Now, it can readily be proved that C > A > 0, so that the residual, (C - A) > 0, as well. Subtracting A from C and algebraically reducing the result yields the residual, which we call the systems "overhead" as
I tl log j
I Tkj I Tiq
The overhead gauges the degree of flexibility remaining in the system.
Just as we substituted the values of the Cone Spring flows into the equation for ascendency, we may similarly substitute into this equation for overhead to yield a value of 79,139 kcal-bits/m2/year. Similarly, substitution into the formula for C yields a value of 135,864 kcal-bits/m2/year, demonstrating that the ascendency and the overhead sum exactly to yield the capacity.
The ecologist reading this book is likely to have a healthy appreciation for those elements in nature that do not resemble tightly constrained behavior, as one finds with autocatalysis. In fact, Chapter 3 was devoted in large measure to describing the existence and role of aleatoric events and ontic openness. Hence, increasing ascendency is only half of our dynamical story. Ascendency accounts for how efficiently and coherently the system processes medium. Using the same mathematics as employed above, however, it is also shown in Box 4.1 how one can compute as well an index called the system overhead, that is complementary to the ascendency and captures how much flexibility the system retains (Ulanowicz and Norden, 1990).
The flexibilities quantified by overhead are manifested as the inefficiencies, inco-herencies, and functional redundancies present in the system. Although these latter properties may encumber overall system performance at processing medium, we saw in Chapter 3 how they become absolutely essential to system survival whenever the system incurs a novel perturbation. At such time, the overhead comes to represent the repertoire of potential tactics from which the system can draw to adapt to the new circumstances. Without sufficient overhead, a system is unable create an effective response to the exigencies of its environment. The configurations we observe in nature, therefore, appear to be the results of a dynamical tension between two antagonistic tendencies (ascendency vs. overhead; Ulanowicz, 2006b). The ecosystem needs this tension in order to persist. Should either direction in the transaction atrophy, the system will become fragile either to external perturbations (low overhead) or internal disorder (low ascendency). System fragility is discussed further in Chapter 8.
One disadvantage of ascendency as an index of directionality is that its calculation requires a large amount of data. Currently, the networks accompanying a seres of ecological stages have not yet been assembled. About the closest situation for which data are available is a comparison of two tidal marsh communities, one of which was perturbed by a 6°C rise in temperature caused by thermal effluent from a nearby nuclear power plant, and the other of which remained unimpacted (Homer et al., 1976) Under the assumption that perturbation regresses an ecosystem to an earlier stage, one would expect the unimpacted system to be more "mature" and exhibit a higher ascendency than the heated system.
Homer et al. parsed the marsh gut ecosystem into 17 compartments. They estimated the biomass in each taxon in mgC/m2 and the flows between taxa in mgC/m2/day. The total system throughputs (T) in the control ecosystem was estimated to be 22,420 mgC/m2/day, and that in the impacted system as 18,050 mgC/m2/day (Ulanowicz, 1986a,b). How much of the decrease could be ascribed to diminution of autocatalytic activities could not be assessed, suffice it to say that the change was in the expected direction. The ascendency in the heated system fell to 22,433 mgC-bits/m2/day from a value of 28,337 mgC-bits/m2/day for the control. The preponderance of the drop could be ascribed to the fall in T, as the corresponding AMC fell by only 0.3%.
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