Discontinuous change in multilevel hierarchical systems

Abstract

Benjamin Franklin, Feb. 1735, Poor Richard's Almanack[20]. I IntroductionThis paper will investigate the phenomenon of discontinuous change in multilevel hierarchical systems, especially interacting ecological-economic systems. In so doing we hope to shed light on both the functioning of hierarchical systems in general and the peculiarities of the interaction between ecological and economic systems in particular. The normal pattern in hierarchies is for higher levels to act as constraints upon lower levels. It is widely argued that this involves higher levels operating on a slower time frequency of oscillation [3,p.30] .' Thus they "slave" the more rapidly oscillating lower levels in the manner described in the synergetics theory of Haken [25,67] But on occasion this normal pattern is upended. A discontinuous change at a lower level triggers a discontinuous change at a higher level. This is the "revolt of the slaved variables"[ 161 and can become the source of a profound systemic transformation throughout the hierarchy. Ecologic-economic systems are widely characterized by multilevel hierarchies in their structure. Levels each have their own time and space scales [43] with the lower tending to be shorter and smaller in space, although there may be exceptions or complications to this.' Gunther and Folke [24] argue that living systems are characterized by a nested embeddedness, as with the organism containing the cell as a constituent part. They call such systems holarchic in order to distinguish them from hierarchies in which lower level elements are not the actual constituents of the higher level ones, as with soldiers and their commanding officer^.^ Each level of a hierarchy can be conceptualized according to its own cyclical dynamical pattern, according to Simon's[57] principle of the "near decomposability of hierarchies." For ecosystems such dynamics may be modeled according to the Holling[28] "4-box" construct. In this model there are successive stages of exploitation, conservation, release, and reorganization. An example is a subsystem of a forest passing through succession, reaching a climax state, collapsing, and being regenerated. Similar cycles occur for the leaves of the forest, but much more rapidly as a lower level of the ecological hierarchy. Although there are some difficulties with the analogy, economic cycles can sometimes be characterized by four stages, the boom, peak, recession, and trough of the classic macroeconomic business cycle.4 Holling [29] has argued that a systemic transformation is most likely to occur within a given level just as reorganization is about to move into exploitation or growth. We suggest here that such a structural break can also occur at the point that the highly conserved system is about to break down in a release. At such junctures disjunctions can occur leading the system to become something else. The former can be thought of as a case of order emerging out of chaos whereas the latter may be just the opposite. In both cases there may be a systemic leap to a new c...

Departures from Gibrat's Law, Discontinuities and City Size Distributions

“…A relative lack of transport infrastructure may encourage the concentration of population in Australia into a few very large cities on a regional basis (Ades and Glaeser, 1995). Rossi-Hansberg and Wright (2004) state that, in order to generate Zipf's law, growth processes at the city level must be scale-invariant. They claim that this is possible via two scenarios: one where the current productivity shocks are the only stochastic force in growth, and are permanent, producing permanent increases in the level of the marginal product of labour, so that the growth rate of the marginal product is independent of scale.…”

Emergence and complexity in Austrian economics

“…This is implied in the evolutionary history of the universe from sub-atomic particles in physics that aggregated into atoms, then later into chemical molecules, then into more complicated organic molecules, into life, into multi-cellular organisms, 7 and so on. This process of the emergence of entirely new levels has been labeled anagenesis by Boulding (1978) and Jantsch (1979), and has been analyzed by Rosser et al (1994). Such processes exhibit not only emergence, but at the biological and social levels involve complex evolutionary processes, much as in the view of the British emergentists, a theme covered more fully below.…”

Ecological, Economic, and New Synthetic Perspectives in Range Management: An Interpretative Essay

“…Second, an implication of the work of Rosser et al (1994) and Carpenter and Gunderson (2001) is that a successful range manager will need to comprehend the connections between slowly changing variables -such as evolution and sediment diagenesis -and faster variables that are typically of concern to humans. Even though slowly moving variables make prediction possible, the self-organizing properties of ecological-economic systems such as rangelands cause uncertainty about them to grow.…”