## K

Figure 7.5 Sketch of the dynamics of ecosystem variables on two scales, both variables are influenced by the disturbances (A and B) with different magnitudes (C and D) and durations (H and J), and both variables are due to orientor dynamics during the phases G, I, and K. The development of the fast variable shows a high variance, which can be averaged to the slow dynamics. The long-term effects of the disturbances A and B can be distinguished on the basis of the orientor differences E (reduced resilience and recovery potential) and F (enhanced potential for resilience and recovery).

to change instead of evaluating a system due to its potential to return to one defined (non-developmental and perhaps extremely brittle) state. A good potential seems to lie in the concept of resilience, if we define it as the capacity of a disturbed system to return to its former complexifying trajectory (not to a certain referential state). Therefore, the reference situation (or the aspired dynamics of ecosystem management) would not be the static lines in Figure 7.5, but the orientor trajectory t. Similar ideas and a distinction of stability features with reference to the systems' stability are discussed in Box 7.3.

Box 7.3 Stability is related to uncorrelated complexity: After Ulanowicz (2002a,b)

Summary: The complexity of the pattern of ecosystem transfers can be gauged by the Shannon-Weaver diversity measure applied to the various flows. This index, in turn, can be decomposed into a component that refers to how the flows are constrained by (correlated with) each other and another that represents the remaining degrees of freedom, which the system can reconfigure into responses to novel perturbations. It is the latter (uncorrelated) complexity that supports system stability. Development: In order to see how system stability is related only to part of the overall system complexity, it helps to resolve the complexity of a flow network into two components, one of which represents coherent complexity and the other, its incoherent counterpart (Rutledge et al., 1976.)

Prior to Rutledge et al., complexity in ecosystems had been reckoned in terms of a single distribution, call it p(a). The most common measure used was the Shannon (1948) "entropy,"

Rutledge et al. (1976) showed how information theory allows for the comparison of two different distributions. Suppose one wishes to choose a "reference" distribution with which to comparep(a). Call the reference distributionp(bj). Now Bayesian probability theory allows one to define the joint probability,p(a, bj), of at occurring jointly with bj. Ulanowicz and Norden (1990) suggested applying the Shannon formula to the joint probability to measure the full "complexity" of a flow network as,

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