Networks and Hierarchies
From Networks and Hierarchies: Approaching Complexity in Evolutionary Theory
The natural world is infinitely complex and hierarchically structured. Hierarchy theory is an approach to understanding the way complex systems work by identifying levels of organization and their relationships in the context of scaling. In a broad sense, a system is a network of functionally interdependent and structurally interconnected components comprising an integrated whole. The complexity arises from intricate, nonlinear interactions of a large number of parts that such systems have, where the whole is more than the sum of its parts: That is, given the properties and the laws of interactions of parts, it is not a trivial matter to infer the properties of the whole.
Coining the term “hierarchy” is attributed to Pseudo-Dionysius the Areopagite, a philosopher and a theologian of the late fifth–early sixth century, who used the Greek word εραρχ α (“rule by priests”) in reference to ranks of celestial beings and ecclesiastical power in early Christian church (Hathaway 1969). Despite its narrow original meaning, hierarchical organization can be recognized in almost every system in the world from the structure of the natural world to all the domains of human life. Hierarchies are manifest in the physical composition of natural and artificial objects, engineered mechanisms, genealogical relationships, classification schemes, and socioeconomic organizations. The relative arrangement of levels and the nature of their interactions vary greatly depending upon the specific kind of hierarchy considered.
That hierarchy is a key structural principle of biological systems was first recognized by Woodger (1929), whose work influenced the development of hier- archical approaches across biological disciplines (e.g., Hennig 1950, 1966; Pattee 1973; Whyte 1969). In biology, the concept of hierarchy acquired a plethora of disparate meanings ranging from the descriptions of organization of knowledge to models of functional interactions of living systems to taxonomic classifications. The pervasiveness of hierarchies in nature was amply captured by Francois Jacob’s maxim, “every object that biology studies is a system of systems” (Jacob 1974).
Biological evolutionary theory is ontologically committed to the existence of nested hierarchies in nature and attempts to explain natural phenomena as a product of complex dynamics of real hierarchical systems. Consistent with the general tendency of complex systems to attain and remain in equilibrium, living systems display remarkable metastability despite non-equilibrial dynamics at all levels of organization triggered by extrinsic disturbances, suggesting that hierarchical systems have some common properties that are independent of their specific content and can be applied across physical, biological, or social sciences.
2.2 Hierarchical Dynamics
Two major types of interactions can be distinguished in a hierarchy: within and between levels. Entities at a given level interact directly with each other in the same dynamic process, whereas entities at different levels only interact in an aggregate fashion (Eldredge and Salthe 1984). The differences in the dynamics of processes between versus within levels ultimately arise from scalar differences (frequently of different orders of magnitude) in process rates, yielding a distinction between strong interactions with high-frequency dynamics within levels and weak interactions with low-frequency dynamics among levels (Simon 1962, 1973). Such non-transitivity of direct effects across levels (Salthe 1985) establishes the levels as quasi-independent (“nearly decomposable” sensu Simon 1962) systems allowing for investigating dynamics of individual levels on their own right (Bunge 1979; Levins 1970). Consequently, the details of within-level interactions can be ignored when considering between-level dynamics (Simon 1962). Scalar differences are also responsible for weaker integration of more inclusive units and weakening the strength of interactions at successive, higher levels of a hierarchy, making it more difficult for the investigator to draw boundaries around and characterize these units from the epistemological standpoint.
Key Sources of Research:
Networks and Hierarchies: Approaching Complexity in Evolutionary Theory
Ilya Tëmkin and Niles Eldredge
“Networks: between markets and hierarchies.”
Thorelli, Hans B.
Strategic management journal 7.1 (1986): 37-51.
Boundaries, Hierarchies and Networks in Complex Systems
COMPLEXITY RISING: FROM HUMAN BEINGS TO HUMAN CIVILIZATION, A COMPLEXITY PROFILE
Yaneer Bar-Yam, New England Complex Systems Institute, Cambridge, MA, USA
On the origins of hierarchy in complex networks
Bernat Corominas-Murtra, Joaquín Goñid, Ricard V. Solé and Carlos Rodríguez-Casoa
The Architecture of Complexity
Herbert A. Simon
Proceedings of the American Philosophical Society, Vol. 106, No. 6. (Dec. 12, 1962), pp. 467-482.
Self-organization, Emergence and the Architecture of Complexity