIERARCHY THEORY

The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.

Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:

Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.

Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.

The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.

The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of - lower levels.

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

Duality in hierarchies: the dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole. Arthur Koestler in his "Ghost in The Machine" referred to the notion of holon, which means an entity in a hierarchy that is at once a whole and at the same time a part. Thus a holon at once operates as a quasi-autonomous whole that integrates its parts, while working to integrate itself into an upper level purpose or role. The lower level answers the question "How?" and the upper level answers the question, "So what?"

Constraint versus possibilities: when one looks at a system there are two separate reasons behind what one sees. First, it is not possible to see something if the parts of the system cannot do what is required of them to achieve the arrangement in the whole. These are the limits of physical possibility. The limits of possibility come from lower levels in the hierarchy. The second entirely separate reason for what one sees is to do with what is allowed by the upper level constraints. An example here would be that mammals have five digits. There is no physical reason for mammals having five digits on their hands and feet, because it comes not from physical limits, but from the constraints of having a mammal heritage. Any number of the digits is possible within the physical limits, but in mammals only five digits are allowed by the biological constraints. Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility. Forget the distinction, and biology becomes pointlessly confused, impossibly complicated chemistry, while chemistry becomes unwieldy physics.

Complexity and self-simplification: Howard Pattee has identified that as a system becomes more elaborately hierarchical its behavior becomes simple. The reason is that, with the emergence of intermediate levels, the lowest level entities become constrained to be far from equilibrium. As a result, the lowest level entities lose degrees of freedom and are held against the upper level constraint to give constant behavior. Deep hierarchical structure indicates elaborate organization, and deep hierarchies are often considered as complex systems by virtue of hierarchical depth.

Complexity versus complicatedness: a hierarchical structure with a large number of lowest level entities, but with simple organization, offers a low flat hierarchy that is complicated rather than complex. The behavior of structurally complicated systems is behaviorally elaborate and so complicated, whereas the behavior of deep hierarchically complex systems is simple.

Hierarchy theory is as much as anything a theory of observation. It has been significantly operationalized in ecology, but has been applied relatively infrequently outside that science. There is a negative reaction to hierarchy theory in the social sciences, by virtue of implications of rigid autocratic systems or authority. When applied in a more general fashion, even liberal and non-authoritarian systems can be described effectively in hierarchical terms. There is a politically correct set of labels that avoid the word hierarchy, but they unnecessarily introduce jargon into a field that has enough special vocabulary as it is.

A SHORT ANNOTATED BIBLIOGRAPHY OF HIERARCHY THEORY.

This bibliography is in chronological order, so that the reader can identify the early classics as opposed to the later refinements. If you must choose just one book to read, turn to the last reference in this bibliography, Ahl and Allen, 1996. Simon, H.. A. 1962. The architecture of complexity. Proceedings of the American philosophical society 106: 467-82. This is the foundation paper of hierarchy theory originating from an economist. It was a re-published in "Sciences of the Artificial" by Simon. It introduces the idea of near-decomposability. If systems were completely decomposable, then there would be no emergent whole, because the parts would exist only separately. The "near" in near-decomposable allows the upper level to emerge from the fact that the parts anre not completely separate.

Koestler, Arthur. 1967. The ghost in the machine. Macmillan, New York. This is a long hard look at human social structure in hierarchical terms. The notion of holon first occurs in this work. This is a classic work, but is easily accessible to the lay public.

Whyte, L.. L.., A. G. Wilson and D. Wilson (eds.). 1969. Hierarchical structures. American Elsevier, New York. This is a classic collection of early scholarly works by some of the founders of hierarchical thinking.

Pattee, H.. H. (ed.) 1973. Hierarchy theory: the challenge or complex systems. Braziller, New York. This edited volume has some classic articles by Pattee, Simon and others.

Allen, T. F. H. and T. B. Starr. 1982. Hierarchy: perspectives for ecological complexity. University Chicago Press. This book has a significant ecological component but is much more generally about hierarchical structure. It is abstract and a somewhat technical treatment but has been the foundation work for the application of hierarchy theory in ecology and complex systems theory at large.

Salthe, S. 1985. Evolving Hierarchical Systems: their structure and representation. Columbia University Press, New York. This book has a strong structural bias, in contrast to the process oriented approach of Allen and the other ecologists in this bibliography. Salthe introduces the notion of the Triadic, where there is a focus on 1) the system as both a whole above the levels below and 2) a part belonging to another level above, 3) not forgetting the level of the structure itself in between. While much biological hierarchy theory takes an anti-realist point view, or is at least reality-agnostic, wherein the ultimate reality of hierarchical arrangement is left moot, Salthe's version of hierarchy theory is concerned with the ultimate reality of structure. The anti-realist view of structure is that it is imposed by the observer, and may or may not correspond to any ultimate reality. If structure does correspond to ultimate, external reality, we could never know that to be so. Salthe's logic is consistent but always takes a structural and ontological position.

O'Neill, R. V., D. DeAngelis, J. Waide and T. F. H. Allen. 1986. A hierarchical concept of ecosystems. Princeton University Press. This is a distinctly ecological application of hierarchy theory, making the critical distinction between process functional ecosystem approaches as opposed to population and community relationships. It is an application of hierarchy theory to ecosystem analysis.

Allen T. F. H. and T. Hoekstra. 1992. Toward a unified ecology. Columbia University Press. This book turns on hierarchy theory, but is principally a book about ecology. It goes beyond the O'Neill et al book, in that it makes the distinction between many types of ecology (landscape, ecosystem, community, organism, population, and biomes) on the one hand, and scale of ecology on the other hand. It ends with practical applications of hierarchy theory and ecological management.

Ahl, V. and T. F. H. Allen. 1996. Hierarchy theory, a vision, vocabulary and epistemology. Columbia University Press. This slim a volume is an interdisciplinary account of a hierarchy theory, and represents the shallow end of the pool. It is the primer version of Allen and Starr 1982. It is full of graphical images to ease the reader into a hierarchical perspective. It makes the distinction between levels of organization and levels of observation. It takes a moderate anti-realist point of view, wherein there may be an external reality, but it is not relevant to the discourse. We only have access to experience, which must of necessity involve observer values and subjectivity. There are examples from a wide discussion of many disciplines. Included are examples from psychology, ecology, the law, political systems and philosophy. It makes reference to the global and technological problems facing humanity, and offers hierarchy theory as one tool in the struggle. The summary of hierarchy theory in the opening paragraphs above comes from this book.

This summary was compiled by

Timothy F. Allen, Professor of Botany,
University of Wisconsin Madison,
Madison Wisconsin 53706 -- 1381.
Email - tfallen@facstaff.wisc.edu